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Програмування","\u002Fcsharp\u002Fsystem-programming-windows\u002Fasync-fundamentals","01.csharp\u002F07.system-programming-windows\u002F12.async-fundamentals",{"title":344,"path":345,"stem":346},"SynchronizationContext та ConfigureAwait — Контекст Виконання","\u002Fcsharp\u002Fsystem-programming-windows\u002Fasync-context-configureawait","01.csharp\u002F07.system-programming-windows\u002F13.async-context-configureawait",{"title":348,"path":349,"stem":350},"Async — Просунуті Паттерни","\u002Fcsharp\u002Fsystem-programming-windows\u002Fasync-advanced","01.csharp\u002F07.system-programming-windows\u002F14.async-advanced",{"title":352,"path":353,"stem":354},"System.Threading.Channels — Async Producer-Consumer","\u002Fcsharp\u002Fsystem-programming-windows\u002Fchannels","01.csharp\u002F07.system-programming-windows\u002F15.channels",{"title":356,"path":357,"stem":358},"Асинхронна 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ОС","\u002Fcsharp\u002Fsystem-programming-windows\u002Fwindows-hooks-services","01.csharp\u002F07.system-programming-windows\u002F20.windows-hooks-services",{"title":376,"path":377,"stem":378},"Системне Програмування C# (Windows) — 07.system-programming-windows","\u002Fcsharp\u002Fsystem-programming-windows\u002Fimplementation_plan","01.csharp\u002F07.system-programming-windows\u002Fimplementation_plan",{"title":380,"icon":132,"path":381,"stem":382,"children":383,"page":59},"Io","\u002Fcsharp\u002Fio","01.csharp\u002F08.io",[384,388,392,396,400],{"title":385,"path":386,"stem":387},"8.1.1. Основи роботи з файловою системою","\u002Fcsharp\u002Fio\u002Ffile-system-basics","01.csharp\u002F08.io\u002F01.file-system-basics",{"title":389,"path":390,"stem":391},"8.1.2. Потоки (Streams) та Серіалізація Даних","\u002Fcsharp\u002Fio\u002Fstreams-serialization","01.csharp\u002F08.io\u002F02.streams-serialization",{"title":393,"path":394,"stem":395},"8.2.1. JSON Serialization з System.Text.Json","\u002Fcsharp\u002Fio\u002Fjson-serialization","01.csharp\u002F08.io\u002F03.json-serialization",{"title":397,"path":398,"stem":399},"8.2.2. XML Serialization та LINQ to XML","\u002Fcsharp\u002Fio\u002Fxml-serialization","01.csharp\u002F08.io\u002F04.xml-serialization",{"title":401,"path":402,"stem":403},"8.2.3. Binary Serialization: MessagePack та Protocol Buffers","\u002Fcsharp\u002Fio\u002Fbinary-serialization","01.csharp\u002F08.io\u002F05.binary-serialization",{"title":405,"icon":132,"path":406,"stem":407,"children":408,"page":59},"Ado Net","\u002Fcsharp\u002Fado-net","01.csharp\u002F09.ado-net",[409,413,417,421,425,429,433,437,441,445,449,453],{"title":410,"path":411,"stem":412},"9.1. Введення в ADO.NET","\u002Fcsharp\u002Fado-net\u002Fintroduction-to-adonet","01.csharp\u002F09.ado-net\u002F01.introduction-to-adonet",{"title":414,"path":415,"stem":416},"9.2. Клас DbConnection — з'єднання з базою даних","\u002Fcsharp\u002Fado-net\u002Fconnection","01.csharp\u002F09.ado-net\u002F02.connection",{"title":418,"path":419,"stem":420},"9.3. Клас DbCommand — виконання SQL-запитів","\u002Fcsharp\u002Fado-net\u002Fcommand-and-queries","01.csharp\u002F09.ado-net\u002F03.command-and-queries",{"title":422,"path":423,"stem":424},"9.4. Клас DbDataReader — ефективне читання даних","\u002Fcsharp\u002Fado-net\u002Fdatareader","01.csharp\u002F09.ado-net\u002F04.datareader",{"title":426,"path":427,"stem":428},"9.5. Параметризовані запити та захист від SQL Injection","\u002Fcsharp\u002Fado-net\u002Fparameters-and-sql-injection","01.csharp\u002F09.ado-net\u002F05.parameters-and-sql-injection",{"title":430,"path":431,"stem":432},"9.6. Транзакції в ADO.NET","\u002Fcsharp\u002Fado-net\u002Ftransactions","01.csharp\u002F09.ado-net\u002F06.transactions",{"title":434,"path":435,"stem":436},"9.7. DbProviderFactory — провайдер-незалежний код","\u002Fcsharp\u002Fado-net\u002Fprovider-factory","01.csharp\u002F09.ado-net\u002F07.provider-factory",{"title":438,"path":439,"stem":440},"9.8. Асинхронний доступ до даних","\u002Fcsharp\u002Fado-net\u002Fasync-data-access","01.csharp\u002F09.ado-net\u002F08.async-data-access",{"title":442,"path":443,"stem":444},"9.9. Від'єднаний режим: DataSet, DataTable, DataRow","\u002Fcsharp\u002Fado-net\u002Fdisconnected-mode-dataset","01.csharp\u002F09.ado-net\u002F09.disconnected-mode-dataset",{"title":446,"path":447,"stem":448},"9.10. DataAdapter — міст між DataSet та базою даних","\u002Fcsharp\u002Fado-net\u002Fdata-adapter","01.csharp\u002F09.ado-net\u002F10.data-adapter",{"title":450,"path":451,"stem":452},"9.11. Data Mapper та Repository: Архітектура доступу до даних","\u002Fcsharp\u002Fado-net\u002Fdata-mapper-repository","01.csharp\u002F09.ado-net\u002F11.data-mapper-repository",{"title":454,"path":455,"stem":456},"9.12. Identity Map, Unit of Work та Specification Pattern","\u002Fcsharp\u002Fado-net\u002Fadvanced-patterns","01.csharp\u002F09.ado-net\u002F12.advanced-patterns",{"title":458,"icon":255,"path":459,"stem":460,"children":461,"page":59},"Ef Core","\u002Fcsharp\u002Fef-core","01.csharp\u002F10.ef-core",[462,466,470,474,478,482,486,490,494,498,502,506,510,514,518,522,526,532,538,542,546,550,554,558,562,566,570,574,578,582,586,590,594,598,602,606,610,614,618,622,626,630,634,638,642,646],{"title":463,"path":464,"stem":465},"Що таке ORM? Від SQL до об'єктів","\u002Fcsharp\u002Fef-core\u002Fwhat-is-orm","01.csharp\u002F10.ef-core\u002F01.what-is-orm",{"title":467,"path":468,"stem":469},"Перший проєкт — від нуля до CRUD","\u002Fcsharp\u002Fef-core\u002Ffirst-project","01.csharp\u002F10.ef-core\u002F02.first-project",{"title":471,"path":472,"stem":473},"DbContext — Серце EF Core","\u002Fcsharp\u002Fef-core\u002Fdbcontext-deep-dive","01.csharp\u002F10.ef-core\u002F03.dbcontext-deep-dive",{"title":475,"path":476,"stem":477},"Провайдери баз даних — Архітектура та Вибір СУБД","\u002Fcsharp\u002Fef-core\u002Fdatabase-providers","01.csharp\u002F10.ef-core\u002F04.database-providers",{"title":479,"path":480,"stem":481},"Конвенції EF Core — Магія без конфігурації","\u002Fcsharp\u002Fef-core\u002Fconventions","01.csharp\u002F10.ef-core\u002F05.conventions",{"title":483,"path":484,"stem":485},"Fluent API та Data Annotations — Явна конфігурація моделі","\u002Fcsharp\u002Fef-core\u002Ffluent-api-vs-annotations","01.csharp\u002F10.ef-core\u002F06.fluent-api-vs-annotations",{"title":487,"path":488,"stem":489},"Зв'язки — One-to-One та One-to-Many","\u002Fcsharp\u002Fef-core\u002Frelationships-basics","01.csharp\u002F10.ef-core\u002F07.relationships-basics",{"title":491,"path":492,"stem":493},"Зв'язки Advanced — Many-to-Many та Складні Сценарії","\u002Fcsharp\u002Fef-core\u002Frelationships-advanced","01.csharp\u002F10.ef-core\u002F08.relationships-advanced",{"title":495,"path":496,"stem":497},"Властивості — Типи, Конвертери, Компаратори (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part1","01.csharp\u002F10.ef-core\u002F09.property-configuration-part1",{"title":499,"path":500,"stem":501},"Властивості — Value Comparers, Generators, Shadow Properties (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fproperty-configuration-part2","01.csharp\u002F10.ef-core\u002F09.property-configuration-part2",{"title":503,"path":504,"stem":505},"Складні типи — Owned Types та Complex Types (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part1","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part1",{"title":507,"path":508,"stem":509},"Складні типи — Complex Types, Keyless Entities, Порівняння (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fcomplex-types-owned-part2","01.csharp\u002F10.ef-core\u002F10.complex-types-owned-part2",{"title":511,"path":512,"stem":513},"JSON Columns — Складні дані у JSON (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part1","01.csharp\u002F10.ef-core\u002F11.json-columns-part1",{"title":515,"path":516,"stem":517},"JSON Columns — Value Comparers, Індекси, Провайдери (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fjson-columns-part2","01.csharp\u002F10.ef-core\u002F11.json-columns-part2",{"title":519,"path":520,"stem":521},"Успадкування — Абстрактні класи та TPH (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finheritance-part1","01.csharp\u002F10.ef-core\u002F12.inheritance-part1",{"title":523,"path":524,"stem":525},"Успадкування — TPT, TPC та Порівняння Стратегій (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finheritance-part2","01.csharp\u002F10.ef-core\u002F12.inheritance-part2",{"title":527,"path":528,"stem":529,"children":530},"Індекси, Обмеження та Схема (Частина 1)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part1","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part1",[531],{"title":527,"path":528,"stem":529},{"title":533,"path":534,"stem":535,"children":536},"Індекси, Обмеження та Схема (Частина 2)","\u002Fcsharp\u002Fef-core\u002Findexes-constraints-part2","01.csharp\u002F10.ef-core\u002F13.indexes-constraints-part2",[537],{"title":533,"path":534,"stem":535},{"title":539,"path":540,"stem":541},"Seed Data — Початкові Дані (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fseeding-part1","01.csharp\u002F10.ef-core\u002F14.seeding-part1",{"title":543,"path":544,"stem":545},"Seed Data — SQL-скрипти, Bogus та Стратегії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fseeding-part2","01.csharp\u002F10.ef-core\u002F14.seeding-part2",{"title":547,"path":548,"stem":549},"Global Query Filters — Глобальні Фільтри (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part1","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part1",{"title":551,"path":552,"stem":553},"Global Query Filters — Підводні камені та Інтеграція (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fglobal-query-filters-part2","01.csharp\u002F10.ef-core\u002F15.global-query-filters-part2",{"title":555,"path":556,"stem":557},"LINQ-запити в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part1","01.csharp\u002F10.ef-core\u002F16.linq-queries-part1",{"title":559,"path":560,"stem":561},"LINQ-запити в EF Core (Частина 2)","\u002Fcsharp\u002Fef-core\u002Flinq-queries-part2","01.csharp\u002F10.ef-core\u002F16.linq-queries-part2",{"title":563,"path":564,"stem":565},"Завантаження Пов'язаних Даних (Частина 1)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part1","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part1",{"title":567,"path":568,"stem":569},"Завантаження Пов'язаних Даних (Частина 2)","\u002Fcsharp\u002Fef-core\u002Floading-related-data-part2","01.csharp\u002F10.ef-core\u002F17.loading-related-data-part2",{"title":571,"path":572,"stem":573},"Raw SQL, Views та Stored Procedures (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part1","01.csharp\u002F10.ef-core\u002F18.raw-sql-part1",{"title":575,"path":576,"stem":577},"Raw SQL — Stored Procedures, DbFunction та Bulk Operations (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fraw-sql-part2","01.csharp\u002F10.ef-core\u002F18.raw-sql-part2",{"title":579,"path":580,"stem":581},"Продвинуті Запити — Compiled Queries, Bulk та Оптимізація (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part1","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part1",{"title":583,"path":584,"stem":585},"Продвинуті Запити — Query Tags, Bulk та Interceptors (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fadvanced-queries-part2","01.csharp\u002F10.ef-core\u002F19.advanced-queries-part2",{"title":587,"path":588,"stem":589},"Change Tracker — Відстеження Змін (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part1","01.csharp\u002F10.ef-core\u002F20.change-tracking-part1",{"title":591,"path":592,"stem":593},"Change Tracker — Графи Об'єктів та Disconnected (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fchange-tracking-part2","01.csharp\u002F10.ef-core\u002F20.change-tracking-part2",{"title":595,"path":596,"stem":597},"Збереження Даних та Транзакції (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part1","01.csharp\u002F10.ef-core\u002F21.saving-data-part1",{"title":599,"path":600,"stem":601},"Збереження Даних — Concurrency та Outbox (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fsaving-data-part2","01.csharp\u002F10.ef-core\u002F21.saving-data-part2",{"title":603,"path":604,"stem":605},"Конкурентність та Блокування (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part1","01.csharp\u002F10.ef-core\u002F22.concurrency-part1",{"title":607,"path":608,"stem":609},"Конкурентність — Дедлоки та Queue Processing (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fconcurrency-part2","01.csharp\u002F10.ef-core\u002F22.concurrency-part2",{"title":611,"path":612,"stem":613},"Міграції в EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part1","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part1",{"title":615,"path":616,"stem":617},"Міграції в EF Core — Основи (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-basics-part2","01.csharp\u002F10.ef-core\u002F23.migrations-basics-part2",{"title":619,"path":620,"stem":621},"Міграції — Просунуті Сценарії (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part1","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part1",{"title":623,"path":624,"stem":625},"Міграції — Просунуті Сценарії (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fmigrations-advanced-part2","01.csharp\u002F10.ef-core\u002F24.migrations-advanced-part2",{"title":627,"path":628,"stem":629},"Управління Схемою та Database-First (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part1","01.csharp\u002F10.ef-core\u002F25.schema-management-part1",{"title":631,"path":632,"stem":633},"Управління Схемою та Database-First (Частина 2)","\u002Fcsharp\u002Fef-core\u002Fschema-management-part2","01.csharp\u002F10.ef-core\u002F25.schema-management-part2",{"title":635,"path":636,"stem":637},"Продуктивність EF Core — Основи (Частина 1)","\u002Fcsharp\u002Fef-core\u002Fperformance-fundamentals-part1","01.csharp\u002F10.ef-core\u002F26.performance-fundamentals-part1",{"title":639,"path":640,"stem":641},"Interceptors в EF Core (Частина 1)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part1","01.csharp\u002F10.ef-core\u002F29.interceptors-part1",{"title":643,"path":644,"stem":645},"Interceptors в EF Core — Connection, Transaction та Materialization (Частина 2)","\u002Fcsharp\u002Fef-core\u002Finterceptors-part2","01.csharp\u002F10.ef-core\u002F29.interceptors-part2",{"title":647,"path":648,"stem":649},"План вивчення Entity Framework Core — Повний курс","\u002Fcsharp\u002Fef-core\u002Fimplementation_plan","01.csharp\u002F10.ef-core\u002Fimplementation_plan",{"title":651,"icon":652,"path":653,"stem":654,"children":655,"page":59},"ASP.NET","i-devicon-dotnetcore","\u002Fcsharp\u002Faspnet","01.csharp\u002F11.aspnet",[656,730,791,869,927,941,967,1057,1111,1182,1212,1289,1346],{"title":657,"icon":658,"path":659,"stem":660,"children":661,"page":59},"Minimal API","i-lucide-network","\u002Fcsharp\u002Faspnet\u002Fminimal-api","01.csharp\u002F11.aspnet\u002F01.minimal-api",[662,666,670,674,678,682,686,690,694,698,702,706,710,714,718,722,726],{"title":663,"path":664,"stem":665},"Вступ до ASP.NET та еволюція фреймворку","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fintroduction","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F01.introduction",{"title":667,"path":668,"stem":669},"Перший додаток на ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Ffirst-application","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F02.first-application",{"title":671,"path":672,"stem":673},"WebApplication, Builder та Dependency Injection","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fwebapplication-builder","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F03.webapplication-builder",{"title":675,"path":676,"stem":677},"Конвеєр запитів та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frequest-pipeline-middleware","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F04.request-pipeline-middleware",{"title":679,"path":680,"stem":681},"Маршрутизація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F05.routing-basics",{"title":683,"path":684,"stem":685},"Маршрутизація в ASP.NET Core: Розширені можливості","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Frouting-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F06.routing-advanced",{"title":687,"path":688,"stem":689},"Статичні файли в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-files","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F07.static-files",{"title":691,"path":692,"stem":693},"Статичні Активи: MapStaticAssets (ASP.NET Core 9.0)","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstatic-assets","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F08.static-assets",{"title":695,"path":696,"stem":697},"Конфігурація в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-fundamentals","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F09.configuration-fundamentals",{"title":699,"path":700,"stem":701},"Конфігурація: Паттерн Options","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fconfiguration-options","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F10.configuration-options",{"title":703,"path":704,"stem":705},"Логування в ASP.NET Core: Основи","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-basics","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F11.logging-basics",{"title":707,"path":708,"stem":709},"Логування: Serilog та Middleware","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Flogging-advanced","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F12.logging-advanced",{"title":711,"path":712,"stem":713},"Управління станом: HttpContext.Items та Cookies","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fstate-management","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F13.state-management",{"title":715,"path":716,"stem":717},"Стан сесії: Sessions","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fsession-state","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F14.session-state",{"title":719,"path":720,"stem":721},"Структура проєкту: від хаосу до архітектури","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fproject-structure","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F15.project-structure",{"title":723,"path":724,"stem":725},"Scalar у Minimal API: повний проєкт і Fluent OpenAPI","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fscalar-openapi-fluent","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F16.scalar-openapi-fluent",{"title":727,"path":728,"stem":729},"Swagger \u002F Swashbuckle у Minimal API: окремий класичний шлях","\u002Fcsharp\u002Faspnet\u002Fminimal-api\u002Fswagger-swashbuckle","01.csharp\u002F11.aspnet\u002F01.minimal-api\u002F17.swagger-swashbuckle",{"title":731,"icon":658,"path":732,"stem":733,"children":734,"page":59},"API","\u002Fcsharp\u002Faspnet\u002Fapi","01.csharp\u002F11.aspnet\u002F02.api",[735,739,743,747,751,755,759,763,767,771,775,779,783,787],{"title":736,"path":737,"stem":738},"Що таке API. Клієнт-серверна архітектура","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fwhat-is-api","01.csharp\u002F11.aspnet\u002F02.api\u002F01.what-is-api",{"title":740,"path":741,"stem":742},"Формати даних: JSON, XML, TOML та бінарні формати","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fdata-formats","01.csharp\u002F11.aspnet\u002F02.api\u002F02.data-formats",{"title":744,"path":745,"stem":746},"Парадигми API та концепція REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-paradigms-rest","01.csharp\u002F11.aspnet\u002F02.api\u002F03.api-paradigms-rest",{"title":748,"path":749,"stem":750},"HTTP-методи, статус-коди та заголовки","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fhttp-methods-status-codes","01.csharp\u002F11.aspnet\u002F02.api\u002F04.http-methods-status-codes",{"title":752,"path":753,"stem":754},"Організація HTTP API за принципами REST","\u002Fcsharp\u002Faspnet\u002Fapi\u002Frest-organizing","01.csharp\u002F11.aspnet\u002F02.api\u002F05.rest-organizing",{"title":756,"path":757,"stem":758},"Номенклатура URL та CRUD-операції","\u002Fcsharp\u002Faspnet\u002Fapi\u002Furl-nomenclature-crud","01.csharp\u002F11.aspnet\u002F02.api\u002F06.url-nomenclature-crud",{"title":760,"path":761,"stem":762},"Правила дизайну: іменування та стандарти","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-naming","01.csharp\u002F11.aspnet\u002F02.api\u002F07.api-design-naming",{"title":764,"path":765,"stem":766},"Валідація, ліміти та обробка помилок","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-validation","01.csharp\u002F11.aspnet\u002F02.api\u002F08.api-design-validation",{"title":768,"path":769,"stem":770},"Обробка помилок у Minimal API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Ferror-handling-http","01.csharp\u002F11.aspnet\u002F02.api\u002F09.error-handling-http",{"title":772,"path":773,"stem":774},"Ідемпотентність та синхронізація стану","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fidempotency-sync","01.csharp\u002F11.aspnet\u002F02.api\u002F10.idempotency-sync",{"title":776,"path":777,"stem":778},"Пагінація та організація списків","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fpagination-lists","01.csharp\u002F11.aspnet\u002F02.api\u002F11.pagination-lists",{"title":780,"path":781,"stem":782},"Безпека API, кешування та інтернаціоналізація","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fsecurity-auth","01.csharp\u002F11.aspnet\u002F02.api\u002F12.security-auth",{"title":784,"path":785,"stem":786},"Процес проєктування API та документування","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fapi-design-process","01.csharp\u002F11.aspnet\u002F02.api\u002F13.api-design-process",{"title":788,"path":789,"stem":790},"OpenAPI: контракт, специфікація та документація API","\u002Fcsharp\u002Faspnet\u002Fapi\u002Fopenapi","01.csharp\u002F11.aspnet\u002F02.api\u002F14.openapi",{"title":792,"icon":793,"path":794,"stem":795,"children":796,"page":59},"Auth","i-lucide-shield-check","\u002Fcsharp\u002Faspnet\u002Fauth","01.csharp\u002F11.aspnet\u002F03.auth",[797,801,805,809,813,817,821,825,829,833,837,841,845,849,853,857,861,865],{"title":798,"path":799,"stem":800},"Основи аутентифікації та авторизації","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauth-fundamentals","01.csharp\u002F11.aspnet\u002F03.auth\u002F01.auth-fundamentals",{"title":802,"path":803,"stem":804},"JWT-аутентифікація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fjwt-authentication","01.csharp\u002F11.aspnet\u002F03.auth\u002F02.jwt-authentication",{"title":806,"path":807,"stem":808},"Авторизація: ролі, політики та resource-based доступ","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fauthorization-policies","01.csharp\u002F11.aspnet\u002F03.auth\u002F03.authorization-policies",{"title":810,"path":811,"stem":812},"Cookie-аутентифікація та ASP.NET Core Identity","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcookie-auth-identity","01.csharp\u002F11.aspnet\u002F03.auth\u002F04.cookie-auth-identity",{"title":814,"path":815,"stem":816},"JWT + Refresh Tokens (HttpOnly Cookie)","\u002Fcsharp\u002Faspnet\u002Fauth\u002F04b.identity-auth-jwt","01.csharp\u002F11.aspnet\u002F03.auth\u002F04b.identity-auth-jwt",{"title":818,"path":819,"stem":820},"Identity: Підтвердження Email та Скидання Пароля","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-email-confirmation","01.csharp\u002F11.aspnet\u002F03.auth\u002F05.identity-email-confirmation",{"title":822,"path":823,"stem":824},"Identity: Двофакторна Аутентифікація (2FA)","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-two-factor","01.csharp\u002F11.aspnet\u002F03.auth\u002F06.identity-two-factor",{"title":826,"path":827,"stem":828},"Identity: Внутрішня Архітектура та Кастомізація","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fidentity-internals","01.csharp\u002F11.aspnet\u002F03.auth\u002F07.identity-internals",{"title":830,"path":831,"stem":832},"OAuth 2.0 та зовнішні провайдери","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-external-providers","01.csharp\u002F11.aspnet\u002F03.auth\u002F08.oauth-external-providers",{"title":834,"path":835,"stem":836},"Безпека на практиці: CORS, HTTPS та захист від атак","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fsecurity-hardening","01.csharp\u002F11.aspnet\u002F03.auth\u002F09.security-hardening",{"title":838,"path":839,"stem":840},"Теорія OAuth 2.0: Поняття, Аналогії та Флоу","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foauth-theory","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oauth-theory",{"title":842,"path":843,"stem":844},"OIDC, OAuth 2.0 та Keycloak в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Foidc-keycloak","01.csharp\u002F11.aspnet\u002F03.auth\u002F10.oidc-keycloak",{"title":846,"path":847,"stem":848},"API Keys аутентифікація в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fapi-keys","01.csharp\u002F11.aspnet\u002F03.auth\u002F11.api-keys",{"title":850,"path":851,"stem":852},"Rate Limiting та Throttling в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frate-limiting","01.csharp\u002F11.aspnet\u002F03.auth\u002F12.rate-limiting",{"title":854,"path":855,"stem":856},"Refresh Token Rotation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frefresh-token-rotation","01.csharp\u002F11.aspnet\u002F03.auth\u002F13.refresh-token-rotation",{"title":858,"path":859,"stem":860},"Certificate Authentication та mTLS в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fcertificate-auth","01.csharp\u002F11.aspnet\u002F03.auth\u002F14.certificate-auth",{"title":862,"path":863,"stem":864},"RBAC, ABAC та ReBAC в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Frbac-abac-rebac","01.csharp\u002F11.aspnet\u002F03.auth\u002F15.rbac-abac-rebac",{"title":866,"path":867,"stem":868},"Multi-tenancy та ізоляція даних в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fauth\u002Fmulti-tenancy","01.csharp\u002F11.aspnet\u002F03.auth\u002F16.multi-tenancy",{"title":870,"icon":871,"path":872,"stem":873,"children":874,"page":59},"Нотифікації","i-lucide-bell","\u002Fcsharp\u002Faspnet\u002Fnotifications","01.csharp\u002F11.aspnet\u002F04.notifications",[875,879,883,887,891,895,899,903,907,911,915,919,923],{"title":876,"path":877,"stem":878},"In-App нотифікації через базу даних","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fin-app-database-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F01.in-app-database-notifications",{"title":880,"path":881,"stem":882},"Polling: Регулярний запит оновлень","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fpolling","01.csharp\u002F11.aspnet\u002F04.notifications\u002F02.polling",{"title":884,"path":885,"stem":886},"Server-Sent Events: Однострімовий push від сервера","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fserver-sent-events","01.csharp\u002F11.aspnet\u002F04.notifications\u002F03.server-sent-events",{"title":888,"path":889,"stem":890},"WebSockets: Двостороннє з'єднання в реальному часі","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fwebsockets","01.csharp\u002F11.aspnet\u002F04.notifications\u002F04.websockets",{"title":892,"path":893,"stem":894},"SignalR: Абстракція над транспортами реального часу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fsignalr","01.csharp\u002F11.aspnet\u002F04.notifications\u002F05.signalr",{"title":896,"path":897,"stem":898},"Background Services: Фонові задачі в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fbackground-services","01.csharp\u002F11.aspnet\u002F04.notifications\u002F06.background-services",{"title":900,"path":901,"stem":902},"Web Push нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fweb-push","01.csharp\u002F11.aspnet\u002F04.notifications\u002F07.web-push",{"title":904,"path":905,"stem":906},"Email нотифікації","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Femail-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F08.email-notifications",{"title":908,"path":909,"stem":910},"Порівняння підходів: Як вибрати правильну технологію нотифікацій","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fchoosing-the-right-approach","01.csharp\u002F11.aspnet\u002F04.notifications\u002F09.choosing-the-right-approach",{"title":912,"path":913,"stem":914},"Hangfire: Надійне планування фонових задач","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire","01.csharp\u002F11.aspnet\u002F04.notifications\u002F10.hangfire",{"title":916,"path":917,"stem":918},"Практика: Конвертація зображень у WebP через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-image-webp","01.csharp\u002F11.aspnet\u002F04.notifications\u002F11.hangfire-image-webp",{"title":920,"path":921,"stem":922},"Практика: Підготовка відео до HLS-стрімінгу через Hangfire","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Fhangfire-video-hls","01.csharp\u002F11.aspnet\u002F04.notifications\u002F12.hangfire-video-hls",{"title":924,"path":925,"stem":926},"Telegram-нотифікації: від одного повідомлення до масових розсилок і мульти-канального підходу","\u002Fcsharp\u002Faspnet\u002Fnotifications\u002Ftelegram-notifications","01.csharp\u002F11.aspnet\u002F04.notifications\u002F13.telegram-notifications",{"title":928,"icon":929,"path":930,"stem":931,"children":932,"page":59},"Інтернаціоналізація","i-lucide-languages","\u002Fcsharp\u002Faspnet\u002Fi18n","01.csharp\u002F11.aspnet\u002F05.i18n",[933,937],{"title":934,"path":935,"stem":936},"Інтернаціоналізація (i18n) у Minimal API: від A до Я","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Finternationalization","01.csharp\u002F11.aspnet\u002F05.i18n\u002F01.internationalization",{"title":938,"path":939,"stem":940},"Humanizer: людиномовні рядки у .NET","\u002Fcsharp\u002Faspnet\u002Fi18n\u002Fhumanizer","01.csharp\u002F11.aspnet\u002F05.i18n\u002F02.humanizer",{"title":942,"icon":943,"path":944,"stem":945,"children":946,"page":59},"Кешування","i-lucide-layers","\u002Fcsharp\u002Faspnet\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching",[947,951,955,959,963],{"title":948,"path":949,"stem":950},"Огляд кешування: чотири рівні і коли що обирати","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fcaching","01.csharp\u002F11.aspnet\u002F06.caching\u002F01.caching",{"title":952,"path":953,"stem":954},"IMemoryCache: кеш в оперативній пам'яті","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fmemory-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F02.memory-cache",{"title":956,"path":957,"stem":958},"IDistributedCache і Redis: розподілений кеш","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fdistributed-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F03.distributed-cache",{"title":960,"path":961,"stem":962},"Response Cache: HTTP-кешування через Cache-Control","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Fresponse-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F04.response-cache",{"title":964,"path":965,"stem":966},"Output Cache: серверний кеш HTTP-відповідей (.NET 7+)","\u002Fcsharp\u002Faspnet\u002Fcaching\u002Foutput-cache","01.csharp\u002F11.aspnet\u002F06.caching\u002F05.output-cache",{"title":968,"icon":969,"path":970,"stem":971,"children":972,"page":59},"Тестування","i-lucide-test-tube","\u002Fcsharp\u002Faspnet\u002Ftesting","01.csharp\u002F11.aspnet\u002F07.testing",[973,977,981,985,989,993,997,1001,1005,1009,1013,1017,1021,1025,1029,1033,1037,1041,1045,1049,1053],{"title":974,"path":975,"stem":976},"Що таке тестування? Від інтуїції до науки","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-is-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F01.what-is-testing",{"title":978,"path":979,"stem":980},"Піраміда тестування — Стратегія, а не Догма","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-pyramid","01.csharp\u002F11.aspnet\u002F07.testing\u002F02.testing-pyramid",{"title":982,"path":983,"stem":984},"Дві Школи Тестування — Лондон проти Детройту","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-schools","01.csharp\u002F11.aspnet\u002F07.testing\u002F03.testing-schools",{"title":986,"path":987,"stem":988},"TDD та BDD — Тести як Дизайн-інструмент","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftdd-and-bdd","01.csharp\u002F11.aspnet\u002F07.testing\u002F04.tdd-and-bdd",{"title":990,"path":991,"stem":992},"Що саме тестувати — Техніки аналізу та Циклomatична складність","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwhat-to-test","01.csharp\u002F11.aspnet\u002F07.testing\u002F05.what-to-test",{"title":994,"path":995,"stem":996},"Тестові Фреймворки — Навіщо вони і що всередині","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftest-frameworks","01.csharp\u002F11.aspnet\u002F07.testing\u002F06.test-frameworks",{"title":998,"path":999,"stem":1000},"xUnit — Факти, Теорії та Lifecycle тестів","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-basics","01.csharp\u002F11.aspnet\u002F07.testing\u002F07.xunit-basics",{"title":1002,"path":1003,"stem":1004},"xUnit Advanced — Fixtures, Кастомізація та Розширення","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fxunit-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F08.xunit-advanced",{"title":1006,"path":1007,"stem":1008},"Moq — Глибоке занурення в мокування","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fmocking-with-moq","01.csharp\u002F11.aspnet\u002F07.testing\u002F09.mocking-with-moq",{"title":1010,"path":1011,"stem":1012},"Тестування Баз Даних — EF Core, SQLite та Testcontainers","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fdatabase-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F10.database-testing",{"title":1014,"path":1015,"stem":1016},"Integration Testing — Частина 1 [Теорія та WebApplicationFactory]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F11.integration-testing",{"title":1018,"path":1019,"stem":1020},"Інтеграційне тестування — Практика","\u002Fcsharp\u002Faspnet\u002Ftesting\u002F11a.integration-testing-practice","01.csharp\u002F11.aspnet\u002F07.testing\u002F11a.integration-testing-practice",{"title":1022,"path":1023,"stem":1024},"Integration Testing — Частина 2 [Просунуті Сценарії та Testcontainers]","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fintegration-testing-advanced","01.csharp\u002F11.aspnet\u002F07.testing\u002F12.integration-testing-advanced",{"title":1026,"path":1027,"stem":1028},"Професійний Postman: Колекції, Змінні та GitHub Інтеграція","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fpostman-professional","01.csharp\u002F11.aspnet\u002F07.testing\u002F13.postman-professional",{"title":1030,"path":1031,"stem":1032},"HttpClient у Тестах Частина 1: Архітектура та MockHttpMessageHandler","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fhttpclient-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F14.httpclient-testing",{"title":1034,"path":1035,"stem":1036},"HttpClient у Тестах Частина 2: WireMock.Net та Resilience","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fwiremock-net","01.csharp\u002F11.aspnet\u002F07.testing\u002F15.wiremock-net",{"title":1038,"path":1039,"stem":1040},"Патерни та Анти-патерни Тестування: Test Smells","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Ftesting-patterns","01.csharp\u002F11.aspnet\u002F07.testing\u002F16.testing-patterns",{"title":1042,"path":1043,"stem":1044},"Просунуті інструменти: Time, Snapshots та Властивості","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fadvanced-testing-tools","01.csharp\u002F11.aspnet\u002F07.testing\u002F17.advanced-testing-tools",{"title":1046,"path":1047,"stem":1048},"Тестування Архітектури з NetArchTest","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Farchitecture-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F18.architecture-testing",{"title":1050,"path":1051,"stem":1052},"Тестування Продуктивності: BenchmarkDotNet, NBomber та k6","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fperformance-testing","01.csharp\u002F11.aspnet\u002F07.testing\u002F19.performance-testing",{"title":1054,"path":1055,"stem":1056},"Залишок плану для курсу \"Тестування ASP.NET Minimal API\"","\u002Fcsharp\u002Faspnet\u002Ftesting\u002Fremaining_plan","01.csharp\u002F11.aspnet\u002F07.testing\u002Fremaining_plan",{"title":1058,"icon":1059,"path":1060,"stem":1061,"children":1062,"page":59},"Платежі","i-lucide-credit-card","\u002Fcsharp\u002Faspnet\u002Fpayments","01.csharp\u002F11.aspnet\u002F08.payments",[1063,1067,1071,1075,1079,1083,1087,1091,1095,1099,1103,1107],{"title":1064,"path":1065,"stem":1066},"Основи платіжної інфраструктури","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-fundamentals","01.csharp\u002F11.aspnet\u002F08.payments\u002F01.payment-fundamentals",{"title":1068,"path":1069,"stem":1070},"Методи оплати в Україні","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-methods-ukraine","01.csharp\u002F11.aspnet\u002F08.payments\u002F02.payment-methods-ukraine",{"title":1072,"path":1073,"stem":1074},"PCI DSS та безпека платежів","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpci-dss-security","01.csharp\u002F11.aspnet\u002F08.payments\u002F03.pci-dss-security",{"title":1076,"path":1077,"stem":1078},"Архітектура платіжної підсистеми","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fpayment-architecture","01.csharp\u002F11.aspnet\u002F08.payments\u002F04.payment-architecture",{"title":1080,"path":1081,"stem":1082},"Інтеграція LiqPay (ПриватБанк)","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fliqpay-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F05.liqpay-integration",{"title":1084,"path":1085,"stem":1086},"Інтеграція Monobank Acquiring API","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fmonobank-acquiring","01.csharp\u002F11.aspnet\u002F08.payments\u002F06.monobank-acquiring",{"title":1088,"path":1089,"stem":1090},"Інтеграція Stripe","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fstripe-integration","01.csharp\u002F11.aspnet\u002F08.payments\u002F07.stripe-integration",{"title":1092,"path":1093,"stem":1094},"Webhooks — глибоке занурення","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fwebhooks-deep-dive","01.csharp\u002F11.aspnet\u002F08.payments\u002F08.webhooks-deep-dive",{"title":1096,"path":1097,"stem":1098},"Підписки та рекурентні платежі","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fsubscriptions-recurring","01.csharp\u002F11.aspnet\u002F08.payments\u002F09.subscriptions-recurring",{"title":1100,"path":1101,"stem":1102},"Повернення коштів та диспути","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Frefunds-disputes","01.csharp\u002F11.aspnet\u002F08.payments\u002F10.refunds-disputes",{"title":1104,"path":1105,"stem":1106},"Тестування платіжних інтеграцій","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Ftesting-payments","01.csharp\u002F11.aspnet\u002F08.payments\u002F11.testing-payments",{"title":1108,"path":1109,"stem":1110},"Чекліст виходу в Production","\u002Fcsharp\u002Faspnet\u002Fpayments\u002Fproduction-checklist","01.csharp\u002F11.aspnet\u002F08.payments\u002F12.production-checklist",{"title":1112,"icon":1113,"items":1114,"path":1127,"stem":1128,"children":1129,"page":59},"Популярні бібліотеки","lucide:box",[1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126],"01.fluent-validation","02.mapster","03.erroror-result-pattern","04.serilog","05.mediatr","06.polly","07.health-checks","08.feature-management","09.fluent-email","10.quest-pdf","11.bogus","12.humanizer-guard","\u002Fcsharp\u002Faspnet\u002Flibraries","01.csharp\u002F11.aspnet\u002F09.libraries",[1130,1134,1138,1142,1146,1150,1154,1158,1162,1166,1170,1174,1178],{"title":1131,"path":1132,"stem":1133},"Валідація з FluentValidation в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-validation","01.csharp\u002F11.aspnet\u002F09.libraries\u002F01.fluent-validation",{"title":1135,"path":1136,"stem":1137},"Маппінг об","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmapster","01.csharp\u002F11.aspnet\u002F09.libraries\u002F02.mapster",{"title":1139,"path":1140,"stem":1141},"Обробка помилок з ErrorOr та Result Pattern в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ferroror-result-pattern","01.csharp\u002F11.aspnet\u002F09.libraries\u002F03.erroror-result-pattern",{"title":1143,"path":1144,"stem":1145},"Структуроване логування з Serilog в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fserilog","01.csharp\u002F11.aspnet\u002F09.libraries\u002F04.serilog",{"title":1147,"path":1148,"stem":1149},"CQRS та Mediator з MediatR в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fmediatr","01.csharp\u002F11.aspnet\u002F09.libraries\u002F05.mediatr",{"title":1151,"path":1152,"stem":1153},"Відмовостійкість з Polly в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fpolly","01.csharp\u002F11.aspnet\u002F09.libraries\u002F06.polly",{"title":1155,"path":1156,"stem":1157},"Health Checks в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F09.libraries\u002F07.health-checks",{"title":1159,"path":1160,"stem":1161},"Feature Management та Feature Flags в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffeature-management","01.csharp\u002F11.aspnet\u002F09.libraries\u002F08.feature-management",{"title":1163,"path":1164,"stem":1165},"Відправка Email з FluentEmail в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Ffluent-email","01.csharp\u002F11.aspnet\u002F09.libraries\u002F09.fluent-email",{"title":1167,"path":1168,"stem":1169},"Генерація PDF з QuestPDF в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fquest-pdf","01.csharp\u002F11.aspnet\u002F09.libraries\u002F10.quest-pdf",{"title":1171,"path":1172,"stem":1173},"Генерація тестових даних з Bogus в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fbogus","01.csharp\u002F11.aspnet\u002F09.libraries\u002F11.bogus",{"title":1175,"path":1176,"stem":1177},"Humanizer та Guard Clauses в ASP.NET Core","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fhumanizer-guard","01.csharp\u002F11.aspnet\u002F09.libraries\u002F12.humanizer-guard",{"title":1179,"path":1180,"stem":1181},"План модуля 10.libraries — Популярні бібліотеки ASP.NET","\u002Fcsharp\u002Faspnet\u002Flibraries\u002Fplan","01.csharp\u002F11.aspnet\u002F09.libraries\u002Fplan",{"title":1183,"icon":1184,"path":1185,"stem":1186,"children":1187,"page":59},"Razor Pages","i-lucide-layout-template","\u002Fcsharp\u002Faspnet\u002Frazor-pages","01.csharp\u002F11.aspnet\u002F10.razor-pages",[1188,1192,1196,1200,1204,1208],{"title":1189,"path":1190,"stem":1191},"Від Minimal API до Razor Pages: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ffrom-minimal-api","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F01.from-minimal-api",{"title":1193,"path":1194,"stem":1195},"PageModel: логіка сторінки Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fpage-model","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F02.page-model",{"title":1197,"path":1198,"stem":1199},"Razor синтаксис: шаблонізатор у .cshtml","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Frazor-syntax","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F03.razor-syntax",{"title":1201,"path":1202,"stem":1203},"Tag Helpers: типізований HTML","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Ftag-helpers","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F04.tag-helpers",{"title":1205,"path":1206,"stem":1207},"Форми і валідація: повний цикл обробки даних","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fforms-validation","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F05.forms-validation",{"title":1209,"path":1210,"stem":1211},"Практичний проєкт: TaskManager на Razor Pages","\u002Fcsharp\u002Faspnet\u002Frazor-pages\u002Fproject-task-manager","01.csharp\u002F11.aspnet\u002F10.razor-pages\u002F06.project-task-manager",{"title":1213,"path":1214,"stem":1215,"children":1216,"page":59},"ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc","01.csharp\u002F11.aspnet\u002F11.mvc",[1217,1221,1225,1229,1233,1237,1241,1245,1249,1253,1257,1261,1265,1269,1273,1277,1281,1285],{"title":1218,"path":1219,"stem":1220},"Патерн MVC: архітектура, що змінила веб","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-pattern","01.csharp\u002F11.aspnet\u002F11.mvc\u002F01.mvc-pattern",{"title":1222,"path":1223,"stem":1224},"Від Razor Pages до MVC: концептуальний перехід","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffrom-razor-pages","01.csharp\u002F11.aspnet\u002F11.mvc\u002F02.from-razor-pages",{"title":1226,"path":1227,"stem":1228},"Controllers та Actions: серце MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fcontrollers-actions","01.csharp\u002F11.aspnet\u002F11.mvc\u002F03.controllers-actions",{"title":1230,"path":1231,"stem":1232},"Маршрутизація в MVC: Convention vs Attribute Routing","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Frouting-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F04.routing-mvc",{"title":1234,"path":1235,"stem":1236},"Model Binding: від HTTP до C#","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmodel-binding","01.csharp\u002F11.aspnet\u002F11.mvc\u002F05.model-binding",{"title":1238,"path":1239,"stem":1240},"Views, ViewData, ViewBag, TempData і ViewModel","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fviews-viewdata-tempdata","01.csharp\u002F11.aspnet\u002F11.mvc\u002F06.views-viewdata-tempdata",{"title":1242,"path":1243,"stem":1244},"Filters: аспектно-орієнтоване програмування в MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffilters","01.csharp\u002F11.aspnet\u002F11.mvc\u002F07.filters",{"title":1246,"path":1247,"stem":1248},"Areas: структурування великих застосунків","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fareas","01.csharp\u002F11.aspnet\u002F11.mvc\u002F08.areas",{"title":1250,"path":1251,"stem":1252},"View Components: повторювані незалежні блоки UI","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fview-components","01.csharp\u002F11.aspnet\u002F11.mvc\u002F09.view-components",{"title":1254,"path":1255,"stem":1256},"Display та Editor Templates","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fdisplay-editor-templates","01.csharp\u002F11.aspnet\u002F11.mvc\u002F10.display-editor-templates",{"title":1258,"path":1259,"stem":1260},"Валідація: IValidatableObject та FluentValidation","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fvalidation-advanced","01.csharp\u002F11.aspnet\u002F11.mvc\u002F11.validation-advanced",{"title":1262,"path":1263,"stem":1264},"HTMX: інтерактивність через HTML-атрибути","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx","01.csharp\u002F11.aspnet\u002F11.mvc\u002F12.htmx",{"title":1266,"path":1267,"stem":1268},"HTMX у ASP.NET Core MVC: серверна інтеграція","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fajax-htmx-mvc","01.csharp\u002F11.aspnet\u002F11.mvc\u002F13.ajax-htmx-mvc",{"title":1270,"path":1271,"stem":1272},"Практичний проєкт: Каталог товарів з HTMX","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fhtmx-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F14.htmx-project",{"title":1274,"path":1275,"stem":1276},"Завантаження та обробка файлів","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Ffile-upload","01.csharp\u002F11.aspnet\u002F11.mvc\u002F15.file-upload",{"title":1278,"path":1279,"stem":1280},"Глобалізація та Локалізація MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fglobalization-localization","01.csharp\u002F11.aspnet\u002F11.mvc\u002F16.globalization-localization",{"title":1282,"path":1283,"stem":1284},"Підсумковий проєкт: Блог-платформа","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fmvc-project","01.csharp\u002F11.aspnet\u002F11.mvc\u002F17.mvc-project",{"title":1286,"path":1287,"stem":1288},"План курсу: ASP.NET Core MVC","\u002Fcsharp\u002Faspnet\u002Fmvc\u002Fplan","01.csharp\u002F11.aspnet\u002F11.mvc\u002Fplan",{"title":1290,"path":1291,"stem":1292,"children":1293,"page":59},"Web Api","\u002Fcsharp\u002Faspnet\u002Fweb-api","01.csharp\u002F11.aspnet\u002F12.web-api",[1294,1298,1302,1306,1310,1314,1318,1322,1326,1330,1334,1338,1342],{"title":1295,"path":1296,"stem":1297},"Від Minimal API до Controller-based API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffrom-minimal-api-to-controllers","01.csharp\u002F11.aspnet\u002F12.web-api\u002F01.from-minimal-api-to-controllers",{"title":1299,"path":1300,"stem":1301},"ControllerBase, ActionResult\u003CT> та Response Types","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontroller-base-actionresult","01.csharp\u002F11.aspnet\u002F12.web-api\u002F02.controller-base-actionresult",{"title":1303,"path":1304,"stem":1305},"Content Negotiation - JSON, XML та власні форматери","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fcontent-negotiation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F03.content-negotiation",{"title":1307,"path":1308,"stem":1309},"Версіонування API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-versioning","01.csharp\u002F11.aspnet\u002F12.web-api\u002F04.api-versioning",{"title":1311,"path":1312,"stem":1313},"ProblemDetails та структурована обробка помилок","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fproblemdetails-error-handling","01.csharp\u002F11.aspnet\u002F12.web-api\u002F05.problemdetails-error-handling",{"title":1315,"path":1316,"stem":1317},"Фільтри у Web API контексті","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Ffilters-for-api","01.csharp\u002F11.aspnet\u002F12.web-api\u002F06.filters-for-api",{"title":1319,"path":1320,"stem":1321},"Пагінація, фільтрація та сортування","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fpagination-filtering-sorting","01.csharp\u002F11.aspnet\u002F12.web-api\u002F07.pagination-filtering-sorting",{"title":1323,"path":1324,"stem":1325},"HATEOAS та Resource Expansion","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhateoas-resource-expansion","01.csharp\u002F11.aspnet\u002F12.web-api\u002F08.hateoas-resource-expansion",{"title":1327,"path":1328,"stem":1329},"Гібридна архітектура - Minimal API + Controllers","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fminimal-api-vs-controllers-hybrid","01.csharp\u002F11.aspnet\u002F12.web-api\u002F09.minimal-api-vs-controllers-hybrid",{"title":1331,"path":1332,"stem":1333},"Документація API - Swashbuckle, NSwag та генерація клієнтів","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fapi-documentation-generation","01.csharp\u002F11.aspnet\u002F12.web-api\u002F10.api-documentation-generation",{"title":1335,"path":1336,"stem":1337},"Health Checks та моніторинг API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fhealth-checks-monitoring","01.csharp\u002F11.aspnet\u002F12.web-api\u002F11.health-checks-monitoring",{"title":1339,"path":1340,"stem":1341},"Підсумковий проєкт - Production-Ready REST API","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fweb-api-project","01.csharp\u002F11.aspnet\u002F12.web-api\u002F12.web-api-project",{"title":1343,"path":1344,"stem":1345},"План курсу: ASP.NET Core Web API (Controllers)","\u002Fcsharp\u002Faspnet\u002Fweb-api\u002Fplan","01.csharp\u002F11.aspnet\u002F12.web-api\u002Fplan",{"title":1347,"icon":1348,"path":1349,"stem":1350,"children":1351,"page":59},"Моніторинг","i-lucide-activity","\u002Fcsharp\u002Faspnet\u002Fmonitoring","01.csharp\u002F11.aspnet\u002F13.monitoring",[1352,1356,1360],{"title":1353,"path":1354,"stem":1355},"Спостережуваність: від console.log до production-систем","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fobservability-intro","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F01.observability-intro",{"title":1357,"path":1358,"stem":1359},"Health Checks: перший рівень observability","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fhealth-checks","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F02.health-checks",{"title":1361,"path":1362,"stem":1363},"Вбудовані метрики .NET 10 та System.Diagnostics.Metrics","\u002Fcsharp\u002Faspnet\u002Fmonitoring\u002Fdotnet-metrics","01.csharp\u002F11.aspnet\u002F13.monitoring\u002F03.dotnet-metrics",{"title":1365,"icon":1366,"path":1367,"stem":1368,"children":1369,"page":59},"Desktop UI","i-lucide-app-window","\u002Fcsharp\u002Fdesktop-ui","01.csharp\u002F12.desktop-ui",[1370,1374,1378,1382,1386,1390,1394,1398,1402,1406,1410,1414,1418,1422,1426,1430,1434,1438,1442,1446,1450,1454,1458,1462,1466,1470,1474,1478,1482,1486,1490,1494,1498,1502,1506,1510,1514,1518,1522,1526,1530,1534,1538,1542,1546,1550,1554,1558,1562,1566,1570,1574,1578,1582,1586,1590,1594,1598,1602,1606,1610,1614,1618,1622,1626,1630,1634,1638,1642,1646,1650],{"title":1371,"path":1372,"stem":1373},"Що таке десктопна розробка?","\u002Fcsharp\u002Fdesktop-ui\u002Fwhat-is-desktop-dev","01.csharp\u002F12.desktop-ui\u002F01.what-is-desktop-dev",{"title":1375,"path":1376,"stem":1377},"Архітектура WPF — як влаштований графічний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-architecture","01.csharp\u002F12.desktop-ui\u002F02.wpf-architecture",{"title":1379,"path":1380,"stem":1381},"Перший WPF-проєкт — від нуля до вікна","\u002Fcsharp\u002Fdesktop-ui\u002Ffirst-wpf-app","01.csharp\u002F12.desktop-ui\u002F03.first-wpf-app",{"title":1383,"path":1384,"stem":1385},"Перший Avalonia-проєкт: WPF для всіх платформ","\u002Fcsharp\u002Fdesktop-ui\u002F03a.first-avalonia-app","01.csharp\u002F12.desktop-ui\u002F03a.first-avalonia-app",{"title":1387,"path":1388,"stem":1389},"XAML: декларативний інтерфейс","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-basics","01.csharp\u002F12.desktop-ui\u002F04.xaml-basics",{"title":1391,"path":1392,"stem":1393},"Fluent UI у WPF — сучасний дизайн Windows 11","\u002Fcsharp\u002Fdesktop-ui\u002F04a.wpf-fluent-ui","01.csharp\u002F12.desktop-ui\u002F04a.wpf-fluent-ui",{"title":1395,"path":1396,"stem":1397},"WPF UI — сучасна бібліотека Fluent контролів","\u002Fcsharp\u002Fdesktop-ui\u002F04b.wpf-ui-library","01.csharp\u002F12.desktop-ui\u002F04b.wpf-ui-library",{"title":1399,"path":1400,"stem":1401},"HandyControl — велика бібліотека UI контролів для WPF","\u002Fcsharp\u002Fdesktop-ui\u002F04c.handycontrol-library","01.csharp\u002F12.desktop-ui\u002F04c.handycontrol-library",{"title":1403,"path":1404,"stem":1405},"Простори імен та ресурси XAML","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-namespaces-resources","01.csharp\u002F12.desktop-ui\u002F05.xaml-namespaces-resources",{"title":1407,"path":1408,"stem":1409},"XAML в Avalonia: ключові відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F05a.avalonia-xaml-differences","01.csharp\u002F12.desktop-ui\u002F05a.avalonia-xaml-differences",{"title":1411,"path":1412,"stem":1413},"Розширення розмітки XAML (Markup Extensions)","\u002Fcsharp\u002Fdesktop-ui\u002Fxaml-markup-extensions","01.csharp\u002F12.desktop-ui\u002F06.xaml-markup-extensions",{"title":1415,"path":1416,"stem":1417},"Панелі Layout: StackPanel, WrapPanel, DockPanel","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part1","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part1",{"title":1419,"path":1420,"stem":1421},"Grid, Canvas, UniformGrid","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-panels-part2","01.csharp\u002F12.desktop-ui\u002F07.layout-panels-part2",{"title":1423,"path":1424,"stem":1425},"Просунуті техніки Layout","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-advanced","01.csharp\u002F12.desktop-ui\u002F08.layout-advanced",{"title":1427,"path":1428,"stem":1429},"Адаптивний Layout та найкращі практики","\u002Fcsharp\u002Fdesktop-ui\u002Flayout-responsive","01.csharp\u002F12.desktop-ui\u002F09.layout-responsive",{"title":1431,"path":1432,"stem":1433},"Layout в Avalonia: відмінності та нові можливості","\u002Fcsharp\u002Fdesktop-ui\u002F09a.layout-avalonia","01.csharp\u002F12.desktop-ui\u002F09a.layout-avalonia",{"title":1435,"path":1436,"stem":1437},"Button, Image, ProgressBar та інші базові контроли","\u002Fcsharp\u002Fdesktop-ui\u002Fbasic-controls","01.csharp\u002F12.desktop-ui\u002F10.basic-controls",{"title":1439,"path":1440,"stem":1441},"Контроли в Avalonia: відмінності від WPF","\u002Fcsharp\u002Fdesktop-ui\u002F10a.controls-avalonia","01.csharp\u002F12.desktop-ui\u002F10a.controls-avalonia",{"title":1443,"path":1444,"stem":1445},"Текстові контроли — TextBlock, TextBox, RichTextBox","\u002Fcsharp\u002Fdesktop-ui\u002Ftext-controls","01.csharp\u002F12.desktop-ui\u002F11.text-controls",{"title":1447,"path":1448,"stem":1449},"Контроли вибору — CheckBox, RadioButton, ComboBox, ListBox, DatePicker","\u002Fcsharp\u002Fdesktop-ui\u002Fselection-controls","01.csharp\u002F12.desktop-ui\u002F12.selection-controls",{"title":1451,"path":1452,"stem":1453},"Content Model — GroupBox, Expander, TabControl, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fcontent-controls","01.csharp\u002F12.desktop-ui\u002F13.content-controls",{"title":1455,"path":1456,"stem":1457},"UI\u002FUX принципи десктопних застосунків","\u002Fcsharp\u002Fdesktop-ui\u002F13a.ui-ux-principles","01.csharp\u002F12.desktop-ui\u002F13a.ui-ux-principles",{"title":1459,"path":1460,"stem":1461},"Dependency Properties — Концепція та Value Resolution","\u002Fcsharp\u002Fdesktop-ui\u002Fdependency-properties-part1","01.csharp\u002F12.desktop-ui\u002F14.dependency-properties-part1",{"title":1463,"path":1464,"stem":1465},"Avalonia Property System — StyledProperty та DirectProperty","\u002Fcsharp\u002Fdesktop-ui\u002F14a.avalonia-property-system","01.csharp\u002F12.desktop-ui\u002F14a.avalonia-property-system",{"title":1467,"path":1468,"stem":1469},"Attached Properties — Властивості без меж","\u002Fcsharp\u002Fdesktop-ui\u002Fattached-properties","01.csharp\u002F12.desktop-ui\u002F15.attached-properties",{"title":1471,"path":1472,"stem":1473},"Routed Events — Маршрутизація подій у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Frouted-events","01.csharp\u002F12.desktop-ui\u002F16.routed-events",{"title":1475,"path":1476,"stem":1477},"Data Binding — Від Code-Behind до Декларативності","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part1","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part1",{"title":1479,"path":1480,"stem":1481},"INotifyPropertyChanged — Живе оновлення UI","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-basics-part2","01.csharp\u002F12.desktop-ui\u002F17.data-binding-basics-part2",{"title":1483,"path":1484,"stem":1485},"Compiled Bindings в Avalonia — Безпека на етапі компіляції","\u002Fcsharp\u002Fdesktop-ui\u002F17a.avalonia-compiled-bindings","01.csharp\u002F12.desktop-ui\u002F17a.avalonia-compiled-bindings",{"title":1487,"path":1488,"stem":1489},"Просунутий Data Binding — ElementName, RelativeSource, MultiBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-binding-advanced","01.csharp\u002F12.desktop-ui\u002F18.data-binding-advanced",{"title":1491,"path":1492,"stem":1493},"Value Converters — Перетворення типів даних у Data Binding","\u002Fcsharp\u002Fdesktop-ui\u002Fvalue-converters","01.csharp\u002F12.desktop-ui\u002F19.value-converters",{"title":1495,"path":1496,"stem":1497},"Data Templates — Візуалізація об'єктів у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-templates","01.csharp\u002F12.desktop-ui\u002F20.data-templates",{"title":1499,"path":1500,"stem":1501},"Collections Binding Part 1 — ObservableCollection та ItemsControl","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part1","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part1",{"title":1503,"path":1504,"stem":1505},"Collections Binding Part 2 — ICollectionView, Filtering, Sorting та Virtualization","\u002Fcsharp\u002Fdesktop-ui\u002Fcollections-binding-part2","01.csharp\u002F12.desktop-ui\u002F21.collections-binding-part2",{"title":1507,"path":1508,"stem":1509},"MVVM Pattern — Від Spaghetti Code до архітектури","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-pattern","01.csharp\u002F12.desktop-ui\u002F22.mvvm-pattern",{"title":1511,"path":1512,"stem":1513},"ViewModel Implementation — Від BaseViewModel до валідації","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-implementation","01.csharp\u002F12.desktop-ui\u002F23.viewmodel-implementation",{"title":1515,"path":1516,"stem":1517},"Commands — Від event handlers до декларативних команд","\u002Fcsharp\u002Fdesktop-ui\u002Fcommands","01.csharp\u002F12.desktop-ui\u002F24.commands",{"title":1519,"path":1520,"stem":1521},"MVVM Toolkit — MVVM без boilerplate через Source Generators","\u002Fcsharp\u002Fdesktop-ui\u002Fmvvm-toolkit","01.csharp\u002F12.desktop-ui\u002F25.mvvm-toolkit",{"title":1523,"path":1524,"stem":1525},"Messenger Pattern — Комунікація між ViewModel без прямих посилань","\u002Fcsharp\u002Fdesktop-ui\u002Fmessenger-pattern","01.csharp\u002F12.desktop-ui\u002F26.messenger-pattern",{"title":1527,"path":1528,"stem":1529},"Стилі WPF — CSS для десктопу","\u002Fcsharp\u002Fdesktop-ui\u002Fstyles-basics","01.csharp\u002F12.desktop-ui\u002F27.styles-basics",{"title":1531,"path":1532,"stem":1533},"CSS-like стилі Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F27a.avalonia-css-styling","01.csharp\u002F12.desktop-ui\u002F27a.avalonia-css-styling",{"title":1535,"path":1536,"stem":1537},"Control Templates — Частина 1. Концепція та TemplateBinding","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part1","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part1",{"title":1539,"path":1540,"stem":1541},"Control Templates — Частина 2. Named Parts та ContentPresenter","\u002Fcsharp\u002Fdesktop-ui\u002Fcontrol-templates-part2","01.csharp\u002F12.desktop-ui\u002F28.control-templates-part2",{"title":1543,"path":1544,"stem":1545},"Control Themes в Avalonia — нова ера стилізації","\u002Fcsharp\u002Fdesktop-ui\u002F28a.avalonia-control-themes","01.csharp\u002F12.desktop-ui\u002F28a.avalonia-control-themes",{"title":1547,"path":1548,"stem":1549},"Triggers та Visual State Manager у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Ftriggers-visual-states","01.csharp\u002F12.desktop-ui\u002F29.triggers-visual-states",{"title":1551,"path":1552,"stem":1553},"Pseudo-classes в Avalonia — замість WPF Triggers","\u002Fcsharp\u002Fdesktop-ui\u002F29a.avalonia-pseudo-classes","01.csharp\u002F12.desktop-ui\u002F29a.avalonia-pseudo-classes",{"title":1555,"path":1556,"stem":1557},"Теми та ресурсні словники у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fresources-themes","01.csharp\u002F12.desktop-ui\u002F30.resources-themes",{"title":1559,"path":1560,"stem":1561},"Avalonia Themes — Fluent Design та система тематизації","\u002Fcsharp\u002Fdesktop-ui\u002F30a.avalonia-themes-fluent","01.csharp\u002F12.desktop-ui\u002F30a.avalonia-themes-fluent",{"title":1563,"path":1564,"stem":1565},"Контроли колекцій — глибоке занурення","\u002Fcsharp\u002Fdesktop-ui\u002Fcollection-controls","01.csharp\u002F12.desktop-ui\u002F31.collection-controls",{"title":1567,"path":1568,"stem":1569},"DataGrid — колонки та базове відображення","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part1","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part1",{"title":1571,"path":1572,"stem":1573},"DataGrid — сортування, фільтрація, редагування","\u002Fcsharp\u002Fdesktop-ui\u002Fdatagrid-part2","01.csharp\u002F12.desktop-ui\u002F32.datagrid-part2",{"title":1575,"path":1576,"stem":1577},"TreeView та GridView","\u002Fcsharp\u002Fdesktop-ui\u002Ftreeview-listview","01.csharp\u002F12.desktop-ui\u002F33.treeview-listview",{"title":1579,"path":1580,"stem":1581},"Меню, Toolbar, ContextMenu, StatusBar","\u002Fcsharp\u002Fdesktop-ui\u002Fmenus-toolbars","01.csharp\u002F12.desktop-ui\u002F34.menus-toolbars",{"title":1583,"path":1584,"stem":1585},"Навігація та керування вікнами. Частина 1: вікна та сторінки","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part1","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part1",{"title":1587,"path":1588,"stem":1589},"Навігація та керування вікнами. Частина 2: MVVM-навігація","\u002Fcsharp\u002Fdesktop-ui\u002Fnavigation-windows-part2","01.csharp\u002F12.desktop-ui\u002F35.navigation-windows-part2",{"title":1591,"path":1592,"stem":1593},"Avalonia — Навігація та діалоги","\u002Fcsharp\u002Fdesktop-ui\u002F35a.avalonia-navigation-dialogs","01.csharp\u002F12.desktop-ui\u002F35a.avalonia-navigation-dialogs",{"title":1595,"path":1596,"stem":1597},"Діалоги та File Pickers у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fdialogs-file-pickers","01.csharp\u002F12.desktop-ui\u002F36.dialogs-file-pickers",{"title":1599,"path":1600,"stem":1601},"UserControl: компонентний підхід у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fuser-controls","01.csharp\u002F12.desktop-ui\u002F37.user-controls",{"title":1603,"path":1604,"stem":1605},"Custom Controls: Lookless Controls у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fcustom-controls","01.csharp\u002F12.desktop-ui\u002F38.custom-controls",{"title":1607,"path":1608,"stem":1609},"Avalonia TemplatedControl — Lookless Controls","\u002Fcsharp\u002Fdesktop-ui\u002F38a.avalonia-templated-controls","01.csharp\u002F12.desktop-ui\u002F38a.avalonia-templated-controls",{"title":1611,"path":1612,"stem":1613},"Анімації у WPF: Storyboard та Easing Functions","\u002Fcsharp\u002Fdesktop-ui\u002Fanimations-transitions","01.csharp\u002F12.desktop-ui\u002F39.animations-transitions",{"title":1615,"path":1616,"stem":1617},"Анімації в Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002F39a.avalonia-animations","01.csharp\u002F12.desktop-ui\u002F39a.avalonia-animations",{"title":1619,"path":1620,"stem":1621},"2D Графіка та Мультимедіа у WPF","\u002Fcsharp\u002Fdesktop-ui\u002Fmedia-graphics","01.csharp\u002F12.desktop-ui\u002F40.media-graphics",{"title":1623,"path":1624,"stem":1625},"Dependency Injection у WPF та Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Fdi-integration","01.csharp\u002F12.desktop-ui\u002F41.di-integration",{"title":1627,"path":1628,"stem":1629},"SQLite та EF Core у десктопних додатках","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part1","01.csharp\u002F12.desktop-ui\u002F42.data-persistence-part1",{"title":1631,"path":1632,"stem":1633},"Repository Pattern та Unit of Work","\u002Fcsharp\u002Fdesktop-ui\u002Fdata-persistence-part2","01.csharp\u002F12.desktop-ui\u002F43.data-persistence-part2",{"title":1635,"path":1636,"stem":1637},"Тестування ViewModels","\u002Fcsharp\u002Fdesktop-ui\u002Fviewmodel-testing","01.csharp\u002F12.desktop-ui\u002F44.viewmodel-testing",{"title":1639,"path":1640,"stem":1641},"Avalonia Headless Testing — тестування UI без вікон","\u002Fcsharp\u002Fdesktop-ui\u002F44a.avalonia-headless-testing","01.csharp\u002F12.desktop-ui\u002F44a.avalonia-headless-testing",{"title":1643,"path":1644,"stem":1645},"Кросплатформна розробка з Avalonia","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-cross-platform","01.csharp\u002F12.desktop-ui\u002F45.avalonia-cross-platform",{"title":1647,"path":1648,"stem":1649},"Пакування та розгортання Avalonia додатків","\u002Fcsharp\u002Fdesktop-ui\u002Favalonia-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F46.avalonia-packaging-deployment",{"title":1651,"path":1652,"stem":1653},"Розгортання WPF застосунків","\u002Fcsharp\u002Fdesktop-ui\u002Fwpf-packaging-deployment","01.csharp\u002F12.desktop-ui\u002F47.wpf-packaging-deployment",{"title":1655,"icon":658,"path":1656,"stem":1657,"children":1658,"page":59},"Network Programming","\u002Fcsharp\u002Fnetwork-programming","01.csharp\u002F13.network-programming",[1659,1663,1667,1671,1675,1679,1683,1687,1691,1695,1699],{"title":1660,"path":1661,"stem":1662},"Основи комп'ютерних мереж","\u002Fcsharp\u002Fnetwork-programming\u002Ffoundations","01.csharp\u002F13.network-programming\u002F01.foundations",{"title":1664,"path":1665,"stem":1666},"Модель OSI та стек TCP\u002FIP","\u002Fcsharp\u002Fnetwork-programming\u002Fosi-model","01.csharp\u002F13.network-programming\u002F02.osi-model",{"title":1668,"path":1669,"stem":1670},"IP-протокол та адресація","\u002Fcsharp\u002Fnetwork-programming\u002Fip-addressing","01.csharp\u002F13.network-programming\u002F03.ip-addressing",{"title":1672,"path":1673,"stem":1674},"UDP — протокол без з'єднання","\u002Fcsharp\u002Fnetwork-programming\u002Fudp","01.csharp\u002F13.network-programming\u002F05.udp",{"title":1676,"path":1677,"stem":1678},"UDP Broadcast та Multicast","\u002Fcsharp\u002Fnetwork-programming\u002Fudp-broadcast-multicast","01.csharp\u002F13.network-programming\u002F06.udp-broadcast-multicast",{"title":1680,"path":1681,"stem":1682},"HTTP — протокол вебу","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-fundamentals","01.csharp\u002F13.network-programming\u002F07.http-fundamentals",{"title":1684,"path":1685,"stem":1686},"HttpListener — вбудований HTTP-сервер .NET","\u002Fcsharp\u002Fnetwork-programming\u002F07a.http-listener","01.csharp\u002F13.network-programming\u002F07a.http-listener",{"title":1688,"path":1689,"stem":1690},"HTTP Advanced — cookies, аутентифікація та HTTPS","\u002Fcsharp\u002Fnetwork-programming\u002Fhttp-advanced","01.csharp\u002F13.network-programming\u002F08.http-advanced",{"title":1692,"path":1693,"stem":1694},"SMTP та протоколи електронної пошти","\u002Fcsharp\u002Fnetwork-programming\u002Fsmtp","01.csharp\u002F13.network-programming\u002F09.smtp",{"title":1696,"path":1697,"stem":1698},"WebSocket — повнодуплексний протокол реального часу","\u002Fcsharp\u002Fnetwork-programming\u002Fwebsockets","01.csharp\u002F13.network-programming\u002F10.websockets",{"title":1700,"path":1701,"stem":1702},"TLS\u002FSSL — криптографічний захист мережевих з'єднань","\u002Fcsharp\u002Fnetwork-programming\u002Ftls-ssl","01.csharp\u002F13.network-programming\u002F11.tls-ssl",{"title":1704,"path":1705,"stem":1706},"C# & .NET: The Ultimate Roadmap","\u002Fcsharp\u002Froadmap","01.csharp\u002Froadmap",{"title":1708,"icon":1709,"path":1710,"stem":1711,"children":1712,"page":59},"C++","i-devicon-cplusplus","\u002Fcpp","02.cpp",[1713,1717,1721,1725,1729,1733,1737,1741,1745,1748,1752,1756,1760,1764,1768,1772,1776,1780,1784,1788,1792,1796,1800,1804,1808,1812,1816,1820,1824,1828,1832,1836,1840,1844,1848,1852,1856,1860,1864,1868,1872,1876,1880,1884,1888,1892,1896,1900,1904,1908,1912,1916,1920,1924,1928,1932,1936,1940,1944,1948,1952,1956,1960,1964,1968,1972,1976,1980,1984,1988,1992,1996,2000,2004,2008,2012,2016,2020,2024,2028,2032,2036,2040,2044,2048,2052,2056,2060,2064,2068,2072,2076,2080],{"title":1714,"path":1715,"stem":1716},"Вступ у програмування та алгоритми","\u002Fcpp\u002Fintro-algorithms","02.cpp\u002F01.intro-algorithms",{"title":1718,"path":1719,"stem":1720},"Code Style: угоди про оформлення коду","\u002Fcpp\u002Fcode-style","02.cpp\u002F02.code-style",{"title":1722,"path":1723,"stem":1724},"Середовище розробки та перший проєкт","\u002Fcpp\u002Fide-setup","02.cpp\u002F03.ide-setup",{"title":1726,"path":1727,"stem":1728},"Вивід даних на екран","\u002Fcpp\u002Fdata-output","02.cpp\u002F04.data-output",{"title":1730,"path":1731,"stem":1732},"Типи даних, змінні та константи","\u002Fcpp\u002Fdata-types-variables","02.cpp\u002F05.data-types-variables",{"title":1734,"path":1735,"stem":1736},"Ввід даних з клавіатури","\u002Fcpp\u002Fdata-input","02.cpp\u002F06.data-input",{"title":1738,"path":1739,"stem":1740},"Оператори, перетворення типів та логічні операції","\u002Fcpp\u002Foperators-type-conversion","02.cpp\u002F07.operators-type-conversion",{"title":1742,"path":1743,"stem":1744},"Цикли","\u002Fcpp\u002Floops","02.cpp\u002F08.loops",{"title":32,"path":1746,"stem":1747},"\u002Fcpp\u002Farrays","02.cpp\u002F09.arrays",{"title":1749,"path":1750,"stem":1751},"Алгоритми сортування та аналіз складності","\u002Fcpp\u002Fsorting","02.cpp\u002F10.sorting",{"title":1753,"path":1754,"stem":1755},"Алгоритми пошуку","\u002Fcpp\u002Fsearching","02.cpp\u002F11.searching",{"title":1757,"path":1758,"stem":1759},"Функції: основи","\u002Fcpp\u002Ffunctions-basics","02.cpp\u002F12.functions-basics",{"title":1761,"path":1762,"stem":1763},"Функції: прототипи, область видимості та додаткові можливості","\u002Fcpp\u002Ffunctions-scope","02.cpp\u002F13.functions-scope",{"title":1765,"path":1766,"stem":1767},"Функції: перевантаження та шаблони","\u002Fcpp\u002Ffunctions-overloading-templates","02.cpp\u002F14.functions-overloading-templates",{"title":1769,"path":1770,"stem":1771},"Вказівники: основи","\u002Fcpp\u002Fpointers-basics","02.cpp\u002F15.pointers-basics",{"title":1773,"path":1774,"stem":1775},"Посилання (References)","\u002Fcpp\u002Freferences","02.cpp\u002F16.references",{"title":1777,"path":1778,"stem":1779},"Вказівники, const і масиви","\u002Fcpp\u002Fpointers-const-arrays","02.cpp\u002F17.pointers-const-arrays",{"title":1781,"path":1782,"stem":1783},"Адресна арифметика","\u002Fcpp\u002Fpointer-arithmetic","02.cpp\u002F18.pointer-arithmetic",{"title":1785,"path":1786,"stem":1787},"Динамічна пам'ять","\u002Fcpp\u002Fdynamic-memory","02.cpp\u002F19.dynamic-memory",{"title":1789,"path":1790,"stem":1791},"Вказівники типу void","\u002Fcpp\u002Fvoid-pointers","02.cpp\u002F20.void-pointers",{"title":1793,"path":1794,"stem":1795},"Вказівники на вказівники","\u002Fcpp\u002Fpointers-to-pointers","02.cpp\u002F21.pointers-to-pointers",{"title":1797,"path":1798,"stem":1799},"Оператор доступу до членів через вказівник (->)","\u002Fcpp\u002Fmember-access-operator","02.cpp\u002F22.member-access-operator",{"title":1801,"path":1802,"stem":1803},"Цикл for-each (Range-based for)","\u002Fcpp\u002Fforeach-loop","02.cpp\u002F23.foreach-loop",{"title":1805,"path":1806,"stem":1807},"Вказівники на функції","\u002Fcpp\u002Ffunction-pointers","02.cpp\u002F24.function-pointers",{"title":1809,"path":1810,"stem":1811},"Лямбда-вирази","\u002Fcpp\u002Flambdas","02.cpp\u002F25.lambdas",{"title":1813,"path":1814,"stem":1815},"Лямбда-захоплення","\u002Fcpp\u002Flambda-captures","02.cpp\u002F26.lambda-captures",{"title":1817,"path":1818,"stem":1819},"Еліпсис","\u002Fcpp\u002Fellipsis","02.cpp\u002F27.ellipsis",{"title":1821,"path":1822,"stem":1823},"Безпечні альтернативи еліпсису","\u002Fcpp\u002F27a.ellipsis","02.cpp\u002F27a.ellipsis",{"title":1825,"path":1826,"stem":1827},"Аргументи командного рядка","\u002Fcpp\u002Fcommand-line-arguments","02.cpp\u002F28.command-line-arguments",{"title":1829,"path":1830,"stem":1831},"Перерахування (enum)","\u002Fcpp\u002Fenum","02.cpp\u002F29.enum",{"title":1833,"path":1834,"stem":1835},"Класи-перерахування (enum class)","\u002Fcpp\u002Fenum-class","02.cpp\u002F30.enum-class",{"title":1837,"path":1838,"stem":1839},"Псевдоніми типів (typedef і using)","\u002Fcpp\u002Ftype-aliases","02.cpp\u002F31.type-aliases",{"title":1841,"path":1842,"stem":1843},"Системи числення та двійкова арифметика","\u002Fcpp\u002Fnumber-systems","02.cpp\u002F32.number-systems",{"title":1845,"path":1846,"stem":1847},"Структури (struct): агрегування даних","\u002Fcpp\u002Fstruct","02.cpp\u002F33.struct",{"title":1849,"path":1850,"stem":1851},"Структури у функціях","\u002Fcpp\u002Fstruct-functions","02.cpp\u002F34.struct-functions",{"title":1853,"path":1854,"stem":1855},"Масиви структур і вкладені структури","\u002Fcpp\u002Fstruct-arrays","02.cpp\u002F35.struct-arrays",{"title":1857,"path":1858,"stem":1859},"Патерни struct та межі застосування","\u002Fcpp\u002Fstruct-patterns","02.cpp\u002F36.struct-patterns",{"title":1861,"path":1862,"stem":1863},"Символи та таблиця ASCII","\u002Fcpp\u002Fascii-characters","02.cpp\u002F37.ascii-characters",{"title":1865,"path":1866,"stem":1867},"Unicode та кодування UTF","\u002Fcpp\u002Funicode-utf","02.cpp\u002F38.unicode-utf",{"title":1869,"path":1870,"stem":1871},"C-style рядки","\u002Fcpp\u002Fc-strings","02.cpp\u002F39.c-strings",{"title":1873,"path":1874,"stem":1875},"Вступ до std::string","\u002Fcpp\u002Fstd-string-intro","02.cpp\u002F40.std-string-intro",{"title":1877,"path":1878,"stem":1879},"Довжина, ємність та доступ до символів std::string","\u002Fcpp\u002Fstd-string-capacity-access","02.cpp\u002F41.std-string-capacity-access",{"title":1881,"path":1882,"stem":1883},"Модифікація std::string: присвоювання, додавання, вставка, видалення та заміна","\u002Fcpp\u002Fstd-string-modification","02.cpp\u002F42.std-string-modification",{"title":1885,"path":1886,"stem":1887},"Пошук у std::string: find, npos та практичні патерни","\u002Fcpp\u002Fstd-string-search","02.cpp\u002F43.std-string-search",{"title":1889,"path":1890,"stem":1891},"std::string_view: невласницький погляд на рядок без копіювання","\u002Fcpp\u002Fstd-string-view","02.cpp\u002F44.std-string-view",{"title":1893,"path":1894,"stem":1895},"Об'єднання (union): один блок пам'яті, кілька інтерпретацій","\u002Fcpp\u002Funion","02.cpp\u002F45.union",{"title":1897,"path":1898,"stem":1899},"Організація коду: файли, препроцесор, простори імен","\u002Fcpp\u002Fmultifile-programs","02.cpp\u002F46.multifile-programs",{"title":1901,"path":1902,"stem":1903},"Робота з файлами: C-стиль (stdio.h)","\u002Fcpp\u002Fc-style-files","02.cpp\u002F47.c-style-files",{"title":1905,"path":1906,"stem":1907},"Робота з файлами: C++-стиль (fstream)","\u002Fcpp\u002Fcpp-style-files","02.cpp\u002F48.cpp-style-files",{"title":1909,"path":1910,"stem":1911},"Введення в ООП: від процедур до об'єктів","\u002Fcpp\u002Foop-intro","02.cpp\u002F49.oop-intro",{"title":1913,"path":1914,"stem":1915},"Класи, об'єкти та методи","\u002Fcpp\u002Fclasses-objects-methods","02.cpp\u002F50.classes-objects-methods",{"title":1917,"path":1918,"stem":1919},"Специфікатори доступу та інкапсуляція","\u002Fcpp\u002Faccess-specifiers-encapsulation","02.cpp\u002F51.access-specifiers-encapsulation",{"title":1921,"path":1922,"stem":1923},"Конструктори: гарантована ініціалізація об'єктів","\u002Fcpp\u002Fconstructors","02.cpp\u002F52.constructors",{"title":1925,"path":1926,"stem":1927},"Списки ініціалізації та делегуючі конструктори","\u002Fcpp\u002Finit-lists-delegating","02.cpp\u002F53.init-lists-delegating",{"title":1929,"path":1930,"stem":1931},"Деструктори та ідіома RAII","\u002Fcpp\u002Fdestructors-raii","02.cpp\u002F54.destructors-raii",{"title":1933,"path":1934,"stem":1935},"Прихований покажчик this","\u002Fcpp\u002Fthis-pointer","02.cpp\u002F55.this-pointer",{"title":1937,"path":1938,"stem":1939},"Розподіл класу на заголовковий файл та файл реалізації","\u002Fcpp\u002Fclass-header-source","02.cpp\u002F56.class-header-source",{"title":1941,"path":1942,"stem":1943},"Класи та const","\u002Fcpp\u002Fconst-classes","02.cpp\u002F57.const-classes",{"title":1945,"path":1946,"stem":1947},"Статичні члени класу","\u002Fcpp\u002Fstatic-members","02.cpp\u002F58.static-members",{"title":1949,"path":1950,"stem":1951},"Конструктор копіювання та запобігання копіюванню","\u002Fcpp\u002Fcopy-constructor","02.cpp\u002F59.copy-constructor",{"title":1953,"path":1954,"stem":1955},"Дружні функції та класи","\u002Fcpp\u002Ffriend-functions-classes","02.cpp\u002F60.friend-functions-classes",{"title":1957,"path":1958,"stem":1959},"Анонімні об'єкти та вкладені типи","\u002Fcpp\u002Fanonymous-objects-nested-types","02.cpp\u002F61.anonymous-objects-nested-types",{"title":1961,"path":1962,"stem":1963},"Вимірювання часу виконання: RAII-таймер","\u002Fcpp\u002Ftiming-raii-timer","02.cpp\u002F62.timing-raii-timer",{"title":1965,"path":1966,"stem":1967},"Перевантаження операторів: основи та арифметика","\u002Fcpp\u002Foperator-overloading-basics","02.cpp\u002F63.operator-overloading-basics",{"title":1969,"path":1970,"stem":1971},"Перевантаження операторів: методи класу та спеціальні оператори","\u002Fcpp\u002Foperator-overloading-methods","02.cpp\u002F64.operator-overloading-methods",{"title":1973,"path":1974,"stem":1975},"Приведення типів, explicit та delete","\u002Fcpp\u002Ftypecast-explicit-delete","02.cpp\u002F65.typecast-explicit-delete",{"title":1977,"path":1978,"stem":1979},"Глибоке копіювання та оператор присвоювання","\u002Fcpp\u002Fdeep-copy-assignment","02.cpp\u002F66.deep-copy-assignment",{"title":1981,"path":1982,"stem":1983},"Зв'язки між об'єктами: композиція та агрегація","\u002Fcpp\u002Fcomposition-aggregation","02.cpp\u002F67.composition-aggregation",{"title":1985,"path":1986,"stem":1987},"Асоціація та залежність між об","\u002Fcpp\u002Fassociation-dependency","02.cpp\u002F68.association-dependency",{"title":1989,"path":1990,"stem":1991},"Контейнерні класи та `std::initializer_list`","\u002Fcpp\u002Fcontainer-classes-initializer-list","02.cpp\u002F69.container-classes-initializer-list",{"title":1993,"path":1994,"stem":1995},"Вступ до наслідування: базові поняття та відношення «is-a»","\u002Fcpp\u002Finheritance-intro","02.cpp\u002F70.inheritance-intro",{"title":1997,"path":1998,"stem":1999},"Конструктори, деструктори та порядок ініціалізації в ієрархіях","\u002Fcpp\u002Finheritance-constructors-destructors","02.cpp\u002F71.inheritance-constructors-destructors",{"title":2001,"path":2002,"stem":2003},"Специфікатор `protected` та види наслідування","\u002Fcpp\u002Finheritance-access-specifiers","02.cpp\u002F72.inheritance-access-specifiers",{"title":2005,"path":2006,"stem":2007},"Перевизначення методів та приховування імен","\u002Fcpp\u002Fmethod-overriding-hiding","02.cpp\u002F73.method-overriding-hiding",{"title":2009,"path":2010,"stem":2011},"Множинне наслідування та проблема ромба","\u002Fcpp\u002Fmultiple-inheritance-diamond","02.cpp\u002F74.multiple-inheritance-diamond",{"title":2013,"path":2014,"stem":2015},"Вказівники на базовий клас та віртуальні функції","\u002Fcpp\u002Fvirtual-functions-polymorphism","02.cpp\u002F75.virtual-functions-polymorphism",{"title":2017,"path":2018,"stem":2019},"Специфікатори override, final та віртуальні деструктори","\u002Fcpp\u002Foverride-final-virtual-destructors","02.cpp\u002F76.override-final-virtual-destructors",{"title":2021,"path":2022,"stem":2023},"Внутрішні механізми поліморфізму: vtable, vptr та зв'язування","\u002Fcpp\u002Fvirtual-table-binding","02.cpp\u002F77.virtual-table-binding",{"title":2025,"path":2026,"stem":2027},"Абстрактні класи та чисті віртуальні функції","\u002Fcpp\u002Fabstract-classes-interfaces","02.cpp\u002F78.abstract-classes-interfaces",{"title":2029,"path":2030,"stem":2031},"Зрізка об'єктів, віртуальне наслідування та поліморфний вивід","\u002Fcpp\u002Fslicing-virtual-base-io","02.cpp\u002F79.slicing-virtual-base-io",{"title":2033,"path":2034,"stem":2035},"Динамічне приведення типів (`dynamic_cast`) та RTTI","\u002Fcpp\u002Fdynamic-cast-rtti","02.cpp\u002F80.dynamic-cast-rtti",{"title":2037,"path":2038,"stem":2039},"Шаблони функцій: узагальнене програмування","\u002Fcpp\u002Ffunction-templates","02.cpp\u002F81.function-templates",{"title":2041,"path":2042,"stem":2043},"Шаблони класів та NTTP-параметри","\u002Fcpp\u002Fclass-templates-nttp","02.cpp\u002F82.class-templates-nttp",{"title":2045,"path":2046,"stem":2047},"Повна (явна) спеціалізація шаблонів","\u002Fcpp\u002Ffull-template-specialization","02.cpp\u002F83.full-template-specialization",{"title":2049,"path":2050,"stem":2051},"Часткова спеціалізація шаблонів класів","\u002Fcpp\u002Fpartial-template-specialization","02.cpp\u002F84.partial-template-specialization",{"title":2053,"path":2054,"stem":2055},"Механізм винятків: try, catch, throw та розкручування стеку","\u002Fcpp\u002Fexceptions-basics","02.cpp\u002F85.exceptions-basics",{"title":2057,"path":2058,"stem":2059},"Ієрархія std::exception та власні класи винятків","\u002Fcpp\u002Fexception-hierarchy-custom","02.cpp\u002F86.exception-hierarchy-custom",{"title":2061,"path":2062,"stem":2063},"Повторне генерування винятків та функціональний try-блок","\u002Fcpp\u002Frethrow-function-try","02.cpp\u002F87.rethrow-function-try",{"title":2065,"path":2066,"stem":2067},"Безпека винятків, noexcept та деструктори","\u002Fcpp\u002Fsafety-noexcept","02.cpp\u002F88.safety-noexcept",{"title":2069,"path":2070,"stem":2071},"Стаття 89 — Власні структури даних: стек та черга","\u002Fcpp\u002Fcustom-stack-queue","02.cpp\u002F89.custom-stack-queue",{"title":2073,"path":2074,"stem":2075},"Стаття 90 — Власні структури даних: однозв'язаний список","\u002Fcpp\u002Flinked-list","02.cpp\u002F90.linked-list",{"title":2077,"path":2078,"stem":2079},"Стаття 91 — Власні структури даних: бінарне дерево пошуку","\u002Fcpp\u002Fbinary-search-tree","02.cpp\u002F91.binary-search-tree",{"title":2081,"path":2082,"stem":2083},"Стаття 92 — Власні структури даних: хеш-таблиця","\u002Fcpp\u002Fhash-table","02.cpp\u002F92.hash-table",{"title":2085,"icon":2086,"path":2087,"stem":2088,"children":2089,"page":59},"JavaScript","i-devicon-javascript","\u002Fjavascript","03.javascript",[2090,2116,2170,2192,2496,2534,2552],{"title":2091,"icon":2092,"path":2093,"stem":2094,"children":2095,"page":59},"Events","i-lucide-mouse-pointer-click","\u002Fjavascript\u002Fevents","03.javascript\u002F01.events",[2096,2100,2104,2108,2112],{"title":2097,"path":2098,"stem":2099},"Вступ до подій браузера","\u002Fjavascript\u002Fevents\u002Fintro","03.javascript\u002F01.events\u002F01.intro",{"title":2101,"path":2102,"stem":2103},"Бульбашковий механізм (Bubbling) та занурення (Capturing)","\u002Fjavascript\u002Fevents\u002Fbubbling-capturing","03.javascript\u002F01.events\u002F02.bubbling-capturing",{"title":2105,"path":2106,"stem":2107},"Делегування подій (Event Delegation)","\u002Fjavascript\u002Fevents\u002Fdelegate-events","03.javascript\u002F01.events\u002F03.delegate-events",{"title":2109,"path":2110,"stem":2111},"Типові дії браузера та preventDefault()","\u002Fjavascript\u002Fevents\u002Fprevent-default","03.javascript\u002F01.events\u002F04.prevent-default",{"title":2113,"path":2114,"stem":2115},"Запуск користувацьких подій (Custom Events)","\u002Fjavascript\u002Fevents\u002Fcustom-events","03.javascript\u002F01.events\u002F05.custom-events",{"title":2117,"icon":2118,"path":2119,"stem":2120,"children":2121,"page":59},"Network","i-lucide-globe","\u002Fjavascript\u002Fnetwork","03.javascript\u002F02.network",[2122,2126,2130,2134,2138,2142,2146,2150,2154,2158,2162,2166],{"title":2123,"path":2124,"stem":2125},"Fetch API - Сучасний підхід до HTTP-запитів","\u002Fjavascript\u002Fnetwork\u002F01-fetch-api","03.javascript\u002F02.network\u002F01-fetch-api",{"title":2127,"path":2128,"stem":2129},"FormData - Робота з формами та файлами","\u002Fjavascript\u002Fnetwork\u002F02-formdata","03.javascript\u002F02.network\u002F02-formdata",{"title":2131,"path":2132,"stem":2133},"Відстеження прогресу завантаження","\u002Fjavascript\u002Fnetwork\u002F03-download-progress","03.javascript\u002F02.network\u002F03-download-progress",{"title":2135,"path":2136,"stem":2137},"Переривання fetch-запитів","\u002Fjavascript\u002Fnetwork\u002F04-abort-requests","03.javascript\u002F02.network\u002F04-abort-requests",{"title":2139,"path":2140,"stem":2141},"CORS - Запити між різними джерелами","\u002Fjavascript\u002Fnetwork\u002F05-cors","03.javascript\u002F02.network\u002F05-cors",{"title":2143,"path":2144,"stem":2145},"Fetch API - Повний довідник опцій","\u002Fjavascript\u002Fnetwork\u002F06-fetch-options","03.javascript\u002F02.network\u002F06-fetch-options",{"title":2147,"path":2148,"stem":2149},"URL Objects - Робота з посиланнями","\u002Fjavascript\u002Fnetwork\u002F07-url-objects","03.javascript\u002F02.network\u002F07-url-objects",{"title":2151,"path":2152,"stem":2153},"XMLHttpRequest - AJAX та низькорівневі запити","\u002Fjavascript\u002Fnetwork\u002F08-xmlhttprequest","03.javascript\u002F02.network\u002F08-xmlhttprequest",{"title":2155,"path":2156,"stem":2157},"Відновлюване завантаження файлів","\u002Fjavascript\u002Fnetwork\u002F09-resumable-upload","03.javascript\u002F02.network\u002F09-resumable-upload",{"title":2159,"path":2160,"stem":2161},"Cookies, document.cookie та світ після \"Cookiepocalypse\"","\u002Fjavascript\u002Fnetwork\u002F10-cookies","03.javascript\u002F02.network\u002F10-cookies",{"title":2163,"path":2164,"stem":2165},"js-cookie: Керування Cookies без Болю","\u002Fjavascript\u002Fnetwork\u002F11-js-cookie","03.javascript\u002F02.network\u002F11-js-cookie",{"title":2167,"path":2168,"stem":2169},"Axios: Потужний HTTP-клієнт для JavaScript","\u002Fjavascript\u002Fnetwork\u002F12-axios","03.javascript\u002F02.network\u002F12-axios",{"title":2171,"icon":2172,"path":2173,"stem":2174,"children":2175,"page":59},"Bom","i-lucide-monitor","\u002Fjavascript\u002Fbom","03.javascript\u002F03.bom",[2176,2180,2184,2188],{"title":2177,"path":2178,"stem":2179},"LocalStorage, SessionStorage та patterns збереження даних","\u002Fjavascript\u002Fbom\u002F01-localstorage","03.javascript\u002F03.bom\u002F01-localstorage",{"title":2181,"path":2182,"stem":2183},"Location Object - Керування адресою сторінки","\u002Fjavascript\u002Fbom\u002F02-location-object","03.javascript\u002F03.bom\u002F02-location-object",{"title":2185,"path":2186,"stem":2187},"History API - Керування історією браузера","\u002Fjavascript\u002Fbom\u002F03-history-api","03.javascript\u002F03.bom\u002F03-history-api",{"title":2189,"path":2190,"stem":2191},"Navigator Object - Ідентифікація та Можливості Пристрою","\u002Fjavascript\u002Fbom\u002F04-navigator-object","03.javascript\u002F03.bom\u002F04-navigator-object",{"title":2193,"icon":2194,"path":2195,"stem":2196,"children":2197},"React","i-devicon-react","\u002Fjavascript\u002Freact","03.javascript\u002F04.react\u002Findex",[2198,2199,2203,2207,2211,2215,2278,2313,2465],{"title":2193,"path":2195,"stem":2196},{"title":2200,"path":2201,"stem":2202},"Робота з Формами в React","\u002Fjavascript\u002Freact\u002Freact-forms","03.javascript\u002F04.react\u002F01.react-forms",{"title":2204,"path":2205,"stem":2206},"React Hook Form: Професійна Робота з Формами","\u002Fjavascript\u002Freact\u002Freact-hook-form","03.javascript\u002F04.react\u002F02.react-hook-form",{"title":2208,"path":2209,"stem":2210},"React Hook Form: Глибоке Розуміння Архітектури та Оптимізації","\u002Fjavascript\u002Freact\u002Freact-hook-form-new","03.javascript\u002F04.react\u002F02.react-hook-form-new",{"title":2212,"path":2213,"stem":2214},"Axios та React: Професійна Архітектура Запитів","\u002Fjavascript\u002Freact\u002Fdata-fetching-axios","03.javascript\u002F04.react\u002F03.data-fetching-axios",{"title":2216,"icon":132,"path":2217,"stem":2218,"children":2219},"Tanstack Query","\u002Fjavascript\u002Freact\u002Ftanstack-query","03.javascript\u002F04.react\u002F04.tanstack-query\u002Findex",[2220,2222,2226,2230,2234,2238,2242,2246,2250,2254,2258,2262,2266,2270,2274],{"title":2221,"path":2217,"stem":2218},"TanStack Query: Майстерність Керування Станом Сервера",{"title":2223,"path":2224,"stem":2225},"Парадигма Server State: Чому useEffect недостатньо","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-state-paradigm","03.javascript\u002F04.react\u002F04.tanstack-query\u002F01.server-state-paradigm",{"title":2227,"path":2228,"stem":2229},"Встановлення та Налаштування: Фундамент","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Finstallation-and-devtools","03.javascript\u002F04.react\u002F04.tanstack-query\u002F02.installation-and-devtools",{"title":2231,"path":2232,"stem":2233},"Основи Запитів та Магія Ключів","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fquery-basics-and-keys","03.javascript\u002F04.react\u002F04.tanstack-query\u002F03.query-basics-and-keys",{"title":2235,"path":2236,"stem":2237},"Синхронізація Даних: Життєвий Цикл Запиту","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fdata-synchronization","03.javascript\u002F04.react\u002F04.tanstack-query\u002F04.data-synchronization",{"title":2239,"path":2240,"stem":2241},"Мутації та Інвалідація: Зміна Даних","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fmutations-and-invalidation","03.javascript\u002F04.react\u002F04.tanstack-query\u002F05.mutations-and-invalidation",{"title":2243,"path":2244,"stem":2245},"Оптимістичні Оновлення: Швидше за Світло","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Foptimistic-updates","03.javascript\u002F04.react\u002F04.tanstack-query\u002F06.optimistic-updates",{"title":2247,"path":2248,"stem":2249},"Пагінація та Infinite Scroll","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fpagination-and-load-more","03.javascript\u002F04.react\u002F04.tanstack-query\u002F07.pagination-and-load-more",{"title":2251,"path":2252,"stem":2253},"Просунуті Патерни та Оптимізація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F04.tanstack-query\u002F08.advanced-patterns",{"title":2255,"path":2256,"stem":2257},"Архітектура та Best Practices","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Farchitecture-and-best-practices","03.javascript\u002F04.react\u002F04.tanstack-query\u002F09.architecture-and-best-practices",{"title":2259,"path":2260,"stem":2261},"Server-Side Rendering (SSR) та Гідратація","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fserver-side-rendering","03.javascript\u002F04.react\u002F04.tanstack-query\u002F10.server-side-rendering",{"title":2263,"path":2264,"stem":2265},"Стратегії Тестування","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Ftesting-strategies","03.javascript\u002F04.react\u002F04.tanstack-query\u002F11.testing-strategies",{"title":2267,"path":2268,"stem":2269},"Аутентифікація та Обробка Помилок","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fauthentication-and-errors","03.javascript\u002F04.react\u002F04.tanstack-query\u002F12.authentication-and-errors",{"title":2271,"path":2272,"stem":2273},"React Suspense та Майбутнє","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Freact-suspense","03.javascript\u002F04.react\u002F04.tanstack-query\u002F13.react-suspense",{"title":2275,"path":2276,"stem":2277},"Глибоке Занурення в Продуктивність","\u002Fjavascript\u002Freact\u002Ftanstack-query\u002Fperformance-deep-dive","03.javascript\u002F04.react\u002F04.tanstack-query\u002F14.performance-deep-dive",{"title":2279,"icon":2194,"path":2280,"stem":2281,"children":2282},"React Router","\u002Fjavascript\u002Freact\u002Freact-router","03.javascript\u002F04.react\u002F05.react-router\u002Findex",[2283,2285,2289,2293,2297,2301,2305,2309],{"title":2284,"path":2280,"stem":2281},"React Router: Навігаційна система сучасного вебу",{"title":2286,"path":2287,"stem":2288},"Налаштування та Базовий Роутинг","\u002Fjavascript\u002Freact\u002Freact-router\u002Fsetup-and-basic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F01.setup-and-basic-routing",{"title":2290,"path":2291,"stem":2292},"Динамічна Навігація","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnavigation-and-links","03.javascript\u002F04.react\u002F05.react-router\u002F02.navigation-and-links",{"title":2294,"path":2295,"stem":2296},"Вкладені Маршрути та Макети","\u002Fjavascript\u002Freact\u002Freact-router\u002Fnested-routes-and-layouts","03.javascript\u002F04.react\u002F05.react-router\u002F03.nested-routes-and-layouts",{"title":2298,"path":2299,"stem":2300},"Динамічні Маршрути та Параметри","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdynamic-routing","03.javascript\u002F04.react\u002F05.react-router\u002F04.dynamic-routing",{"title":2302,"path":2303,"stem":2304},"Data APIs: Loaders та Actions","\u002Fjavascript\u002Freact\u002Freact-router\u002Fdata-loading","03.javascript\u002F04.react\u002F05.react-router\u002F05.data-loading",{"title":2306,"path":2307,"stem":2308},"Просунуті Патерни","\u002Fjavascript\u002Freact\u002Freact-router\u002Fadvanced-patterns","03.javascript\u002F04.react\u002F05.react-router\u002F06.advanced-patterns",{"title":2310,"path":2311,"stem":2312},"Legacy Routing: Компонентний підхід","\u002Fjavascript\u002Freact\u002Freact-router\u002Flegacy-routing","03.javascript\u002F04.react\u002F05.react-router\u002F07.legacy-routing",{"title":2314,"icon":132,"path":2315,"stem":2316,"children":2317},"Redux","\u002Fjavascript\u002Freact\u002Fredux","03.javascript\u002F04.react\u002F06.redux\u002Findex",[2318,2320,2336,2365,2374,2395,2411,2440],{"title":2319,"path":2315,"stem":2316},"Redux: Еволюція управління станом",{"title":14,"icon":15,"path":2321,"stem":2322,"children":2323,"page":59},"\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals",[2324,2328,2332],{"title":2325,"path":2326,"stem":2327},"Вступ до State Management","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fintro-state-management","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F01.intro-state-management",{"title":2329,"path":2330,"stem":2331},"Філософія Redux та Три Принципи","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fredux-philosophy","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F02.redux-philosophy",{"title":2333,"path":2334,"stem":2335},"Чисті функції та Іммутабельність","\u002Fjavascript\u002Freact\u002Fredux\u002Ffundamentals\u002Fpure-functions-immutability","03.javascript\u002F04.react\u002F06.redux\u002F01.fundamentals\u002F03.pure-functions-immutability",{"title":2337,"icon":132,"path":2338,"stem":2339,"children":2340,"page":59},"Classic Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux",[2341,2345,2349,2353,2357,2361],{"title":2342,"path":2343,"stem":2344},"Створення Store (Classic Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fstore-setup","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F01.store-setup",{"title":2346,"path":2347,"stem":2348},"Actions, Constants та Action Creators","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Factions-constants","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F02.actions-constants",{"title":2350,"path":2351,"stem":2352},"Логіка Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freducers","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F03.reducers",{"title":2354,"path":2355,"stem":2356},"Комбінування Reducers (Root Reducer)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fdata-flow","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F04.data-flow",{"title":2358,"path":2359,"stem":2360},"Підключення до React (React-Redux)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Freact-redux-connection","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F05.react-redux-connection",{"title":2362,"path":2363,"stem":2364},"Middleware та Асинхронність (Redux Thunk)","\u002Fjavascript\u002Freact\u002Fredux\u002Fclassic-redux\u002Fmiddleware-thunk","03.javascript\u002F04.react\u002F06.redux\u002F02.classic-redux\u002F06.middleware-thunk",{"title":2366,"icon":132,"path":2367,"stem":2368,"children":2369,"page":59},"Transition To Rtk","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk",[2370],{"title":2371,"path":2372,"stem":2373},"Проблеми класичного Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftransition-to-rtk\u002Fproblems-with-classic","03.javascript\u002F04.react\u002F06.redux\u002F03.transition-to-rtk\u002F01.problems-with-classic",{"title":2375,"icon":132,"path":2376,"stem":2377,"children":2378,"page":59},"Redux Toolkit","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit",[2379,2383,2387,2391],{"title":2380,"path":2381,"stem":2382},"Налаштування Store з configureStore","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fconfigure-store","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F01.configure-store",{"title":2384,"path":2385,"stem":2386},"createSlice: Революція в Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fcreate-slice","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F02.create-slice",{"title":2388,"path":2389,"stem":2390},"Асинхронність з createAsyncThunk","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fasync-thunks","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F03.async-thunks",{"title":2392,"path":2393,"stem":2394},"04. Entity Adapter: Керування нормалізованим станом","\u002Fjavascript\u002Freact\u002Fredux\u002Fredux-toolkit\u002Fentity-adapter","03.javascript\u002F04.react\u002F06.redux\u002F04.redux-toolkit\u002F04.entity-adapter",{"title":2396,"icon":92,"path":2397,"stem":2398,"children":2399,"page":59},"Advanced","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced",[2400,2404,2408],{"title":2401,"path":2402,"stem":2403},"Мемоізація та Селектори: Повний Гайд по Reselect","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Fselectors-reselect","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F01.selectors-reselect",{"title":2405,"path":2406,"stem":2407},"RTK Query: Архітектура Серверного Кешу","\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Frtk-query-intro","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F02.rtk-query-intro",{"title":2255,"path":2409,"stem":2410},"\u002Fjavascript\u002Freact\u002Fredux\u002Fadvanced\u002Farchitecture-best-practices","03.javascript\u002F04.react\u002F06.redux\u002F05.advanced\u002F03.architecture-best-practices",{"title":2412,"icon":132,"path":2413,"stem":2414,"children":2415,"page":59},"Project Kanban","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban",[2416,2420,2424,2428,2432,2436],{"title":2417,"path":2418,"stem":2419},"Проєкт: Kanban Board (Trello Clone)","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fproject-overview","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F01.project-overview",{"title":2421,"path":2422,"stem":2423},"Налаштування та Типізація","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fsetup-and-types","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F02.setup-and-types",{"title":2425,"path":2426,"stem":2427},"Board Slice: Серце Дошки","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fboard-slice","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F03.board-slice",{"title":2429,"path":2430,"stem":2431},"Логіка Drag & Drop","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Fdrag-and-drop-logic","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F04.drag-and-drop-logic",{"title":2433,"path":2434,"stem":2435},"Інтеграція з RTK Query","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Frtk-query-integration","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F05.rtk-query-integration",{"title":2437,"path":2438,"stem":2439},"Optimistic Updates","\u002Fjavascript\u002Freact\u002Fredux\u002Fproject-kanban\u002Foptimistic-updates","03.javascript\u002F04.react\u002F06.redux\u002F06.project-kanban\u002F06.optimistic-updates",{"title":2441,"icon":132,"path":2442,"stem":2443,"children":2444,"page":59},"Testing","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting","03.javascript\u002F04.react\u002F06.redux\u002F07.testing",[2445,2449,2453,2457,2461],{"title":2446,"path":2447,"stem":2448},"Тестування Redux","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Fintro-testing","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F01.intro-testing",{"title":2450,"path":2451,"stem":2452},"Тестування Reducers","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-reducers","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F02.testing-reducers",{"title":2454,"path":2455,"stem":2456},"Тестування Селекторів","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-selectors","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F03.testing-selectors",{"title":2458,"path":2459,"stem":2460},"Тестування Компонентів (Integration)","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-components","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F04.testing-components",{"title":2462,"path":2463,"stem":2464},"Тестування Async Thunks","\u002Fjavascript\u002Freact\u002Fredux\u002Ftesting\u002Ftesting-thunks","03.javascript\u002F04.react\u002F06.redux\u002F07.testing\u002F05.testing-thunks",{"title":2466,"icon":132,"path":2467,"stem":2468,"children":2469},"Ui Libraries","\u002Fjavascript\u002Freact\u002Fui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002Findex",[2470,2472,2476,2480,2484,2488,2492],{"title":2471,"path":2467,"stem":2468},"UI Бібліотеки в React",{"title":2473,"path":2474,"stem":2475},"Вступ до UI Бібліотек: Навіщо Винаходити Велосипед Двічі?","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fintroduction-to-ui-libraries","03.javascript\u002F04.react\u002F07.ui-libraries\u002F01.introduction-to-ui-libraries",{"title":2477,"path":2478,"stem":2479},"Філософія shadcn\u002Fui: \"Not a Component Library\"","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-philosophy","03.javascript\u002F04.react\u002F07.ui-libraries\u002F02.shadcn-philosophy",{"title":2481,"path":2482,"stem":2483},"Установка та Налаштування shadcn\u002Fui","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-installation","03.javascript\u002F04.react\u002F07.ui-libraries\u002F03.shadcn-installation",{"title":2485,"path":2486,"stem":2487},"Базові Компоненти shadcn\u002Fui: Фундамент Інтерфейсу","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-basics","03.javascript\u002F04.react\u002F07.ui-libraries\u002F04.shadcn-components-basics",{"title":2489,"path":2490,"stem":2491},"Компоненти Форм: Побудова Інтерактивних Form","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-forms","03.javascript\u002F04.react\u002F07.ui-libraries\u002F05.shadcn-components-forms",{"title":2493,"path":2494,"stem":2495},"Складні Компоненти: Dialog, Dropdown, Table та Command","\u002Fjavascript\u002Freact\u002Fui-libraries\u002Fshadcn-components-advanced","03.javascript\u002F04.react\u002F07.ui-libraries\u002F06.shadcn-components-advanced",{"title":2497,"icon":2498,"path":2499,"stem":2500,"children":2501,"page":59},"TypeScript","i-devicon-typescript","\u002Fjavascript\u002Ftypescript","03.javascript\u002F05.typescript",[2502,2506,2510,2514,2518,2522,2526,2530],{"title":2503,"path":2504,"stem":2505},"TypeScript: Броня для вашого коду","\u002Fjavascript\u002Ftypescript\u002Fintro-and-basic-types","03.javascript\u002F05.typescript\u002F01.intro-and-basic-types",{"title":2507,"path":2508,"stem":2509},"Майстерність Моделювання Даних: Інтерфейси та Просунуті Типи","\u002Fjavascript\u002Ftypescript\u002Finterfaces-and-advanced-types","03.javascript\u002F05.typescript\u002F02.interfaces-and-advanced-types",{"title":2511,"path":2512,"stem":2513},"Алхімія Типів: Generics та Utility Types","\u002Fjavascript\u002Ftypescript\u002Fgenerics-and-utilities","03.javascript\u002F05.typescript\u002F03.generics-and-utilities",{"title":2515,"path":2516,"stem":2517},"Архітектура та Шаблони: Класи в TypeScript","\u002Fjavascript\u002Ftypescript\u002Fclasses-and-oop","03.javascript\u002F05.typescript\u002F04.classes-and-oop",{"title":2519,"path":2520,"stem":2521},"Продакшн та Екосистема: Advanced Config & Workflow","\u002Fjavascript\u002Ftypescript\u002Fadvanced-patterns-and-config","03.javascript\u002F05.typescript\u002F05.advanced-patterns-and-config",{"title":2523,"path":2524,"stem":2525},"TypeScript у світі React","\u002Fjavascript\u002Ftypescript\u002Freact-basics","03.javascript\u002F05.typescript\u002F06.react-basics",{"title":2527,"path":2528,"stem":2529},"React + TypeScript: Продвинуті патерни","\u002Fjavascript\u002Ftypescript\u002Freact-advanced","03.javascript\u002F05.typescript\u002F07.react-advanced",{"title":2531,"path":2532,"stem":2533},"React + TypeScript: Екосистема та бібліотеки","\u002Fjavascript\u002Ftypescript\u002Freact-ecosystem","03.javascript\u002F05.typescript\u002F08.react-ecosystem",{"title":2535,"icon":2536,"path":2537,"stem":2538,"children":2539,"page":59},"Асинхронність","i-lucide-refresh-cw","\u002Fjavascript\u002Fasync-programming","03.javascript\u002F06.async-programming",[2540,2544,2548],{"title":2541,"path":2542,"stem":2543},"Event Loop: серце асинхронності в JavaScript","\u002Fjavascript\u002Fasync-programming\u002Fevent-loop-fundamentals","03.javascript\u002F06.async-programming\u002F01.event-loop-fundamentals",{"title":2545,"path":2546,"stem":2547},"Task Queue та Microtask Queue: пріоритети виконання","\u002Fjavascript\u002Fasync-programming\u002Ftask-queues","03.javascript\u002F06.async-programming\u002F02.task-queues",{"title":2549,"path":2550,"stem":2551},"Асинхронні патерни: від Callbacks до Async\u002FAwait","\u002Fjavascript\u002Fasync-programming\u002Fasync-patterns","03.javascript\u002F06.async-programming\u002F03.async-patterns",{"title":2553,"path":2554,"stem":2555},"Atomic Design","\u002Fjavascript\u002Fatomic-design","03.javascript\u002F2.atomic-design",{"title":2557,"icon":2558,"path":2559,"stem":2560,"children":2561,"page":59},"Java","i-devicon-java","\u002Fjava","04.java",[2562,2565,2568,2572,2576,2580,2584],{"title":162,"path":2563,"stem":2564},"\u002Fjava\u002Fdata-mapper-part1","04.java\u002F01.data-mapper-part1",{"title":166,"path":2566,"stem":2567},"\u002Fjava\u002Fdata-mapper-part2","04.java\u002F02.data-mapper-part2",{"title":2569,"path":2570,"stem":2571},"Service Layer: Організація бізнес-логіки","\u002Fjava\u002Fservice-layer","04.java\u002F03.service-layer",{"title":2573,"path":2574,"stem":2575},"Rich Domain Model та State Pattern","\u002Fjava\u002Frich-domain-model","04.java\u002F04.rich-domain-model",{"title":2577,"path":2578,"stem":2579},"Патерни для складної бізнес-логіки","\u002Fjava\u002Fbusiness-logic-patterns","04.java\u002F05.business-logic-patterns",{"title":2581,"path":2582,"stem":2583},"Обробка помилок та валідація","\u002Fjava\u002Ferror-handling-validation","04.java\u002F06.error-handling-validation",{"title":2585,"path":2586,"stem":2587,"children":2588,"page":59},"Проектування баз даних","\u002Fjava\u002Fpr2","04.java\u002Fpr2",[2589,2593,2597,2601,2605,2609,2613,2617,2621,2625,2629,2633,2637,2641,2645,2649,2653,2657,2661,2665,2669,2673,2677,2681,2685,2689,2693,2697,2701,2705,2709,2713,2717,2721,2725,2729,2733],{"title":2590,"path":2591,"stem":2592},"Концептуальне моделювання: Мистецтво розуміння предметної області","\u002Fjava\u002Fpr2\u002Fconceptual-modeling","04.java\u002Fpr2\u002F01.conceptual-modeling",{"title":2594,"path":2595,"stem":2596},"Логічне моделювання: Від бізнес-ідей до структур даних","\u002Fjava\u002Fpr2\u002Flogical-modeling","04.java\u002Fpr2\u002F02.logical-modeling",{"title":2598,"path":2599,"stem":2600},"Нормалізація: Гігієна даних та боротьба з аномаліями","\u002Fjava\u002Fpr2\u002Fnormalization","04.java\u002Fpr2\u002F03.normalization",{"title":2602,"path":2603,"stem":2604},"Фізична схема: Від абстракції до DDL","\u002Fjava\u002Fpr2\u002Fphysical-schema","04.java\u002Fpr2\u002F04.physical-schema",{"title":2606,"path":2607,"stem":2608},"Архітектурна класифікація таблиць","\u002Fjava\u002Fpr2\u002Ftable-classification","04.java\u002Fpr2\u002F05.table-classification",{"title":2610,"path":2611,"stem":2612},"Database Migrations: Версіонування схеми з Flyway","\u002Fjava\u002Fpr2\u002Fdatabase-migrations","04.java\u002Fpr2\u002F06.database-migrations",{"title":2614,"path":2615,"stem":2616},"А що, якби це була не реляційна БД?","\u002Fjava\u002Fpr2\u002Fbeyond-relational","04.java\u002Fpr2\u002F07.beyond-relational",{"title":2618,"path":2619,"stem":2620},"Object-Relational Impedance Mismatch: Два світи, що не хочуть дружити","\u002Fjava\u002Fpr2\u002Fimpedance-mismatch","04.java\u002Fpr2\u002F09.impedance-mismatch",{"title":2622,"path":2623,"stem":2624},"JDBC: Перший контакт із базою даних","\u002Fjava\u002Fpr2\u002Fjdbc-fundamentals","04.java\u002Fpr2\u002F10.jdbc-fundamentals",{"title":2626,"path":2627,"stem":2628},"Якість коду: Spotless, SpotBugs та SonarQube","\u002Fjava\u002Fpr2\u002F10a.code-quality","04.java\u002Fpr2\u002F10a.code-quality",{"title":2630,"path":2631,"stem":2632},"Connection Pool: Патерн Object Pool для JDBC-з'єднань","\u002Fjava\u002Fpr2\u002Fconnection-pool","04.java\u002Fpr2\u002F11.connection-pool",{"title":2634,"path":2635,"stem":2636},"Row Data Gateway: Об'єкт як обгортка рядка таблиці","\u002Fjava\u002Fpr2\u002Frow-data-gateway","04.java\u002Fpr2\u002F12.row-data-gateway",{"title":2638,"path":2639,"stem":2640},"Table Data Gateway: Фасад таблиці як архітектурний відступ","\u002Fjava\u002Fpr2\u002Ftable-data-gateway","04.java\u002Fpr2\u002F13.table-data-gateway",{"title":2642,"path":2643,"stem":2644},"Repository + Data Mapper: Правильна шарова архітектура з JDBC","\u002Fjava\u002Fpr2\u002Frepository-data-mapper","04.java\u002Fpr2\u002F14.repository-data-mapper",{"title":2646,"path":2647,"stem":2648},"Identity Map: Кешування сутностей у рамках сесії","\u002Fjava\u002Fpr2\u002Fidentity-map","04.java\u002Fpr2\u002F15.identity-map",{"title":2650,"path":2651,"stem":2652},"Unit of Work: Відстеження змін і координація JDBC-транзакцій","\u002Fjava\u002Fpr2\u002Funit-of-work","04.java\u002Fpr2\u002F16.unit-of-work",{"title":2654,"path":2655,"stem":2656},"Strategy: Замінювані SQL-стратегії для підтримки різних СУБД","\u002Fjava\u002Fpr2\u002Fstrategy-sql","04.java\u002Fpr2\u002F17.strategy-sql",{"title":2658,"path":2659,"stem":2660},"Proxy: Lazy Loading для One-To-Many колекцій","\u002Fjava\u002Fpr2\u002Fproxy-lazy-loading","04.java\u002Fpr2\u002F18.proxy-lazy-loading",{"title":2662,"path":2663,"stem":2664},"Generic Repository через Java Reflection: анотації та динамічний SQL","\u002Fjava\u002Fpr2\u002Fgeneric-repository-reflection","04.java\u002Fpr2\u002F19.generic-repository-reflection",{"title":2666,"path":2667,"stem":2668},"Specification Pattern: Композиція бізнес-правил для складних запитів","\u002Fjava\u002Fpr2\u002Fspecification-pattern","04.java\u002Fpr2\u002F20.specification-pattern",{"title":2670,"path":2671,"stem":2672},"Розширені можливості Specification Pattern: підзапити, агрегації та гібридний підхід","\u002Fjava\u002Fpr2\u002F20a.advanced-specifications","04.java\u002Fpr2\u002F20a.advanced-specifications",{"title":2674,"path":2675,"stem":2676},"Асинхронність у JDBC: Від блокуючих викликів до CompletableFuture","\u002Fjava\u002Fpr2\u002Fasynchronous-jdbc","04.java\u002Fpr2\u002F21.asynchronous-jdbc",{"title":2678,"path":2679,"stem":2680},"Інтеграційне тестування JDBC-репозиторіїв: Embedded H2 та патерн AAA","\u002Fjava\u002Fpr2\u002Fintegration-testing-h2","04.java\u002Fpr2\u002F22.integration-testing-h2",{"title":2682,"path":2683,"stem":2684},"Testcontainers: Тестування з реальною PostgreSQL у Docker-контейнерах","\u002Fjava\u002Fpr2\u002Fintegration-testing-testcontainers","04.java\u002Fpr2\u002F23.integration-testing-testcontainers",{"title":2686,"path":2687,"stem":2688},"Google Guice: Впровадження залежностей у JavaFX-проєкті","\u002Fjava\u002Fpr2\u002Fdependency-injection-guice","04.java\u002Fpr2\u002F24.dependency-injection-guice",{"title":2690,"path":2691,"stem":2692},"JavaFX: Основи побудови графічних інтерфейсів","\u002Fjava\u002Fpr2\u002Fjavafx-fundamentals","04.java\u002Fpr2\u002F25.javafx-fundamentals",{"title":2694,"path":2695,"stem":2696},"Properties та Bindings: Реактивність у JavaFX","\u002Fjava\u002Fpr2\u002Fjavafx-properties-bindings","04.java\u002Fpr2\u002F26.javafx-properties-bindings",{"title":2698,"path":2699,"stem":2700},"MVC vs MVP vs MVVM: Еволюція архітектурних патернів UI","\u002Fjava\u002Fpr2\u002Fui-architecture-patterns","04.java\u002Fpr2\u002F27.ui-architecture-patterns",{"title":2702,"path":2703,"stem":2704},"MVVM на практиці: Побудова ViewModel","\u002Fjava\u002Fpr2\u002Fmvvm-viewmodel-implementation","04.java\u002Fpr2\u002F28.mvvm-viewmodel-implementation",{"title":2706,"path":2707,"stem":2708},"View та Controller: Зв'язування з ViewModel через FXML","\u002Fjava\u002Fpr2\u002Fmvvm-view-controller","04.java\u002Fpr2\u002F29.mvvm-view-controller",{"title":2710,"path":2711,"stem":2712},"Інтеграція MVVM з Guice: Автоматична ін'єкція залежностей","\u002Fjava\u002Fpr2\u002Fmvvm-guice-integration","04.java\u002Fpr2\u002F30.mvvm-guice-integration",{"title":2714,"path":2715,"stem":2716},"Валідація та обробка помилок у MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-validation-error-handling","04.java\u002Fpr2\u002F31.mvvm-validation-error-handling",{"title":2718,"path":2719,"stem":2720},"Навігація та управління екранами у JavaFX MVVM","\u002Fjava\u002Fpr2\u002Fmvvm-navigation-screen-management","04.java\u002Fpr2\u002F32.mvvm-navigation-screen-management",{"title":2722,"path":2723,"stem":2724},"Тестування JavaFX MVVM-додатків","\u002Fjava\u002Fpr2\u002Fmvvm-testing","04.java\u002Fpr2\u002F33.mvvm-testing",{"title":2726,"path":2727,"stem":2728},"Стилізація та теми у JavaFX: CSS та User Experience","\u002Fjava\u002Fpr2\u002Fjavafx-styling-themes","04.java\u002Fpr2\u002F34.javafx-styling-themes",{"title":2730,"path":2731,"stem":2732},"AtlantaFX: Сучасні теми для JavaFX додатків","\u002Fjava\u002Fpr2\u002Fatlantafx-modern-themes","04.java\u002Fpr2\u002F35.atlantafx-modern-themes",{"title":2734,"path":2735,"stem":2736},"Пакування та розповсюдження JavaFX-додатків","\u002Fjava\u002Fpr2\u002Fjar-packaging-distribution","04.java\u002Fpr2\u002F36.jar-packaging-distribution",{"title":2738,"icon":2739,"path":2740,"stem":2741,"children":2742,"page":59},"Python","i-devicon-python","\u002Fpython","05.python",[2743,2747,2750,2754,2758,2762,2766,2770,2774,2778,2782,2786,2790,2794,2798,2859],{"title":2744,"path":2745,"stem":2746},"Модулі, Пакети та Віртуальні Середовища","\u002Fpython\u002Fmodules-packages-venv","05.python\u002F00.modules-packages-venv",{"title":71,"path":2748,"stem":2749},"\u002Fpython\u002Fclasses-objects","05.python\u002F01.classes-objects",{"title":2751,"path":2752,"stem":2753},"Інкапсуляція, Керування Доступом та Властивості","\u002Fpython\u002Fencapsulation","05.python\u002F02.encapsulation",{"title":2755,"path":2756,"stem":2757},"Наслідування, MRO та суперсила super()","\u002Fpython\u002Finheritance-mro","05.python\u002F03.inheritance-mro",{"title":2759,"path":2760,"stem":2761},"Абстракція — ABC проти Статичних Протоколів (PEP 544)","\u002Fpython\u002Fabstraction-protocols","05.python\u002F04.abstraction-protocols",{"title":2763,"path":2764,"stem":2765},"Магічні методи (Dunder) та Емуляція протоколів","\u002Fpython\u002Fdunder-methods","05.python\u002F05.dunder-methods",{"title":2767,"path":2768,"stem":2769},"Декоратори та Керування життєвим циклом методів","\u002Fpython\u002Fdecorators-static-class","05.python\u002F06.decorators-static-class",{"title":2771,"path":2772,"stem":2773},"Дескриптори — Магія доступу до атрибутів","\u002Fpython\u002Fdescriptors","05.python\u002F07.descriptors",{"title":2775,"path":2776,"stem":2777},"Метакласи — Динамічне створення класів під капотом CPython","\u002Fpython\u002Fmetaclasses","05.python\u002F08.metaclasses",{"title":2779,"path":2780,"stem":2781},"Dataclasses, NamedTuple та сучасні контейнери Python","\u002Fpython\u002Fmodern-containers","05.python\u002F09.modern-containers",{"title":2783,"path":2784,"stem":2785},"GIL та модель конкурентності CPython — фундамент перед потоками і процесами","\u002Fpython\u002Fgil-concurrency-intro","05.python\u002F11.gil-concurrency-intro",{"title":2787,"path":2788,"stem":2789},"Threading — конкурентність для I\u002FO-bound задач","\u002Fpython\u002Fthreading","05.python\u002F12.threading",{"title":2791,"path":2792,"stem":2793},"Multiprocessing — справжній паралелізм для CPU-bound задач","\u002Fpython\u002Fmultiprocessing","05.python\u002F13.multiprocessing",{"title":2795,"path":2796,"stem":2797},"asyncio — кооперативна конкурентність та event loop","\u002Fpython\u002Fasyncio","05.python\u002F14.asyncio",{"title":2799,"icon":92,"path":2800,"stem":2801,"children":2802,"page":59},"FastAPI","\u002Fpython\u002Ffastapi","05.python\u002Ffastapi",[2803,2807,2811,2815,2819,2823,2827,2831,2835,2839,2843,2847,2851,2855],{"title":2804,"path":2805,"stem":2806},"Глибокий Typing та Pydantic v2 — від анотацій до валідації","\u002Fpython\u002Ffastapi\u002Ftyping-pydantic","05.python\u002Ffastapi\u002F15.typing-pydantic",{"title":2808,"path":2809,"stem":2810},"WSGI, ASGI та Python Web-екосистема","\u002Fpython\u002Ffastapi\u002Fwsgi-asgi-ecosystem","05.python\u002Ffastapi\u002F16.wsgi-asgi-ecosystem",{"title":2812,"path":2813,"stem":2814},"FastAPI: Перший додаток, Uvicorn та OpenAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-intro","05.python\u002Ffastapi\u002F17.fastapi-intro",{"title":2816,"path":2817,"stem":2818},"Маршрутизація, параметри запитів та APIRouter","\u002Fpython\u002Ffastapi\u002Ffastapi-routing-params","05.python\u002Ffastapi\u002F18.fastapi-routing-params",{"title":2820,"path":2821,"stem":2822},"Pydantic v2 у FastAPI — схеми, валідація та серіалізація","\u002Fpython\u002Ffastapi\u002Ffastapi-pydantic-schemas","05.python\u002Ffastapi\u002F19.fastapi-pydantic-schemas",{"title":2824,"path":2825,"stem":2826},"Dependency Injection — серце архітектури FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-dependency-injection","05.python\u002Ffastapi\u002F20.fastapi-dependency-injection",{"title":2828,"path":2829,"stem":2830},"Обробка помилок, Middleware та CORS у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-errors-middleware","05.python\u002Ffastapi\u002F21.fastapi-errors-middleware",{"title":2832,"path":2833,"stem":2834},"SQLAlchemy 2.0 — ORM, Core та Async Engine","\u002Fpython\u002Ffastapi\u002Fsqlalchemy-orm","05.python\u002Ffastapi\u002F22.sqlalchemy-orm",{"title":2836,"path":2837,"stem":2838},"Alembic — міграції бази даних","\u002Fpython\u002Ffastapi\u002Falembic-migrations","05.python\u002Ffastapi\u002F23.alembic-migrations",{"title":2840,"path":2841,"stem":2842},"Repository Pattern та Clean Architecture у FastAPI","\u002Fpython\u002Ffastapi\u002Ffastapi-repository-clean-arch","05.python\u002Ffastapi\u002F24.fastapi-repository-clean-arch",{"title":2844,"path":2845,"stem":2846},"Автентифікація та авторизація — JWT, OAuth2, RBAC","\u002Fpython\u002Ffastapi\u002Ffastapi-auth-security","05.python\u002Ffastapi\u002F25.fastapi-auth-security",{"title":2848,"path":2849,"stem":2850},"Тестування FastAPI — pytest, httpx, fixtures","\u002Fpython\u002Ffastapi\u002Ffastapi-testing","05.python\u002Ffastapi\u002F26.fastapi-testing",{"title":2852,"path":2853,"stem":2854},"Async на повну — Background Tasks, WebSockets, SSE та Celery","\u002Fpython\u002Ffastapi\u002Ffastapi-async-advanced","05.python\u002Ffastapi\u002F27.fastapi-async-advanced",{"title":2856,"path":2857,"stem":2858},"Deployment — Docker, CI\u002FCD, Monitoring","\u002Fpython\u002Ffastapi\u002Ffastapi-deployment","05.python\u002Ffastapi\u002F28.fastapi-deployment",{"title":2860,"path":2861,"stem":2862},"[object Object]","\u002Fpython\u002Foop-plan","05.python\u002Foop-plan",{"title":2864,"icon":2865,"path":2866,"stem":2867,"children":2868,"page":59},"Бази даних","i-lucide-database","\u002Fdatabases","06.databases",[2869,2899,2922,2959,2988,3006,3040,3052,3061],{"title":2870,"icon":2871,"path":2872,"stem":2873,"children":2874,"page":59},"Intro","i-lucide-play","\u002Fdatabases\u002Fintro","06.databases\u002F01.intro",[2875,2879,2883,2887,2891,2895],{"title":2876,"path":2877,"stem":2878},"Введення в теорію баз даних","\u002Fdatabases\u002Fintro\u002Fintroduction-to-databases","06.databases\u002F01.intro\u002F01.introduction-to-databases",{"title":2880,"path":2881,"stem":2882},"Реляційна модель даних","\u002Fdatabases\u002Fintro\u002Frelational-model-theory","06.databases\u002F01.intro\u002F02.relational-model-theory",{"title":2884,"path":2885,"stem":2886},"ER-моделювання","\u002Fdatabases\u002Fintro\u002Fer-modeling","06.databases\u002F01.intro\u002F03.er-modeling",{"title":2888,"path":2889,"stem":2890},"Логічне проектування БД","\u002Fdatabases\u002Fintro\u002Flogical-schema","06.databases\u002F01.intro\u002F04.logical-schema",{"title":2892,"path":2893,"stem":2894},"Класифікація таблиць","\u002Fdatabases\u002Fintro\u002Ftable-classification","06.databases\u002F01.intro\u002F05.table-classification",{"title":2896,"path":2897,"stem":2898},"PlantUML для баз даних","\u002Fdatabases\u002Fintro\u002Fplantuml-diagrams","06.databases\u002F01.intro\u002F06.plantuml-diagrams",{"title":2900,"icon":2865,"path":2901,"stem":2902,"children":2903,"page":59},"MS SQL Server Start","\u002Fdatabases\u002Fms-sql-server-start","06.databases\u002F02.ms-sql-server-start",[2904,2908,2914,2918],{"title":2905,"path":2906,"stem":2907},"Типи даних у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fdata-types","06.databases\u002F02.ms-sql-server-start\u002F01.data-types",{"title":2909,"path":2910,"stem":2911,"children":2912},"Індекси у MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-indexes","06.databases\u002F02.ms-sql-server-start\u002F02.sql-indexes",[2913],{"title":2909,"path":2910,"stem":2911},{"title":2915,"path":2916,"stem":2917},"Системні бази даних MS SQL Server","\u002Fdatabases\u002Fms-sql-server-start\u002Fsystem-databases","06.databases\u002F02.ms-sql-server-start\u002F03.system-databases",{"title":2919,"path":2920,"stem":2921},"Огляд мови SQL та запитів","\u002Fdatabases\u002Fms-sql-server-start\u002Fsql-queries-overview","06.databases\u002F02.ms-sql-server-start\u002F04.sql-queries-overview",{"title":2923,"icon":2865,"path":2924,"stem":2925,"children":2926,"page":59},"SQL","\u002Fdatabases\u002Fsql","06.databases\u002F03.sql",[2927,2931,2935,2939,2943,2947,2951,2955],{"title":2928,"path":2929,"stem":2930},"Налаштування демонстраційної бази даних","\u002Fdatabases\u002Fsql\u002Fsample-database-setup","06.databases\u002F03.sql\u002F00.sample-database-setup",{"title":2932,"path":2933,"stem":2934},"DDL - Створення таблиць (CREATE TABLE)","\u002Fdatabases\u002Fsql\u002Fddl-create-table","06.databases\u002F03.sql\u002F01.ddl-create-table",{"title":2936,"path":2937,"stem":2938},"DDL - Зміна та видалення таблиць (ALTER, DROP)","\u002Fdatabases\u002Fsql\u002Fddl-alter-drop-table","06.databases\u002F03.sql\u002F02.ddl-alter-drop-table",{"title":2940,"path":2941,"stem":2942},"SELECT запити - Основи","\u002Fdatabases\u002Fsql\u002Fselect-queries-fundamentals","06.databases\u002F03.sql\u002F03.select-queries-fundamentals",{"title":2944,"path":2945,"stem":2946},"SELECT запити - Розширені можливості","\u002Fdatabases\u002Fsql\u002Fselect-queries-advanced","06.databases\u002F03.sql\u002F04.select-queries-advanced",{"title":2948,"path":2949,"stem":2950},"INSERT запити - Додавання даних","\u002Fdatabases\u002Fsql\u002Finsert-queries","06.databases\u002F03.sql\u002F05.insert-queries",{"title":2952,"path":2953,"stem":2954},"UPDATE та DELETE запити","\u002Fdatabases\u002Fsql\u002Fupdate-delete-queries","06.databases\u002F03.sql\u002F06.update-delete-queries",{"title":2956,"path":2957,"stem":2958},"Транзакції в SQL","\u002Fdatabases\u002Fsql\u002Ftransactions","06.databases\u002F03.sql\u002F07.transactions",{"title":2960,"icon":2865,"path":2961,"stem":2962,"children":2963,"page":59},"Multi Table Databases","\u002Fdatabases\u002Fmulti-table-databases","06.databases\u002F04.multi-table-databases",[2964,2968,2972,2976,2980,2984],{"title":2965,"path":2966,"stem":2967},"Зв'язки та нормалізація БД","\u002Fdatabases\u002Fmulti-table-databases\u002Frelationships-and-normalization","06.databases\u002F04.multi-table-databases\u002F00.relationships-and-normalization",{"title":2969,"path":2970,"stem":2971},"INNER JOIN - З'єднання таблиць","\u002Fdatabases\u002Fmulti-table-databases\u002Finner-join","06.databases\u002F04.multi-table-databases\u002F01.inner-join",{"title":2973,"path":2974,"stem":2975},"OUTER JOINs - LEFT, RIGHT, FULL","\u002Fdatabases\u002Fmulti-table-databases\u002Fouter-joins","06.databases\u002F04.multi-table-databases\u002F02.outer-joins",{"title":2977,"path":2978,"stem":2979},"CROSS та SELF JOINs","\u002Fdatabases\u002Fmulti-table-databases\u002Fcross-self-joins","06.databases\u002F04.multi-table-databases\u002F03.cross-self-joins",{"title":2981,"path":2982,"stem":2983},"Підзапити (Subqueries)","\u002Fdatabases\u002Fmulti-table-databases\u002Fsubqueries","06.databases\u002F04.multi-table-databases\u002F04.subqueries",{"title":2985,"path":2986,"stem":2987},"Агрегації з JOIN","\u002Fdatabases\u002Fmulti-table-databases\u002Faggregations-with-joins","06.databases\u002F04.multi-table-databases\u002F05.aggregations-with-joins",{"title":2989,"icon":2990,"path":2991,"stem":2992,"children":2993,"page":59},"Aggregate Functions","i-lucide-calculator","\u002Fdatabases\u002Faggregate-functions","06.databases\u002F05.aggregate-functions",[2994,2998,3002],{"title":2995,"path":2996,"stem":2997},"Функції агрегування в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fintroduction-aggregate-functions","06.databases\u002F05.aggregate-functions\u002F01.introduction-aggregate-functions",{"title":2999,"path":3000,"stem":3001},"Групування даних в MS SQL Server","\u002Fdatabases\u002Faggregate-functions\u002Fgrouping-data","06.databases\u002F05.aggregate-functions\u002F02.grouping-data",{"title":3003,"path":3004,"stem":3005},"Підзапити з агрегатними функціями","\u002Fdatabases\u002Faggregate-functions\u002Fsubqueries-aggregates","06.databases\u002F05.aggregate-functions\u002F03.subqueries-aggregates",{"title":3007,"icon":3008,"path":3009,"stem":3010,"children":3011,"page":59},"Тригери та зберігаємі процедури","i-lucide-database-zap","\u002Fdatabases\u002Ftriggers-stored-procedures","06.databases\u002F07.triggers-stored-procedures",[3012,3016,3020,3024,3028,3032,3036],{"title":3013,"path":3014,"stem":3015},"DML-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fdml-triggers","06.databases\u002F07.triggers-stored-procedures\u002F01.dml-triggers",{"title":3017,"path":3018,"stem":3019},"DDL-тригери","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fddl-triggers","06.databases\u002F07.triggers-stored-procedures\u002F02.ddl-triggers",{"title":3021,"path":3022,"stem":3023},"Transact-SQL розширення","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransact-sql-extensions","06.databases\u002F07.triggers-stored-procedures\u002F03.transact-sql-extensions",{"title":3025,"path":3026,"stem":3027},"Транзакції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Ftransactions","06.databases\u002F07.triggers-stored-procedures\u002F04.transactions",{"title":3029,"path":3030,"stem":3031},"Зберігаємі процедури","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fstored-procedures","06.databases\u002F07.triggers-stored-procedures\u002F05.stored-procedures",{"title":3033,"path":3034,"stem":3035},"Користувацькі функції","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fuser-defined-functions","06.databases\u002F07.triggers-stored-procedures\u002F06.user-defined-functions",{"title":3037,"path":3038,"stem":3039},"Безпека баз даних","\u002Fdatabases\u002Ftriggers-stored-procedures\u002Fsecurity","06.databases\u002F07.triggers-stored-procedures\u002F08.security",{"title":3037,"icon":793,"path":3041,"stem":3042,"children":3043,"page":59},"\u002Fdatabases\u002Fsecurity","06.databases\u002F08.security",[3044,3048],{"title":3045,"path":3046,"stem":3047},"Вступ до безпеки баз даних","\u002Fdatabases\u002Fsecurity\u002Fintroduction","06.databases\u002F08.security\u002F01.introduction",{"title":3049,"path":3050,"stem":3051},"Системні представлення та метадані","\u002Fdatabases\u002Fsecurity\u002Fsystem-views","06.databases\u002F08.security\u002F02.system-views",{"title":3053,"icon":3054,"path":3055,"stem":3056,"children":3057,"page":59},"Резервне копіювання та відновлення","i-lucide-database-backup","\u002Fdatabases\u002Fbackup-recovery","06.databases\u002F09.backup-recovery",[3058],{"title":3053,"path":3059,"stem":3060},"\u002Fdatabases\u002Fbackup-recovery\u002Fbackup-restore","06.databases\u002F09.backup-recovery\u002F01.backup-restore",{"title":3062,"icon":3063,"path":3064,"stem":3065,"children":3066,"page":59},"Повнотекстовий пошук","i-lucide-search","\u002Fdatabases\u002Ffull-text-search","06.databases\u002F10.full-text-search",[3067],{"title":3062,"path":3068,"stem":3069},"\u002Fdatabases\u002Ffull-text-search\u002Ffull-text-search","06.databases\u002F10.full-text-search\u002F01.full-text-search",{"title":3071,"icon":3072,"path":3073,"stem":3074,"children":3075,"page":59},"Tools","i-lucide-wrench","\u002Ftools","07.tools",[3076,3152],{"title":3077,"icon":3078,"path":3079,"stem":3080,"children":3081},"Docker","i-simple-icons-docker","\u002Ftools\u002Fdocker","07.tools\u002F01.docker\u002Findex",[3082,3084,3088,3092,3096,3100,3104,3108,3112,3116,3120,3124,3128,3132,3136,3140,3144,3148],{"title":3083,"path":3079,"stem":3080},"Docker: від нуля до production",{"title":3085,"path":3086,"stem":3087},"Контейнеризація — від проблеми до рішення","\u002Ftools\u002Fdocker\u002Fcontainerization-concept","07.tools\u002F01.docker\u002F01.containerization-concept",{"title":3089,"path":3090,"stem":3091},"Docker — що це і навіщо?","\u002Ftools\u002Fdocker\u002Fdocker-what-and-why","07.tools\u002F01.docker\u002F02.docker-what-and-why",{"title":3093,"path":3094,"stem":3095},"Архітектура Docker Engine","\u002Ftools\u002Fdocker\u002Fdocker-architecture","07.tools\u002F01.docker\u002F03.docker-architecture",{"title":3097,"path":3098,"stem":3099},"Встановлення Docker","\u002Ftools\u002Fdocker\u002Finstallation","07.tools\u002F01.docker\u002F04.installation",{"title":3101,"path":3102,"stem":3103},"Перший контейнер — docker run","\u002Ftools\u002Fdocker\u002Ffirst-container","07.tools\u002F01.docker\u002F05.first-container",{"title":3105,"path":3106,"stem":3107},"Життєвий цикл контейнера","\u002Ftools\u002Fdocker\u002Fcontainer-lifecycle","07.tools\u002F01.docker\u002F06.container-lifecycle",{"title":3109,"path":3110,"stem":3111},"Docker Images — фундаментальні концепції","\u002Ftools\u002Fdocker\u002Fdocker-images-fundamentals","07.tools\u002F01.docker\u002F07.docker-images-fundamentals",{"title":3113,"path":3114,"stem":3115},"Dockerfile — основи","\u002Ftools\u002Fdocker\u002Fdockerfile-basics","07.tools\u002F01.docker\u002F08.dockerfile-basics",{"title":3117,"path":3118,"stem":3119},"Dockerfile — просунуті техніки","\u002Ftools\u002Fdocker\u002Fdockerfile-advanced","07.tools\u002F01.docker\u002F09.dockerfile-advanced",{"title":3121,"path":3122,"stem":3123},"Build Context та кешування шарів","\u002Ftools\u002Fdocker\u002Fbuild-context-and-cache","07.tools\u002F01.docker\u002F10.build-context-and-cache",{"title":3125,"path":3126,"stem":3127},"Реєстри Docker-образів","\u002Ftools\u002Fdocker\u002Fimage-registries","07.tools\u002F01.docker\u002F11.image-registries",{"title":3129,"path":3130,"stem":3131},"Контейнеризація .NET додатків","\u002Ftools\u002Fdocker\u002Fdotnet-containerization","07.tools\u002F01.docker\u002F12.dotnet-containerization",{"title":3133,"path":3134,"stem":3135},"Томи та збереження даних","\u002Ftools\u002Fdocker\u002Fvolumes-and-data","07.tools\u002F01.docker\u002F13.volumes-and-data",{"title":3137,"path":3138,"stem":3139},"Основи мережі в Docker","\u002Ftools\u002Fdocker\u002Fnetworking-basics","07.tools\u002F01.docker\u002F14.networking-basics",{"title":3141,"path":3142,"stem":3143},"Змінні оточення та конфігурація","\u002Ftools\u002Fdocker\u002Fenvironment-and-configuration","07.tools\u002F01.docker\u002F15.environment-and-configuration",{"title":3145,"path":3146,"stem":3147},"Docker Compose — оркестрація контейнерів","\u002Ftools\u002Fdocker\u002Fdocker-compose-basics","07.tools\u002F01.docker\u002F16.docker-compose-basics",{"title":3149,"path":3150,"stem":3151},"Docker Compose — Multi-Service застосунки","\u002Ftools\u002Fdocker\u002Fcompose-multi-service","07.tools\u002F01.docker\u002F17.compose-multi-service",{"title":3153,"icon":3154,"path":3155,"stem":3156,"children":3157},"Kubernetes","simple-icons:kubernetes","\u002Ftools\u002Fkubernetes","07.tools\u002F02.kubernetes\u002Findex",[3158,3160,3164,3168,3172,3176,3180,3184,3188],{"title":3159,"path":3155,"stem":3156},"Kubernetes: від розробки до production",{"title":3161,"path":3162,"stem":3163},"Kubernetes — коли Docker Compose більше не вистачає","\u002Ftools\u002Fkubernetes\u002Fwhy-kubernetes","07.tools\u002F02.kubernetes\u002F01.why-kubernetes",{"title":3165,"path":3166,"stem":3167},"Архітектура Kubernetes — анатомія кластера","\u002Ftools\u002Fkubernetes\u002Fkubernetes-architecture","07.tools\u002F02.kubernetes\u002F02.kubernetes-architecture",{"title":3169,"path":3170,"stem":3171},"Локальне середовище — minikube, kind та k3s","\u002Ftools\u002Fkubernetes\u002Flocal-environment","07.tools\u002F02.kubernetes\u002F03.local-environment",{"title":3173,"path":3174,"stem":3175},"Pod — атомарна одиниця Kubernetes","\u002Ftools\u002Fkubernetes\u002Fpods-and-containers","07.tools\u002F02.kubernetes\u002F04.pods-and-containers",{"title":3177,"path":3178,"stem":3179},"Патерни використання Pod","\u002Ftools\u002Fkubernetes\u002Fpod-patterns","07.tools\u002F02.kubernetes\u002F05.pod-patterns",{"title":3181,"path":3182,"stem":3183},"Deployment — декларативне управління Pod","\u002Ftools\u002Fkubernetes\u002Fdeployment-basics","07.tools\u002F02.kubernetes\u002F06.deployment-basics",{"title":3185,"path":3186,"stem":3187},"Rolling Updates та управління життєвим циклом Deployment","\u002Ftools\u002Fkubernetes\u002Fdeployment-rolling-updates","07.tools\u002F02.kubernetes\u002F07.deployment-rolling-updates",{"title":3189,"path":3190,"stem":3191},"Service — мережева абстракція для Pod","\u002Ftools\u002Fkubernetes\u002Fservices-networking","07.tools\u002F02.kubernetes\u002F08.services-networking",{"title":3193,"icon":3194,"path":3195,"stem":3196,"children":3197,"page":59},"Software Engineering","i-lucide-code-2","\u002Fsoftware-engineering","09.software-engineering",[3198,3202,3206,3210,3214,3218,3222,3226,3230,3234,3238],{"title":3199,"path":3200,"stem":3201},"1. Аналіз предметної області. Експертні знання та складність","\u002Fsoftware-engineering\u002Fintro-subdomains","09.software-engineering\u002F01.intro-subdomains",{"title":3203,"path":3204,"stem":3205},"2. Обмежені контексти. Інтеграція обмежених контекстів","\u002Fsoftware-engineering\u002Fintegrating-limited-contexts","09.software-engineering\u002F02.integrating-limited-contexts",{"title":3207,"path":3208,"stem":3209},"3. Реалізація простої бізнес-логіки","\u002Fsoftware-engineering\u002Fsimple","09.software-engineering\u002F03.simple",{"title":3211,"path":3212,"stem":3213},"4. Опрацювання складної бізнес-логіки","\u002Fsoftware-engineering\u002Fcomplex-business-logic","09.software-engineering\u002F04.complex-business-logic",{"title":3215,"path":3216,"stem":3217},"5. Моделювання фактора часу. Подієво-орієнтована архітектура.","\u002Fsoftware-engineering\u002Fmodelling-the-time-factor","09.software-engineering\u002F05.modelling-the-time-factor",{"title":3219,"path":3220,"stem":3221},"6. Архітектурні патерни","\u002Fsoftware-engineering\u002Farchitectural-patterns","09.software-engineering\u002F06.architectural-patterns",{"title":3223,"path":3224,"stem":3225},"Паттерни взаємодії","\u002Fsoftware-engineering\u002Fpatterns-of-interaction","09.software-engineering\u002F07.patterns-of-interaction",{"title":3227,"path":3228,"stem":3229},"Евристика проєктування","\u002Fsoftware-engineering\u002Fdesign-heuristics","09.software-engineering\u002F08.design-heuristics",{"title":3231,"path":3232,"stem":3233},"Еволюція проєктних рішень","\u002Fsoftware-engineering\u002Fevolution-of-design-solutions","09.software-engineering\u002F09.evolution-of-design-solutions",{"title":3235,"path":3236,"stem":3237},"EventStorming","\u002Fsoftware-engineering\u002Feventstorming","09.software-engineering\u002F10.eventstorming",{"title":3239,"path":3240,"stem":3241},"DDD на практиці","\u002Fsoftware-engineering\u002Fddd-in-practice","09.software-engineering\u002F11.ddd-in-practice",{"title":3243,"icon":943,"path":3244,"stem":3245,"children":3246,"page":59},"DDD","\u002Fddd","10.ddd",[3247,3251,3255,3259,3263,3267,3271,3275,3279,3283,3287,3291,3295],{"title":3248,"path":3249,"stem":3250},"Аналіз предметної області","\u002Fddd\u002Fdomain-analysis","10.ddd\u002F01.domain-analysis",{"title":3252,"path":3253,"stem":3254},"Експертні знання про предметну область","\u002Fddd\u002Fdomain-expert-knowledge","10.ddd\u002F02.domain-expert-knowledge",{"title":3256,"path":3257,"stem":3258},"Як осмислити складність предметної області","\u002Fddd\u002Fmanaging-domain-complexity","10.ddd\u002F03.managing-domain-complexity",{"title":3260,"path":3261,"stem":3262},"Інтеграція обмежених контекстів","\u002Fddd\u002Fbounded-context-integration","10.ddd\u002F04.bounded-context-integration",{"title":3264,"path":3265,"stem":3266},"Реалізація простої бізнес-логіки","\u002Fddd\u002Fsimple-business-logic","10.ddd\u002F05.simple-business-logic",{"title":3268,"path":3269,"stem":3270},"Обробка складної бізнес-логіки","\u002Fddd\u002Fcomplex-business-logic","10.ddd\u002F06.complex-business-logic",{"title":3272,"path":3273,"stem":3274},"Моделювання фактора часу","\u002Fddd\u002Ftime-modeling","10.ddd\u002F07.time-modeling",{"title":3276,"path":3277,"stem":3278},"Глава 8. Архітектурні Патерни","\u002Fddd\u002Farchitectural-patterns","10.ddd\u002F08.architectural-patterns",{"title":3280,"path":3281,"stem":3282},"Глава 9. Патерни Взаємодії","\u002Fddd\u002Finteraction-patterns","10.ddd\u002F09.interaction-patterns",{"title":3284,"path":3285,"stem":3286},"Глава 10. Проектні Евристики","\u002Fddd\u002Fdesign-heuristics","10.ddd\u002F10.design-heuristics",{"title":3288,"path":3289,"stem":3290},"Глава 11. Еволюція Проектних Рішень","\u002Fddd\u002Fevolution-of-design-decisions","10.ddd\u002F11.evolution-of-design-decisions",{"title":3292,"path":3293,"stem":3294},"Глава 12. EventStorming","\u002Fddd\u002Fevent-storming","10.ddd\u002F12.event-storming",{"title":3296,"path":3297,"stem":3298},"Глава 13. DDD на Практиці","\u002Fddd\u002Fddd-in-practice","10.ddd\u002F13.ddd-in-practice",{"title":3300,"icon":3301,"path":3302,"stem":3303,"children":3304,"page":59},"Media Streaming","i-lucide-video","\u002Fmedia-streaming","11.media-streaming",[3305,3309,3313,3317,3321,3325,3329],{"title":3306,"path":3307,"stem":3308},"01. Магія Стрімінгу: Що відбувається, коли ви натискаєте \"Play\"","\u002Fmedia-streaming\u002Fintroduction","11.media-streaming\u002F01.introduction",{"title":3310,"path":3311,"stem":3312},"02. Анатомія Медіа: Кодеки, Контейнери та Стиснення","\u002Fmedia-streaming\u002Faudio-video-anatomy","11.media-streaming\u002F02.audio-video-anatomy",{"title":3314,"path":3315,"stem":3316},"03. The Gym: FFmpeg Deep Dive","\u002Fmedia-streaming\u002Fffmpeg-gym","11.media-streaming\u002F03.ffmpeg-gym",{"title":3318,"path":3319,"stem":3320},"04. HLS Protocol: HTTP Live Streaming у Деталях","\u002Fmedia-streaming\u002Fhls-protocol","11.media-streaming\u002F04.hls-protocol",{"title":3322,"path":3323,"stem":3324},"05. DASH Protocol: Відкритий Стандарт","\u002Fmedia-streaming\u002Fdash-protocol","11.media-streaming\u002F05.dash-protocol",{"title":3326,"path":3327,"stem":3328},"06. Масштабування: CDN та Adaptive Bitrate","\u002Fmedia-streaming\u002Fcdn-and-adaptive-bitrate","11.media-streaming\u002F06.cdn-and-adaptive-bitrate",{"title":3330,"path":3331,"stem":3332},"07. Війна із Затримкою (Latency)","\u002Fmedia-streaming\u002Frealtime-latency","11.media-streaming\u002F07.realtime-latency",{"title":3334,"icon":3335,"path":3336,"stem":3337,"children":3338,"page":59},"HTML & CSS","i-devicon-html5","\u002Fhtml-css","12.html-css",[3339,3343,3347,3351,3355,3359,3363,3367,3371,3375,3379,3383,3387,3391,3395,3399,3403,3407,3411,3415,3419,3423,3427,3431,3435,3439,3443,3447,3451,3455],{"title":3340,"path":3341,"stem":3342},"Вступ до HTML. Структура документа","\u002Fhtml-css\u002Fintro-html-structure","12.html-css\u002F01.intro-html-structure",{"title":3344,"path":3345,"stem":3346},"Форматування тексту в HTML","\u002Fhtml-css\u002Fhtml-text-formatting","12.html-css\u002F02.html-text-formatting",{"title":3348,"path":3349,"stem":3350},"Посилання та зображення в HTML","\u002Fhtml-css\u002Fhtml-links-images","12.html-css\u002F03.html-links-images",{"title":3352,"path":3353,"stem":3354},"Списки та таблиці в HTML","\u002Fhtml-css\u002Fhtml-lists-tables","12.html-css\u002F04.html-lists-tables",{"title":3356,"path":3357,"stem":3358},"Форми в HTML","\u002Fhtml-css\u002Fhtml-forms","12.html-css\u002F05.html-forms",{"title":3360,"path":3361,"stem":3362},"Семантичні елементи HTML5","\u002Fhtml-css\u002Fhtml-semantic-elements","12.html-css\u002F06.html-semantic-elements",{"title":3364,"path":3365,"stem":3366},"Мультимедіа та розширені елементи HTML","\u002Fhtml-css\u002Fhtml-multimedia-advanced","12.html-css\u002F07.html-multimedia-advanced",{"title":3368,"path":3369,"stem":3370},"Мікророзмітка та SEO в HTML","\u002Fhtml-css\u002Fhtml-microdata-seo","12.html-css\u002F08.html-microdata-seo",{"title":3372,"path":3373,"stem":3374},"Вступ до CSS. Селектори та специфічність","\u002Fhtml-css\u002Fcss-intro-selectors","12.html-css\u002F09.css-intro-selectors",{"title":3376,"path":3377,"stem":3378},"Блокова модель CSS. Відступи. Box Sizing","\u002Fhtml-css\u002Fcss-box-model","12.html-css\u002F10.css-box-model",{"title":3380,"path":3381,"stem":3382},"Розміри у CSS: повний довідник одиниць і ключових слів","\u002Fhtml-css\u002F10a.css-sizing","12.html-css\u002F10a.css-sizing",{"title":3384,"path":3385,"stem":3386},"Типографіка в CSS. Шрифти та текст","\u002Fhtml-css\u002Fcss-typography","12.html-css\u002F11.css-typography",{"title":3388,"path":3389,"stem":3390},"Кольори та фони в CSS","\u002Fhtml-css\u002Fcss-colors-backgrounds","12.html-css\u002F12.css-colors-backgrounds",{"title":3392,"path":3393,"stem":3394},"Тіні та фільтри в CSS","\u002Fhtml-css\u002F12b.css-shadows-filters","12.html-css\u002F12b.css-shadows-filters",{"title":3396,"path":3397,"stem":3398},"CSS Flexbox: Фундамент гнучких макетів","\u002Fhtml-css\u002Fcss-flexbox-fundamentals","12.html-css\u002F13.css-flexbox-fundamentals",{"title":3400,"path":3401,"stem":3402},"CSS Flexbox: Вирівнювання та Позиціонування","\u002Fhtml-css\u002Fcss-flexbox-alignment-sizing-and-patterns","12.html-css\u002F14.css-flexbox-alignment-sizing-and-patterns",{"title":3404,"path":3405,"stem":3406},"CSS Grid. Двовимірний макет. Частина 1","\u002Fhtml-css\u002Fcss-layout-grid","12.html-css\u002F15.css-layout-grid",{"title":3408,"path":3409,"stem":3410},"CSS Grid. Двовимірний макет. Частина 2","\u002Fhtml-css\u002Fcss-layout-grid-advanced","12.html-css\u002F16.css-layout-grid-advanced",{"title":3412,"path":3413,"stem":3414},"Позиціонування в CSS. Z-index. Stacking Context","\u002Fhtml-css\u002Fcss-positioning","12.html-css\u002F17.css-positioning",{"title":3416,"path":3417,"stem":3418},"CSS Анімації та Переходи","\u002Fhtml-css\u002Fcss-animations-transitions","12.html-css\u002F18.css-animations-transitions",{"title":3420,"path":3421,"stem":3422},"Адаптивний дизайн. Media Queries. Частина 1","\u002Fhtml-css\u002Fcss-responsive-media-queries","12.html-css\u002F19.css-responsive-media-queries",{"title":3424,"path":3425,"stem":3426},"Адаптивний дизайн. Частина 2: clamp(), Container Queries, @layer","\u002Fhtml-css\u002Fcss-responsive-advanced","12.html-css\u002F20.css-responsive-advanced",{"title":3428,"path":3429,"stem":3430},"CSS Custom Properties. Методології. Сучасний CSS","\u002Fhtml-css\u002Fcss-variables-methodologies","12.html-css\u002F21.css-variables-methodologies",{"title":3432,"path":3433,"stem":3434},"Сучасний CSS 2023–2025: Нові можливості","\u002Fhtml-css\u002Fcss-modern-features","12.html-css\u002F22.css-modern-features",{"title":3436,"path":3437,"stem":3438},"CSS Nesting, @layer, @scope та @property: нативний препроцесор","\u002Fhtml-css\u002F22a.css-nesting-modern-syntax","12.html-css\u002F22a.css-nesting-modern-syntax",{"title":3440,"path":3441,"stem":3442},"CSS для форм та інтерактивних станів","\u002Fhtml-css\u002Fcss-forms-interactive-states","12.html-css\u002F23.css-forms-interactive-states",{"title":3444,"path":3445,"stem":3446},"Доступність у CSS (CSS Accessibility)","\u002Fhtml-css\u002Fcss-accessibility","12.html-css\u002F24.css-accessibility",{"title":3448,"path":3449,"stem":3450},"CSS-функції та сучасні sizing primitives","\u002Fhtml-css\u002Fcss-functions-sizing","12.html-css\u002F25.css-functions-sizing",{"title":3452,"path":3453,"stem":3454},"Rendering Pipeline і CSS Performance","\u002Fhtml-css\u002Fcss-rendering-performance","12.html-css\u002F26.css-rendering-performance",{"title":3456,"path":3457,"stem":3458},"CSS Best Practices: типові ситуації та правильні рішення","\u002Fhtml-css\u002Fcss-best-practices","12.html-css\u002F27.css-best-practices",{"title":3460,"path":3461,"stem":3462,"children":3463,"page":59},"AWS","\u002Faws","13.aws",[3464,3468,3472,3476,3480,3484,3488,3492,3496,3500,3504,3508,3512,3516,3520,3524,3528,3532],{"title":3465,"path":3466,"stem":3467},"Реєстрація AWS акаунту та студентські програми","\u002Faws\u002Faccount-registration","13.aws\u002F00.account-registration",{"title":3469,"path":3470,"stem":3471},"Вступ до хмарних обчислень та AWS","\u002Faws\u002Fintroduction-to-cloud","13.aws\u002F01.introduction-to-cloud",{"title":3473,"path":3474,"stem":3475},"AWS IAM — Identity and Access Management","\u002Faws\u002Fiam","13.aws\u002F02.iam",{"title":3477,"path":3478,"stem":3479},"AWS IAM CLI — Довідник команд","\u002Faws\u002F02a.iam-doc","13.aws\u002F02a.iam-doc",{"title":3481,"path":3482,"stem":3483},"Docker та контейнеризація в AWS — ECR, ECS та Fargate","\u002Faws\u002Fdocker-ecs","13.aws\u002F03.docker-ecs",{"title":3485,"path":3486,"stem":3487},"AWS ECR \u002F ECS CLI — Довідник команд","\u002Faws\u002F03a.docker-ecs-doc","13.aws\u002F03a.docker-ecs-doc",{"title":3489,"path":3490,"stem":3491},"Amazon EC2 — Elastic Compute Cloud","\u002Faws\u002Fec2","13.aws\u002F04.ec2",{"title":3493,"path":3494,"stem":3495},"AWS EC2 CLI — Довідник команд","\u002Faws\u002F04a.ec2-doc","13.aws\u002F04a.ec2-doc",{"title":3497,"path":3498,"stem":3499},"Elastic Load Balancing та Auto Scaling","\u002Faws\u002Falb-asg","13.aws\u002F05.alb-asg",{"title":3501,"path":3502,"stem":3503},"Amazon S3 — Simple Storage Service","\u002Faws\u002Fs3","13.aws\u002F06.s3",{"title":3505,"path":3506,"stem":3507},"Amazon CloudFront — Content Delivery Network","\u002Faws\u002Fcloudfront","13.aws\u002F07.cloudfront",{"title":3509,"path":3510,"stem":3511},"Amazon RDS — Relational Database Service","\u002Faws\u002Frds","13.aws\u002F08.rds",{"title":3513,"path":3514,"stem":3515},"Amazon DynamoDB — NoSQL Database","\u002Faws\u002Fdynamodb","13.aws\u002F09.dynamodb",{"title":3517,"path":3518,"stem":3519},"AWS Lambda та Serverless Compute","\u002Faws\u002Flambda","13.aws\u002F10.lambda",{"title":3521,"path":3522,"stem":3523},"Amazon Bedrock - Foundation Models, RAG та Agents","\u002Faws\u002Fbedrock","13.aws\u002F22.bedrock",{"title":3525,"path":3526,"stem":3527},"Amazon Rekognition - Комп'ютерний зір","\u002Faws\u002Frekognition","13.aws\u002F23.rekognition",{"title":3529,"path":3530,"stem":3531},"Amazon Textract - Інтелектуальний аналіз документів","\u002Faws\u002Ftextract","13.aws\u002F24.textract",{"title":3533,"path":3534,"stem":3535},"Amazon Polly, Transcribe, Comprehend та Translate","\u002Faws\u002Faudio-nlp-services","13.aws\u002F25.audio-nlp-services",{"title":3537,"path":3538,"stem":3539,"children":3540,"page":59},"Ai Development","\u002Fai-development","14.ai-development",[3541],{"title":3542,"path":3543,"stem":3544,"children":3545,"page":59},"Foundations","\u002Fai-development\u002Ffoundations","14.ai-development\u002F00.foundations",[3546],{"title":3547,"path":3548,"stem":3549},"Модуль 0.1. Що таке Large Language Model (LLM)","\u002Fai-development\u002Ffoundations\u002Fwhat-is-llm","14.ai-development\u002F00.foundations\u002F01.what-is-llm",{"title":3551,"path":3552,"stem":3553,"children":3554,"page":59},"React Native","\u002Freact-native","15.react-native",[3555,3576],{"title":3556,"path":3557,"stem":3558,"children":3559,"page":59},"Version1","\u002Freact-native\u002Fversion1","15.react-native\u002Fversion1",[3560,3564,3568,3572],{"title":3561,"path":3562,"stem":3563},"Що таке React Native","\u002Freact-native\u002Fversion1\u002Fwhat-is-react-native","15.react-native\u002Fversion1\u002F01.what-is-react-native",{"title":3565,"path":3566,"stem":3567},"Як влаштований React Native «під капотом»","\u002Freact-native\u002Fversion1\u002Freact-native-architecture","15.react-native\u002Fversion1\u002F02.react-native-architecture",{"title":3569,"path":3570,"stem":3571},"Від React до React Native: ключові відмінності","\u002Freact-native\u002Fversion1\u002Freact-native-vs-react","15.react-native\u002Fversion1\u002F03.react-native-vs-react",{"title":3573,"path":3574,"stem":3575},"View та Text — фундаментальні будівельні блоки","\u002Freact-native\u002Fversion1\u002Fview-and-text","15.react-native\u002Fversion1\u002F04.view-and-text",{"title":3577,"path":3578,"stem":3579,"children":3580,"page":59},"Version2","\u002Freact-native\u002Fversion2","15.react-native\u002Fversion2",[3581,3585,3589,3593,3597,3601,3605,3609,3613,3617,3621,3625,3629,3633,3637,3641,3645,3649,3653,3657,3661,3665,3669,3673,3677,3681,3685],{"title":3582,"path":3583,"stem":3584},"React Native — навіщо він потрібен","\u002Freact-native\u002Fversion2\u002Fwhy-react-native","15.react-native\u002Fversion2\u002F01.why-react-native",{"title":3586,"path":3587,"stem":3588},"Налаштування середовища розробки","\u002Freact-native\u002Fversion2\u002Fenvironment-setup","15.react-native\u002Fversion2\u002F02.environment-setup",{"title":3590,"path":3591,"stem":3592},"Expo і класичний React Native — два шляхи одного фреймворку","\u002Freact-native\u002Fversion2\u002Fexpo-vs-cli-landscape","15.react-native\u002Fversion2\u002F03.expo-vs-cli-landscape",{"title":3594,"path":3595,"stem":3596},"Середовище Expo — перший запуск","\u002Freact-native\u002Fversion2\u002Fexpo-setup-and-tooling","15.react-native\u002Fversion2\u002F04.expo-setup-and-tooling",{"title":3598,"path":3599,"stem":3600},"Структура проєкту та перші UI-примітиви","\u002Freact-native\u002Fversion2\u002Fproject-structure-and-conventions","15.react-native\u002Fversion2\u002F05.project-structure-and-conventions",{"title":3602,"path":3603,"stem":3604},"Базові компоненти React Native","\u002Freact-native\u002Fversion2\u002Fcore-components","15.react-native\u002Fversion2\u002F06.core-components",{"title":3606,"path":3607,"stem":3608},"Flexbox і layout у React Native","\u002Freact-native\u002Fversion2\u002Fflexbox-and-layout","15.react-native\u002Fversion2\u002F07.flexbox-and-layout",{"title":3610,"path":3611,"stem":3612},"StyleSheet і теми (light \u002F dark)","\u002Freact-native\u002Fversion2\u002Fstylesheet-and-theming","15.react-native\u002Fversion2\u002F08.stylesheet-and-theming",{"title":3614,"path":3615,"stem":3616},"Списки та віртуалізація","\u002Freact-native\u002Fversion2\u002Flists-and-virtualization","15.react-native\u002Fversion2\u002F09.lists-and-virtualization",{"title":3618,"path":3619,"stem":3620},"Форми, ввід і валідація","\u002Freact-native\u002Fversion2\u002Fforms-input-validation","15.react-native\u002Fversion2\u002F10.forms-input-validation",{"title":3622,"path":3623,"stem":3624},"Основи Expo Router","\u002Freact-native\u002Fversion2\u002Fexpo-router-basics","15.react-native\u002Fversion2\u002F11.expo-router-basics",{"title":3626,"path":3627,"stem":3628},"Вкладені навігатори та модалки","\u002Freact-native\u002Fversion2\u002Fnested-navigators-and-modals","15.react-native\u002Fversion2\u002F12.nested-navigators-and-modals",{"title":3630,"path":3631,"stem":3632},"Deep linking і параметри маршрутів","\u002Freact-native\u002Fversion2\u002Fdeep-linking-and-params","15.react-native\u002Fversion2\u002F13.deep-linking-and-params",{"title":3634,"path":3635,"stem":3636},"Робота з мережею та життєвий цикл застосунку","\u002Freact-native\u002Fversion2\u002Fnetworking-and-app-lifecycle","15.react-native\u002Fversion2\u002F14.networking-and-app-lifecycle",{"title":3638,"path":3639,"stem":3640},"Redux Toolkit на мобільних платформах","\u002Freact-native\u002Fversion2\u002Fredux-toolkit-on-mobile","15.react-native\u002Fversion2\u002F15.redux-toolkit-on-mobile",{"title":3642,"path":3643,"stem":3644},"RTK Query на мобільних платформах","\u002Freact-native\u002Fversion2\u002Frtk-query-mobile","15.react-native\u002Fversion2\u002F16.rtk-query-mobile",{"title":3646,"path":3647,"stem":3648},"Автентифікація та Безпечне Зберігання","\u002Freact-native\u002Fversion2\u002Fauth-secure-storage","15.react-native\u002Fversion2\u002F18.auth-secure-storage",{"title":3650,"path":3651,"stem":3652},"Локальне сховище — AsyncStorage, MMKV, SQLite","\u002Freact-native\u002Fversion2\u002Flocal-storage-mmkv-sqlite","15.react-native\u002Fversion2\u002F19.local-storage-mmkv-sqlite",{"title":3654,"path":3655,"stem":3656},"Офлайн-First і синхронізація","\u002Freact-native\u002Fversion2\u002Foffline-first-sync","15.react-native\u002Fversion2\u002F20.offline-first-sync",{"title":3658,"path":3659,"stem":3660},"Камера, медіа та файлова система","\u002Freact-native\u002Fversion2\u002Fcamera-media-filesystem","15.react-native\u002Fversion2\u002F21.camera-media-filesystem",{"title":3662,"path":3663,"stem":3664},"Карти та геолокація","\u002Freact-native\u002Fversion2\u002Fmaps-and-location","15.react-native\u002Fversion2\u002F22.maps-and-location",{"title":3666,"path":3667,"stem":3668},"Жести та дотики","\u002Freact-native\u002Fversion2\u002Fgestures-and-touch","15.react-native\u002Fversion2\u002F23.gestures-and-touch",{"title":3670,"path":3671,"stem":3672},"Анімації з Reanimated","\u002Freact-native\u002Fversion2\u002Freanimated-animations","15.react-native\u002Fversion2\u002F24.reanimated-animations",{"title":3674,"path":3675,"stem":3676},"Push і локальні сповіщення","\u002Freact-native\u002Fversion2\u002Fpush-and-local-notifications","15.react-native\u002Fversion2\u002F25.push-and-local-notifications",{"title":3678,"path":3679,"stem":3680},"Інтернаціоналізація та доступність","\u002Freact-native\u002Fversion2\u002Faccessibility-and-i18n","15.react-native\u002Fversion2\u002F26.accessibility-and-i18n",{"title":3682,"path":3683,"stem":3684},"EAS Build та профілі збірки","\u002Freact-native\u002Fversion2\u002Feas-build-and-profiles","15.react-native\u002Fversion2\u002F29.eas-build-and-profiles",{"title":3686,"path":3687,"stem":3688},"Публікація в App Store та Google Play","\u002Freact-native\u002Fversion2\u002Fapp-store-play-release","15.react-native\u002Fversion2\u002F30.app-store-play-release",{"title":3690,"path":3691,"stem":3692,"children":3693,"page":59},"Ai Python","\u002Fai-python","16.ai-python",[3694,3703,3712,3721,3750,3776,3801,3834,3851,3864,3873,3886,3895,3916,3929,3950],{"title":3695,"path":3696,"stem":3697,"children":3698,"page":59},"Intro To Ai","\u002Fai-python\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai",[3699],{"title":3700,"path":3701,"stem":3702},"Вступ до штучного інтелекту та машинного навчання","\u002Fai-python\u002Fintro-to-ai\u002Fintro-to-ai","16.ai-python\u002F01.intro-to-ai\u002F01.intro-to-ai",{"title":3704,"path":3705,"stem":3706,"children":3707,"page":59},"Jupyter Notebook","\u002Fai-python\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook",[3708],{"title":3709,"path":3710,"stem":3711},"Знайомство з Jupyter Notebook та JupyterLab","\u002Fai-python\u002Fjupyter-notebook\u002Fjupyter-notebook","16.ai-python\u002F02.jupyter-notebook\u002F02.jupyter-notebook",{"title":3713,"path":3714,"stem":3715,"children":3716,"page":59},"Numpy Pandas","\u002Fai-python\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas",[3717],{"title":3718,"path":3719,"stem":3720},"Робота з даними з використанням NumPy і pandas","\u002Fai-python\u002Fnumpy-pandas\u002Fnumpy-pandas","16.ai-python\u002F03.numpy-pandas\u002F03.numpy-pandas",{"title":3722,"path":3723,"stem":3724,"children":3725,"page":59},"Statistics Basics","\u002Fai-python\u002Fstatistics-basics","16.ai-python\u002F04.statistics-basics",[3726,3730,3734,3738,3742,3746],{"title":3727,"path":3728,"stem":3729},"Випадкові величини та їх типи","\u002Fai-python\u002Fstatistics-basics\u002Frandom-variables","16.ai-python\u002F04.statistics-basics\u002F01.random-variables",{"title":3731,"path":3732,"stem":3733},"Міри центральної тенденції","\u002Fai-python\u002Fstatistics-basics\u002Fcentral-tendency","16.ai-python\u002F04.statistics-basics\u002F02.central-tendency",{"title":3735,"path":3736,"stem":3737},"Міри варіації (розсіювання)","\u002Fai-python\u002Fstatistics-basics\u002Fvariability","16.ai-python\u002F04.statistics-basics\u002F03.variability",{"title":3739,"path":3740,"stem":3741},"Розподіли випадкових величин","\u002Fai-python\u002Fstatistics-basics\u002Fdistributions","16.ai-python\u002F04.statistics-basics\u002F04.distributions",{"title":3743,"path":3744,"stem":3745},"Кореляція та взаємозв'язки","\u002Fai-python\u002Fstatistics-basics\u002Fcorrelation","16.ai-python\u002F04.statistics-basics\u002F05.correlation",{"title":3747,"path":3748,"stem":3749},"Викиди та аномалії","\u002Fai-python\u002Fstatistics-basics\u002Foutliers","16.ai-python\u002F04.statistics-basics\u002F06.outliers",{"title":3751,"path":3752,"stem":3753,"children":3754},"Візуалізація даних за допомогою matplotlib","\u002Fai-python\u002Fdata-visualization","16.ai-python\u002F05.data-visualization\u002Findex",[3755,3756,3760,3764,3768,3772],{"title":3751,"path":3752,"stem":3753},{"title":3757,"path":3758,"stem":3759},"Основи matplotlib — Figure, Axes та перший графік","\u002Fai-python\u002Fdata-visualization\u002Fmatplotlib-basics","16.ai-python\u002F05.data-visualization\u002F01.matplotlib-basics",{"title":3761,"path":3762,"stem":3763},"Візуалізація розподілів — гістограми та box plots","\u002Fai-python\u002Fdata-visualization\u002Fdistributions","16.ai-python\u002F05.data-visualization\u002F02.distributions",{"title":3765,"path":3766,"stem":3767},"Візуалізація залежностей — scatter plots та кореляція","\u002Fai-python\u002Fdata-visualization\u002Frelationships","16.ai-python\u002F05.data-visualization\u002F03.relationships",{"title":3769,"path":3770,"stem":3771},"Візуалізація категоріальних даних — bar charts та pie charts","\u002Fai-python\u002Fdata-visualization\u002Fcategorical","16.ai-python\u002F05.data-visualization\u002F04.categorical",{"title":3773,"path":3774,"stem":3775},"Композиції та стилізація — subplots та багатопанельні дашборди","\u002Fai-python\u002Fdata-visualization\u002Fsubplots-styling","16.ai-python\u002F05.data-visualization\u002F05.subplots-styling",{"title":3777,"path":3778,"stem":3779,"children":3780,"page":59},"Linear Regression","\u002Fai-python\u002Flinear-regression","16.ai-python\u002F06.linear-regression",[3781,3785,3789,3793,3797],{"title":3782,"path":3783,"stem":3784},"Регресійна задача та лінійна регресія з однією змінною","\u002Fai-python\u002Flinear-regression\u002Fregression-task","16.ai-python\u002F06.linear-regression\u002F01.regression-task",{"title":3786,"path":3787,"stem":3788},"Метрики якості регресії — як оцінити модель","\u002Fai-python\u002Flinear-regression\u002Fquality-metrics","16.ai-python\u002F06.linear-regression\u002F02.quality-metrics",{"title":3790,"path":3791,"stem":3792},"Градієнтний спуск — як модель навчається","\u002Fai-python\u002Flinear-regression\u002Fgradient-descent","16.ai-python\u002F06.linear-regression\u002F03.gradient-descent",{"title":3794,"path":3795,"stem":3796},"Множинна лінійна регресія — модель з багатьма ознаками","\u002Fai-python\u002Flinear-regression\u002Fmultiple-regression","16.ai-python\u002F06.linear-regression\u002F04.multiple-regression",{"title":3798,"path":3799,"stem":3800},"Практичні завдання та резюме модуля","\u002Fai-python\u002Flinear-regression\u002Fpractice","16.ai-python\u002F06.linear-regression\u002F05.practice",{"title":3802,"path":3803,"stem":3804,"children":3805,"page":59},"Practical Regression","\u002Fai-python\u002Fpractical-regression","16.ai-python\u002F07.practical-regression",[3806,3810,3814,3818,3822,3826,3830],{"title":3807,"path":3808,"stem":3809},"Знайомство з scikit-learn","\u002Fai-python\u002Fpractical-regression\u002Fintro-scikit-learn","16.ai-python\u002F07.practical-regression\u002F01.intro-scikit-learn",{"title":3811,"path":3812,"stem":3813},"Exploratory Data Analysis датасету Housing Prices","\u002Fai-python\u002Fpractical-regression\u002Fhousing-dataset-eda","16.ai-python\u002F07.practical-regression\u002F02.housing-dataset-eda",{"title":3815,"path":3816,"stem":3817},"Попередня обробка даних (Data Preprocessing)","\u002Fai-python\u002Fpractical-regression\u002Fdata-preprocessing","16.ai-python\u002F07.practical-regression\u002F03.data-preprocessing",{"title":3819,"path":3820,"stem":3821},"Train\u002FTest Split та перша повноцінна модель","\u002Fai-python\u002Fpractical-regression\u002Ftrain-test-split","16.ai-python\u002F07.practical-regression\u002F04.train-test-split",{"title":3823,"path":3824,"stem":3825},"Перенавчання та недонавчання","\u002Fai-python\u002Fpractical-regression\u002Foverfitting-underfitting","16.ai-python\u002F07.practical-regression\u002F05.overfitting-underfitting",{"title":3827,"path":3828,"stem":3829},"Крос-валідація (Cross-Validation)","\u002Fai-python\u002Fpractical-regression\u002Fcross-validation","16.ai-python\u002F07.practical-regression\u002F06.cross-validation",{"title":3831,"path":3832,"stem":3833},"Гіперпараметри та їх оптимізація","\u002Fai-python\u002Fpractical-regression\u002Fhyperparameter-tuning","16.ai-python\u002F07.practical-regression\u002F07.hyperparameter-tuning",{"title":3835,"path":3836,"stem":3837,"children":3838,"page":59},"Polynomial Regression","\u002Fai-python\u002Fpolynomial-regression","16.ai-python\u002F08.polynomial-regression",[3839,3843,3847],{"title":3840,"path":3841,"stem":3842},"Нелінійні залежності та поліноміальна регресія","\u002Fai-python\u002Fpolynomial-regression\u002Fnonlinear-patterns","16.ai-python\u002F08.polynomial-regression\u002F01.nonlinear-patterns",{"title":3844,"path":3845,"stem":3846},"Регуляризація в регресії — Ridge та Lasso","\u002Fai-python\u002Fpolynomial-regression\u002Fregularization-methods","16.ai-python\u002F08.polynomial-regression\u002F02.regularization-methods",{"title":3848,"path":3849,"stem":3850},"Практика — поліноміальна регресія та регуляризація на Housing Prices","\u002Fai-python\u002Fpolynomial-regression\u002Fhousing-prices-practice","16.ai-python\u002F08.polynomial-regression\u002F03.housing-prices-practice",{"title":3852,"path":3853,"stem":3854,"children":3855,"page":59},"Decision Trees Random Forest","\u002Fai-python\u002Fdecision-trees-random-forest","16.ai-python\u002F09.decision-trees-random-forest",[3856,3860],{"title":3857,"path":3858,"stem":3859},"Дерева рішень — моделі з прозорою та зрозумілою логікою","\u002Fai-python\u002Fdecision-trees-random-forest\u002Fdecision-trees","16.ai-python\u002F09.decision-trees-random-forest\u002F01.decision-trees",{"title":3861,"path":3862,"stem":3863},"Random Forest — ансамблі дерев рішень","\u002Fai-python\u002Fdecision-trees-random-forest\u002Frandom-forest","16.ai-python\u002F09.decision-trees-random-forest\u002F02.random-forest",{"title":3865,"path":3866,"stem":3867,"children":3868,"page":59},"Gradient Boosting","\u002Fai-python\u002Fgradient-boosting","16.ai-python\u002F10.gradient-boosting",[3869],{"title":3870,"path":3871,"stem":3872},"Градієнтний бустинг та XGBoost — послідовне виправлення помилок","\u002Fai-python\u002Fgradient-boosting\u002Fgradient-boosting-xgboost","16.ai-python\u002F10.gradient-boosting\u002F01.gradient-boosting-xgboost",{"title":3874,"path":3875,"stem":3876,"children":3877,"page":59},"Logistic Regression Classification","\u002Fai-python\u002Flogistic-regression-classification","16.ai-python\u002F11.logistic-regression-classification",[3878,3882],{"title":3879,"path":3880,"stem":3881},"Основи класифікації та логістична регресія","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-basics","16.ai-python\u002F11.logistic-regression-classification\u002F01.classification-basics",{"title":3883,"path":3884,"stem":3885},"Метрики якості класифікації","\u002Fai-python\u002Flogistic-regression-classification\u002Fclassification-metrics","16.ai-python\u002F11.logistic-regression-classification\u002F02.classification-metrics",{"title":3887,"path":3888,"stem":3889,"children":3890,"page":59},"Neural Networks Basics","\u002Fai-python\u002Fneural-networks-basics","16.ai-python\u002F12.neural-networks-basics",[3891],{"title":3892,"path":3893,"stem":3894},"Вступ до нейронних мереж — від персептрона до багатошарових мереж","\u002Fai-python\u002Fneural-networks-basics\u002Fperceptron-to-mlp","16.ai-python\u002F12.neural-networks-basics\u002F01.perceptron-to-mlp",{"title":3896,"path":3897,"stem":3898,"children":3899,"page":59},"Pytorch Intro","\u002Fai-python\u002Fpytorch-intro","16.ai-python\u002F13.pytorch-intro",[3900,3904,3908,3912],{"title":3901,"path":3902,"stem":3903},"Тензори та автоматичне диференціювання в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Ftensors-and-autograd","16.ai-python\u002F13.pytorch-intro\u002F01.tensors-and-autograd",{"title":3905,"path":3906,"stem":3907},"Побудова та тренування нейронних мереж у PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fbuilding-and-training","16.ai-python\u002F13.pytorch-intro\u002F02.building-and-training",{"title":3909,"path":3910,"stem":3911},"Робота з даними та регуляризація в PyTorch","\u002Fai-python\u002Fpytorch-intro\u002Fdata-and-regularization","16.ai-python\u002F13.pytorch-intro\u002F03.data-and-regularization",{"title":3913,"path":3914,"stem":3915},"Просунуті теми PyTorch — GPU, оптимізація та deployment","\u002Fai-python\u002Fpytorch-intro\u002Fadvanced-topics","16.ai-python\u002F13.pytorch-intro\u002F04.advanced-topics",{"title":3917,"path":3918,"stem":3919,"children":3920,"page":59},"Activation Functions Heart Disease","\u002Fai-python\u002Factivation-functions-heart-disease","16.ai-python\u002F14.activation-functions-heart-disease",[3921,3925],{"title":3922,"path":3923,"stem":3924},"Функції активації та побудова нейронної мережі для передбачення вад серця","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fheart-disease-prediction","16.ai-python\u002F14.activation-functions-heart-disease\u002F01.heart-disease-prediction",{"title":3926,"path":3927,"stem":3928},"Бонус — Повний приклад Student Performance Prediction","\u002Fai-python\u002Factivation-functions-heart-disease\u002Fstudent-performance-bonus","16.ai-python\u002F14.activation-functions-heart-disease\u002F02.student-performance-bonus",{"title":3930,"path":3931,"stem":3932,"children":3933,"page":59},"Cnn Image Classification","\u002Fai-python\u002Fcnn-image-classification","16.ai-python\u002F15.cnn-image-classification",[3934,3938,3942,3946],{"title":3935,"path":3936,"stem":3937},"Основи згорткових нейронних мереж — чому не MLP?","\u002Fai-python\u002Fcnn-image-classification\u002Fcnn-fundamentals","16.ai-python\u002F15.cnn-image-classification\u002F01.cnn-fundamentals",{"title":3939,"path":3940,"stem":3941},"Практична імплементація CNN для класифікації MNIST","\u002Fai-python\u002Fcnn-image-classification\u002Fmnist-classification","16.ai-python\u002F15.cnn-image-classification\u002F02.mnist-classification",{"title":3943,"path":3944,"stem":3945},"Глибші CNN та аугментація даних для CIFAR-10","\u002Fai-python\u002Fcnn-image-classification\u002Fcifar10-and-data-augmentation","16.ai-python\u002F15.cnn-image-classification\u002F03.cifar10-and-data-augmentation",{"title":3947,"path":3948,"stem":3949},"Transfer Learning та візуалізація внутрішніх представлень CNN","\u002Fai-python\u002Fcnn-image-classification\u002Ftransfer-learning-and-visualization","16.ai-python\u002F15.cnn-image-classification\u002F04.transfer-learning-and-visualization",{"title":3951,"path":3952,"stem":3953,"children":3954,"page":59},"Batching Normalization Deep Networks","\u002Fai-python\u002Fbatching-normalization-deep-networks","16.ai-python\u002F16.batching-normalization-deep-networks",[3955,3959,3963,3967,3971,3975,3979],{"title":3956,"path":3957,"stem":3958},"Mini-batch Gradient Descent та ефективна обробка даних","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fmini-batch-gradient-descent","16.ai-python\u002F16.batching-normalization-deep-networks\u002F01.mini-batch-gradient-descent",{"title":3960,"path":3961,"stem":3962},"Ініціалізація ваг — фундамент стабільного навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fweight-initialization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F02.weight-initialization",{"title":3964,"path":3965,"stem":3966},"Batch Normalization — прорив у глибокому навчанні","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fbatch-normalization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F03.batch-normalization",{"title":3968,"path":3969,"stem":3970},"Dropout та комбіновані стратегії регуляризації","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdropout-and-regularization","16.ai-python\u002F16.batching-normalization-deep-networks\u002F04.dropout-and-regularization",{"title":3972,"path":3973,"stem":3974},"Проєктування глибоких мереж — від теорії до практики","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Fdeep-networks-architectures","16.ai-python\u002F16.batching-normalization-deep-networks\u002F05.deep-networks-architectures",{"title":3976,"path":3977,"stem":3978},"Планування learning rate — коли та як зменшувати крок навчання","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Flearning-rate-scheduling","16.ai-python\u002F16.batching-normalization-deep-networks\u002F06.learning-rate-scheduling",{"title":3980,"path":3981,"stem":3982},"Підсумковий проєкт — побудова сучасного класифікатора зображень","\u002Fai-python\u002Fbatching-normalization-deep-networks\u002Ffinal-project-deep-classifier","16.ai-python\u002F16.batching-normalization-deep-networks\u002F07.final-project-deep-classifier",{"title":3984,"icon":658,"path":3985,"stem":3986,"children":3987,"page":59},"Клієнт-серверна архітектура","\u002Fclient-server-architecture","17.client-server-architecture",[3988,3992,3996,4000,4004,4008,4012,4016,4020,4024,4028,4032,4036,4040,4044,4048,4052,4056],{"title":3989,"path":3990,"stem":3991},"Архітектура клієнт-серверних систем та основи Go","\u002Fclient-server-architecture\u002Fclient-server-architecture-and-go","17.client-server-architecture\u002F01.client-server-architecture-and-go",{"title":3993,"path":3994,"stem":3995},"Система типів та модель пам’яті мови Go","\u002Fclient-server-architecture\u002Ftype-system-and-memory-model","17.client-server-architecture\u002F02.type-system-and-memory-model",{"title":3997,"path":3998,"stem":3999},"Інтерфейси та модель конкурентності мови Go","\u002Fclient-server-architecture\u002Finterfaces-and-concurrency-model","17.client-server-architecture\u002F03.interfaces-and-concurrency-model",{"title":4001,"path":4002,"stem":4003},"Сокетне програмування та протокол TCP у Go","\u002Fclient-server-architecture\u002Ftcp-socket-programming","17.client-server-architecture\u002F04.tcp-socket-programming",{"title":4005,"path":4006,"stem":4007},"Протокол UDP та датаграмна передача даних","\u002Fclient-server-architecture\u002Fudp-datagram-transmission","17.client-server-architecture\u002F05.udp-datagram-transmission",{"title":4009,"path":4010,"stem":4011},"Криптографічний захист каналів зв","\u002Fclient-server-architecture\u002Ftls-cryptographic-channel-protection","17.client-server-architecture\u002F06.tls-cryptographic-channel-protection",{"title":4013,"path":4014,"stem":4015},"Прикладні мережеві протоколи DNS та SMTP","\u002Fclient-server-architecture\u002Fdns-smtp-application-protocols","17.client-server-architecture\u002F07.dns-smtp-application-protocols",{"title":4017,"path":4018,"stem":4019},"Протокол HTTP та стандартний вебсервер Go","\u002Fclient-server-architecture\u002Fhttp-protocol-and-web-server","17.client-server-architecture\u002F08.http-protocol-and-web-server",{"title":4021,"path":4022,"stem":4023},"Проєктування REST API та маршрутизація засобами Chi","\u002Fclient-server-architecture\u002Frest-api-design-and-chi-routing","17.client-server-architecture\u002F09.rest-api-design-and-chi-routing",{"title":4025,"path":4026,"stem":4027},"Лекція 10. Шарувата архітектура та конвеєри обробки запитів","\u002Fclient-server-architecture\u002Flayered-architecture-and-middleware-pipelines","17.client-server-architecture\u002F10.layered-architecture-and-middleware-pipelines",{"title":4029,"path":4030,"stem":4031},"Лекція 11. Архітектура та маршрутизація фреймворку Gin","\u002Fclient-server-architecture\u002Fgin-framework-architecture-and-routing","17.client-server-architecture\u002F11.gin-framework-architecture-and-routing",{"title":4033,"path":4034,"stem":4035},"Лекція 12. Валідація даних, безпека та документування у Gin","\u002Fclient-server-architecture\u002Fdata-validation-security-and-documentation-in-gin","17.client-server-architecture\u002F12.data-validation-security-and-documentation-in-gin",{"title":4037,"path":4038,"stem":4039},"Лекція 13. Взаємодія з реляційними СУБД та технології ORM","\u002Fclient-server-architecture\u002Frelational-databases-and-orm","17.client-server-architecture\u002F13.relational-databases-and-orm",{"title":4041,"path":4042,"stem":4043},"Потокова передача даних та протокол WebSocket","\u002Fclient-server-architecture\u002Fstreaming-data-and-websockets","17.client-server-architecture\u002F14.streaming-data-and-websockets",{"title":4045,"path":4046,"stem":4047},"Міжсервісна взаємодія на основі протоколу gRPC","\u002Fclient-server-architecture\u002Fgrpc-inter-service-communication","17.client-server-architecture\u002F15.grpc-inter-service-communication",{"title":4049,"path":4050,"stem":4051},"Асинхронний обмін повідомленнями та протоколи черг","\u002Fclient-server-architecture\u002Fasynchronous-message-exchange-and-queue-protocols","17.client-server-architecture\u002F16.asynchronous-message-exchange-and-queue-protocols",{"title":4053,"path":4054,"stem":4055},"Протоколи потокового медіа та технологія WebRTC","\u002Fclient-server-architecture\u002Fstreaming-media-protocols-and-webrtc","17.client-server-architecture\u002F17.streaming-media-protocols-and-webrtc",{"title":4057,"path":4058,"stem":4059},"Моніторинг, безпека та контейнеризація застосунків","\u002Fclient-server-architecture\u002Fmonitoring-security-and-containerization","17.client-server-architecture\u002F18.monitoring-security-and-containerization",{"title":4061,"icon":2118,"path":4062,"stem":4063,"children":4064,"page":59},"Розробка WEB-застосувань","\u002Fweb-development","18.web-development",[4065,4110,4148,4177,4206,4263,4313,4407,4473,4555,4588,4616,4658,4704,4747],{"title":4066,"icon":658,"path":4067,"stem":4068,"children":4069,"page":59},"Архітектура комп'ютерних мереж та мережеві протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols","18.web-development\u002F01.network-architecture-and-protocols",[4070,4074,4078,4082,4086,4090,4094,4098,4102,4106],{"title":4071,"path":4072,"stem":4073},"Еволюція веброзробки та модель клієнт-сервер","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fweb-evolution-client-server","18.web-development\u002F01.network-architecture-and-protocols\u002F01.web-evolution-client-server",{"title":4075,"path":4076,"stem":4077},"Еталонна модель OSI","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fosi-model","18.web-development\u002F01.network-architecture-and-protocols\u002F02.osi-model",{"title":4079,"path":4080,"stem":4081},"Стек протоколів TCP\u002FIP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-ip-stack","18.web-development\u002F01.network-architecture-and-protocols\u002F03.tcp-ip-stack",{"title":4083,"path":4084,"stem":4085},"IP-адресація, порти та сокети","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fip-addressing-ports-sockets","18.web-development\u002F01.network-architecture-and-protocols\u002F04.ip-addressing-ports-sockets",{"title":4087,"path":4088,"stem":4089},"Протоколи TCP та UDP","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Ftcp-udp-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F05.tcp-udp-protocols",{"title":4091,"path":4092,"stem":4093},"Система доменних імен DNS","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fdns-system","18.web-development\u002F01.network-architecture-and-protocols\u002F06.dns-system",{"title":4095,"path":4096,"stem":4097},"Протокол SMTP та поштові протоколи","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fsmtp-email-protocols","18.web-development\u002F01.network-architecture-and-protocols\u002F07.smtp-email-protocols",{"title":4099,"path":4100,"stem":4101},"Протокол WebSocket","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fwebsocket-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F08.websocket-protocol",{"title":4103,"path":4104,"stem":4105},"Протокол SSH","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fssh-protocol","18.web-development\u002F01.network-architecture-and-protocols\u002F09.ssh-protocol",{"title":4107,"path":4108,"stem":4109},"Огляд сучасних серверних технологій","\u002Fweb-development\u002Fnetwork-architecture-and-protocols\u002Fmodern-backend-technologies","18.web-development\u002F01.network-architecture-and-protocols\u002F10.modern-backend-technologies",{"title":4111,"icon":4112,"path":4113,"stem":4114,"children":4115,"page":59},"Протокол HTTP та захищена передача даних HTTPS","i-lucide-lock","\u002Fweb-development\u002Fhttp-and-https","18.web-development\u002F02.http-and-https",[4116,4120,4124,4128,4132,4136,4140,4144],{"title":4117,"path":4118,"stem":4119},"Вступ до протоколу HTTP та еволюція веб-технологій","\u002Fweb-development\u002Fhttp-and-https\u002Fintroduction-and-evolution","18.web-development\u002F02.http-and-https\u002F01.introduction-and-evolution",{"title":4121,"path":4122,"stem":4123},"Анатомія HTTP-запиту","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-request-structure","18.web-development\u002F02.http-and-https\u002F02.http-request-structure",{"title":4125,"path":4126,"stem":4127},"Анатомія HTTP-відповіді","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-response-structure","18.web-development\u002F02.http-and-https\u002F03.http-response-structure",{"title":4129,"path":4130,"stem":4131},"Методи HTTP та їхня семантика","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-methods","18.web-development\u002F02.http-and-https\u002F04.http-methods",{"title":4133,"path":4134,"stem":4135},"Коди статусу HTTP та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-status-codes","18.web-development\u002F02.http-and-https\u002F05.http-status-codes",{"title":4137,"path":4138,"stem":4139},"HTTP-заголовки та їхнє призначення","\u002Fweb-development\u002Fhttp-and-https\u002Fhttp-headers","18.web-development\u002F02.http-and-https\u002F06.http-headers",{"title":4141,"path":4142,"stem":4143},"CORS та механізми безпеки HTTP","\u002Fweb-development\u002Fhttp-and-https\u002Fcors-and-security","18.web-development\u002F02.http-and-https\u002F07.cors-and-security",{"title":4145,"path":4146,"stem":4147},"HTTPS та криптографічні основи TLS","\u002Fweb-development\u002Fhttp-and-https\u002Fhttps-and-tls","18.web-development\u002F02.http-and-https\u002F08.https-and-tls",{"title":4149,"icon":2498,"path":4150,"stem":4151,"children":4152,"page":59},"Система типів мови TypeScript","\u002Fweb-development\u002Ftypescript-type-system","18.web-development\u002F03.typescript-type-system",[4153,4157,4161,4165,4169,4173],{"title":4154,"path":4155,"stem":4156},"Знайомство з TypeScript Compiler","\u002Fweb-development\u002Ftypescript-type-system\u002Fintroduction-compiler-config","18.web-development\u002F03.typescript-type-system\u002F01.introduction-compiler-config",{"title":4158,"path":4159,"stem":4160},"Примітивні типи даних: string, number, boolean","\u002Fweb-development\u002Ftypescript-type-system\u002Fprimitive-special-types","18.web-development\u002F03.typescript-type-system\u002F02.primitive-special-types",{"title":4162,"path":4163,"stem":4164},"Масиви, кортежі та об","\u002Fweb-development\u002Ftypescript-type-system\u002Farrays-tuples-objects","18.web-development\u002F03.typescript-type-system\u002F03.arrays-tuples-objects",{"title":4166,"path":4167,"stem":4168},"Псевдоніми типів, Union типи, Intersection типи та літеральні типи","\u002Fweb-development\u002Ftypescript-type-system\u002Funion-intersection-literals","18.web-development\u002F03.typescript-type-system\u002F04.union-intersection-literals",{"title":4170,"path":4171,"stem":4172},"Type Narrowing (звуження типів)","\u002Fweb-development\u002Ftypescript-type-system\u002Ftype-narrowing","18.web-development\u002F03.typescript-type-system\u002F05.type-narrowing",{"title":4174,"path":4175,"stem":4176},"Типізація функцій","\u002Fweb-development\u002Ftypescript-type-system\u002Ffunctions-typing","18.web-development\u002F03.typescript-type-system\u002F06.functions-typing",{"title":4178,"icon":2498,"path":4179,"stem":4180,"children":4181,"page":59},"Розширені засоби мови TypeScript","\u002Fweb-development\u002Ftypescript-advanced","18.web-development\u002F04.typescript-advanced",[4182,4186,4190,4194,4198,4202],{"title":4183,"path":4184,"stem":4185},"Interfaces та Classes","\u002Fweb-development\u002Ftypescript-advanced\u002Finterfaces-classes","18.web-development\u002F04.typescript-advanced\u002F01.interfaces-classes",{"title":4187,"path":4188,"stem":4189},"Основи Generic типів","\u002Fweb-development\u002Ftypescript-advanced\u002Fgenerics-fundamentals","18.web-development\u002F04.typescript-advanced\u002F02.generics-fundamentals",{"title":4191,"path":4192,"stem":4193},"Enums та Decorators","\u002Fweb-development\u002Ftypescript-advanced\u002Fenums-decorators","18.web-development\u002F04.typescript-advanced\u002F03.enums-decorators",{"title":4195,"path":4196,"stem":4197},"Utility Types","\u002Fweb-development\u002Ftypescript-advanced\u002Futility-types","18.web-development\u002F04.typescript-advanced\u002F04.utility-types",{"title":4199,"path":4200,"stem":4201},"Mapped та Conditional Types","\u002Fweb-development\u002Ftypescript-advanced\u002Fmapped-conditional-types","18.web-development\u002F04.typescript-advanced\u002F05.mapped-conditional-types",{"title":4203,"path":4204,"stem":4205},"Модулі та Strict Mode","\u002Fweb-development\u002Ftypescript-advanced\u002Fmodules-strict-mode","18.web-development\u002F04.typescript-advanced\u002F06.modules-strict-mode",{"title":4207,"icon":4208,"path":4209,"stem":4210,"children":4211,"page":59},"Платформа Node.js як середовище виконання","i-devicon-nodejs","\u002Fweb-development\u002Fnodejs-platform","18.web-development\u002F05.nodejs-platform",[4212,4216,4220,4224,4228,4232,4236,4240,4244,4248,4252,4255,4259],{"title":4213,"path":4214,"stem":4215},"Що таке Node.js та його архітектура","\u002Fweb-development\u002Fnodejs-platform\u002Fwhat-is-nodejs","18.web-development\u002F05.nodejs-platform\u002F01.what-is-nodejs",{"title":4217,"path":4218,"stem":4219},"Event Loop — серце Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fevent-loop","18.web-development\u002F05.nodejs-platform\u002F02.event-loop",{"title":4221,"path":4222,"stem":4223},"Модульні системи: CommonJS vs ES Modules","\u002Fweb-development\u002Fnodejs-platform\u002Fmodule-systems","18.web-development\u002F05.nodejs-platform\u002F03.module-systems",{"title":4225,"path":4226,"stem":4227},"npm та package.json","\u002Fweb-development\u002Fnodejs-platform\u002Fnpm-package-json","18.web-development\u002F05.nodejs-platform\u002F04.npm-package-json",{"title":4229,"path":4230,"stem":4231},"Глобальні об\\","\u002Fweb-development\u002Fnodejs-platform\u002Fglobal-objects","18.web-development\u002F05.nodejs-platform\u002F05.global-objects",{"title":4233,"path":4234,"stem":4235},"Вбудований модуль fs (File System)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-fs","18.web-development\u002F05.nodejs-platform\u002F06.built-in-modules-fs",{"title":4237,"path":4238,"stem":4239},"Вбудований модуль path","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-path","18.web-development\u002F05.nodejs-platform\u002F07.built-in-modules-path",{"title":4241,"path":4242,"stem":4243},"Вбудований модуль http","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-http","18.web-development\u002F05.nodejs-platform\u002F08.built-in-modules-http",{"title":4245,"path":4246,"stem":4247},"Streams — потоки даних у Node.js","\u002Fweb-development\u002Fnodejs-platform\u002Fstreams","18.web-development\u002F05.nodejs-platform\u002F09.streams",{"title":4249,"path":4250,"stem":4251},"Вбудований модуль util (Utilities)","\u002Fweb-development\u002Fnodejs-platform\u002Fbuilt-in-modules-util","18.web-development\u002F05.nodejs-platform\u002F10.built-in-modules-util",{"title":3141,"path":4253,"stem":4254},"\u002Fweb-development\u002Fnodejs-platform\u002Fenvironment-variables","18.web-development\u002F05.nodejs-platform\u002F11.environment-variables",{"title":4256,"path":4257,"stem":4258},"Інструменти налагодження та розробки","\u002Fweb-development\u002Fnodejs-platform\u002Fdebugging-tools","18.web-development\u002F05.nodejs-platform\u002F12.debugging-tools",{"title":4260,"path":4261,"stem":4262},"Продуктивність та Best Practices","\u002Fweb-development\u002Fnodejs-platform\u002Fperformance-best-practices","18.web-development\u002F05.nodejs-platform\u002F13.performance-best-practices",{"title":4264,"icon":4265,"path":4266,"stem":4267,"children":4268,"page":59},"Асинхронне програмування у Node.js","i-lucide-clock","\u002Fweb-development\u002Fasync-programming-nodejs","18.web-development\u002F06.async-programming-nodejs",[4269,4273,4277,4281,4285,4289,4293,4297,4301,4305,4309],{"title":4270,"path":4271,"stem":4272},"Синхронний vs асинхронний код","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fsync-vs-async","18.web-development\u002F06.async-programming-nodejs\u002F01.sync-vs-async",{"title":4274,"path":4275,"stem":4276},"Callbacks — перша парадигма асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fcallbacks","18.web-development\u002F06.async-programming-nodejs\u002F02.callbacks",{"title":4278,"path":4279,"stem":4280},"Promises — стандарт асинхронності","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromises","18.web-development\u002F06.async-programming-nodejs\u002F03.promises",{"title":4282,"path":4283,"stem":4284},"Promise комбінатори","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fpromise-combinators","18.web-development\u002F06.async-programming-nodejs\u002F04.promise-combinators",{"title":4286,"path":4287,"stem":4288},"Async\u002FAwait — синтаксичний цукор над Promises","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fasync-await","18.web-development\u002F06.async-programming-nodejs\u002F05.async-await",{"title":4290,"path":4291,"stem":4292},"Паралельне vs послідовне виконання","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fparallel-vs-sequential","18.web-development\u002F06.async-programming-nodejs\u002F06.parallel-vs-sequential",{"title":4294,"path":4295,"stem":4296},"EventEmitter — подієва модель Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fevent-emitter","18.web-development\u002F06.async-programming-nodejs\u002F07.event-emitter",{"title":4298,"path":4299,"stem":4300},"Worker Threads — багатопотоковість у Node.js","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fworker-threads","18.web-development\u002F06.async-programming-nodejs\u002F08.worker-threads",{"title":4302,"path":4303,"stem":4304},"Child Processes — запуск зовнішніх процесів","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fchild-processes","18.web-development\u002F06.async-programming-nodejs\u002F09.child-processes",{"title":4306,"path":4307,"stem":4308},"Обробка помилок у асинхронному коді","\u002Fweb-development\u002Fasync-programming-nodejs\u002Ferror-handling","18.web-development\u002F06.async-programming-nodejs\u002F10.error-handling",{"title":4310,"path":4311,"stem":4312},"Порівняння Node.js фреймворків","\u002Fweb-development\u002Fasync-programming-nodejs\u002Fnodejs-frameworks","18.web-development\u002F06.async-programming-nodejs\u002F11.nodejs-frameworks",{"title":4314,"icon":4315,"path":4316,"stem":4317,"children":4318,"page":59},"Тема 7. Фреймворк NestJS. Контролери та маршрутизація","i-lucide-route","\u002Fweb-development\u002Fnestjs-controllers-routing","18.web-development\u002F07.nestjs-controllers-routing",[4319,4323,4327,4331,4335,4339,4343,4347,4351,4355,4359,4363,4367,4371,4375,4379,4383,4387,4391,4395,4399,4403],{"title":4320,"path":4321,"stem":4322},"Філософія та архітектура NestJS","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-philosophy","18.web-development\u002F07.nestjs-controllers-routing\u002F01.nestjs-philosophy",{"title":4324,"path":4325,"stem":4326},"Три стовпи архітектури: модулі, контролери, провайдери","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fthree-pillars","18.web-development\u002F07.nestjs-controllers-routing\u002F02.three-pillars",{"title":4328,"path":4329,"stem":4330},"Інверсія керування (IoC) та ін","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fioc-and-di","18.web-development\u002F07.nestjs-controllers-routing\u002F03.ioc-and-di",{"title":4332,"path":4333,"stem":4334},"Встановлення NestJS CLI та створення проєкту","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-setup","18.web-development\u002F07.nestjs-controllers-routing\u002F04.nestjs-cli-setup",{"title":4336,"path":4337,"stem":4338},"Структура проєкту NestJS та конвенції","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fproject-structure","18.web-development\u002F07.nestjs-controllers-routing\u002F05.project-structure",{"title":4340,"path":4341,"stem":4342},"Контролери: основи маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontrollers-basics","18.web-development\u002F07.nestjs-controllers-routing\u002F06.controllers-basics",{"title":4344,"path":4345,"stem":4346},"Декоратори маршрутизації HTTP-методів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F07.route-decorators",{"title":4348,"path":4349,"stem":4350},"Параметри маршруту та декоратор @Param","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Froute-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F08.route-parameters",{"title":4352,"path":4353,"stem":4354},"Query-параметри та декоратор @Query","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fquery-parameters","18.web-development\u002F07.nestjs-controllers-routing\u002F09.query-parameters",{"title":4356,"path":4357,"stem":4358},"Тіло запиту та декоратор @Body","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-body","18.web-development\u002F07.nestjs-controllers-routing\u002F10.request-body",{"title":4360,"path":4361,"stem":4362},"Робота з заголовками запиту та відповіді","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fheaders-decorators","18.web-development\u002F07.nestjs-controllers-routing\u002F11.headers-decorators",{"title":4364,"path":4365,"stem":4366},"Data Transfer Objects (DTO): визначення та призначення","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fdto-introduction","18.web-development\u002F07.nestjs-controllers-routing\u002F12.dto-introduction",{"title":4368,"path":4369,"stem":4370},"Об'єкти Request та Response","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Frequest-response-objects","18.web-development\u002F07.nestjs-controllers-routing\u002F13.request-response-objects",{"title":4372,"path":4373,"stem":4374},"HTTP-статус коди та декоратор @HttpCode","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fhttp-status-codes","18.web-development\u002F07.nestjs-controllers-routing\u002F14.http-status-codes",{"title":4376,"path":4377,"stem":4378},"Перенаправлення (Redirects) та декоратор @Redirect","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fredirects","18.web-development\u002F07.nestjs-controllers-routing\u002F15.redirects",{"title":4380,"path":4381,"stem":4382},"Асинхронні обробники та Observables","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fasync-handlers","18.web-development\u002F07.nestjs-controllers-routing\u002F16.async-handlers",{"title":4384,"path":4385,"stem":4386},"Маршрутизація за піддоменами та версіонування API","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fsub-domain-routing","18.web-development\u002F07.nestjs-controllers-routing\u002F17.sub-domain-routing",{"title":4388,"path":4389,"stem":4390},"Області видимості контролерів (Scopes)","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcontroller-scopes","18.web-development\u002F07.nestjs-controllers-routing\u002F18.controller-scopes",{"title":4392,"path":4393,"stem":4394},"Основні команди NestJS CLI","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fnestjs-cli-commands","18.web-development\u002F07.nestjs-controllers-routing\u002F19.nestjs-cli-commands",{"title":4396,"path":4397,"stem":4398},"Практичний приклад: створення CRUD-контролера","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fcrud-example","18.web-development\u002F07.nestjs-controllers-routing\u002F20.crud-example",{"title":4400,"path":4401,"stem":4402},"Тестування контролерів","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Ftesting-controllers","18.web-development\u002F07.nestjs-controllers-routing\u002F21.testing-controllers",{"title":4404,"path":4405,"stem":4406},"Best Practices для контролерів та маршрутизації","\u002Fweb-development\u002Fnestjs-controllers-routing\u002Fbest-practices","18.web-development\u002F07.nestjs-controllers-routing\u002F22.best-practices",{"title":4408,"icon":4409,"path":4410,"stem":4411,"children":4412,"page":59},"Тема 8. Провайдери, сервіси та модульна система NestJS","i-lucide-package","\u002Fweb-development\u002Fnestjs-providers-modules","18.web-development\u002F08.nestjs-providers-modules",[4413,4417,4421,4425,4429,4433,4437,4441,4445,4449,4453,4457,4461,4465,4469],{"title":4414,"path":4415,"stem":4416},"Концепція провайдерів у NestJS","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fproviders-concept","18.web-development\u002F08.nestjs-providers-modules\u002F01.providers-concept",{"title":4418,"path":4419,"stem":4420},"Сервіси: інкапсуляція бізнес-логіки","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fservices-business-logic","18.web-development\u002F08.nestjs-providers-modules\u002F02.services-business-logic",{"title":4422,"path":4423,"stem":4424},"Практика ін","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdependency-injection-practice","18.web-development\u002F08.nestjs-providers-modules\u002F03.dependency-injection-practice",{"title":4426,"path":4427,"stem":4428},"Custom Providers: useValue, useClass, useFactory, useExisting","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcustom-providers","18.web-development\u002F08.nestjs-providers-modules\u002F04.custom-providers",{"title":4430,"path":4431,"stem":4432},"Injection Tokens: рядкові та символьні токени","\u002Fweb-development\u002Fnestjs-providers-modules\u002Finjection-tokens","18.web-development\u002F08.nestjs-providers-modules\u002F05.injection-tokens",{"title":4434,"path":4435,"stem":4436},"Опціональні провайдери та декоратор @Optional","\u002Fweb-development\u002Fnestjs-providers-modules\u002Foptional-providers","18.web-development\u002F08.nestjs-providers-modules\u002F07.optional-providers",{"title":4438,"path":4439,"stem":4440},"Структура модулів: imports, controllers, providers, exports","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodules-structure","18.web-development\u002F08.nestjs-providers-modules\u002F08.modules-structure",{"title":4442,"path":4443,"stem":4444},"Feature Modules: ізоляція функціональності","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ffeature-modules","18.web-development\u002F08.nestjs-providers-modules\u002F09.feature-modules",{"title":4446,"path":4447,"stem":4448},"Shared Modules: перевикористання провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fshared-modules","18.web-development\u002F08.nestjs-providers-modules\u002F10.shared-modules",{"title":4450,"path":4451,"stem":4452},"Global Modules та декоратор @Global","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fglobal-modules","18.web-development\u002F08.nestjs-providers-modules\u002F11.global-modules",{"title":4454,"path":4455,"stem":4456},"Dynamic Modules: конфігурація під час виконання","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fdynamic-modules","18.web-development\u002F08.nestjs-providers-modules\u002F12.dynamic-modules",{"title":4458,"path":4459,"stem":4460},"Циклічні залежності та forwardRef","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fcircular-dependencies","18.web-development\u002F08.nestjs-providers-modules\u002F13.circular-dependencies",{"title":4462,"path":4463,"stem":4464},"Lifecycle Hooks: хуки життєвого циклу","\u002Fweb-development\u002Fnestjs-providers-modules\u002Flifecycle-hooks","18.web-development\u002F08.nestjs-providers-modules\u002F14.lifecycle-hooks",{"title":4466,"path":4467,"stem":4468},"ModuleRef: динамічний доступ до провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Fmodule-reference","18.web-development\u002F08.nestjs-providers-modules\u002F15.module-reference",{"title":4470,"path":4471,"stem":4472},"Тестування сервісів та провайдерів","\u002Fweb-development\u002Fnestjs-providers-modules\u002Ftesting-services","18.web-development\u002F08.nestjs-providers-modules\u002F16.testing-services",{"title":4474,"icon":4475,"path":4476,"stem":4477,"children":4478,"page":59},"Тема 9. Валідація даних та конвеєр обробки запитів у NestJS","i-lucide-filter","\u002Fweb-development\u002Fnestjs-validation-pipeline","18.web-development\u002F09.nestjs-validation-pipeline",[4479,4483,4487,4491,4495,4499,4503,4507,4511,4515,4519,4523,4527,4531,4535,4539,4543,4547,4551],{"title":4480,"path":4481,"stem":4482},"Request Pipeline: конвеєр обробки запитів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Frequest-pipeline","18.web-development\u002F09.nestjs-validation-pipeline\u002F01.request-pipeline",{"title":4484,"path":4485,"stem":4486},"Pipes: концепція трансформації та валідації","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipes-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F02.pipes-concept",{"title":4488,"path":4489,"stem":4490},"Вбудовані pipes: ParseIntPipe, ParseBoolPipe, ParseUUIDPipe","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fbuilt-in-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F03.built-in-pipes",{"title":4492,"path":4493,"stem":4494},"ValidationPipe: автоматична валідація DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fvalidation-pipe","18.web-development\u002F09.nestjs-validation-pipeline\u002F04.validation-pipe",{"title":4496,"path":4497,"stem":4498},"Декоратори class-validator для DTO","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fclass-validator-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F05.class-validator-decorators",{"title":4500,"path":4501,"stem":4502},"Створення кастомних валідаторів","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-validators","18.web-development\u002F09.nestjs-validation-pipeline\u002F06.custom-validators",{"title":4504,"path":4505,"stem":4506},"Створення власних Pipes","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-pipes","18.web-development\u002F09.nestjs-validation-pipeline\u002F07.custom-pipes",{"title":4508,"path":4509,"stem":4510},"Основи Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-basics","18.web-development\u002F09.nestjs-validation-pipeline\u002F08.middleware-basics",{"title":4512,"path":4513,"stem":4514},"Практичні приклади Middleware","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fmiddleware-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F09.middleware-examples",{"title":4516,"path":4517,"stem":4518},"Guards: захисні перехоплювачі доступу","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fguards-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F10.guards-concept",{"title":4520,"path":4521,"stem":4522},"Створення кастомних Guards","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-guards","18.web-development\u002F09.nestjs-validation-pipeline\u002F11.custom-guards",{"title":4524,"path":4525,"stem":4526},"Interceptors: перехоплення та трансформація відповідей","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptors-concept","18.web-development\u002F09.nestjs-validation-pipeline\u002F12.interceptors-concept",{"title":4528,"path":4529,"stem":4530},"Практичні приклади Interceptors","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Finterceptor-examples","18.web-development\u002F09.nestjs-validation-pipeline\u002F13.interceptor-examples",{"title":4532,"path":4533,"stem":4534},"Exception Filters: обробка виключень","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F14.exception-filters",{"title":4536,"path":4537,"stem":4538},"Custom Exception Filters: спеціалізовані фільтри","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-exception-filters","18.web-development\u002F09.nestjs-validation-pipeline\u002F15.custom-exception-filters",{"title":4540,"path":4541,"stem":4542},"Execution Context: контекст виконання","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fexecution-context","18.web-development\u002F09.nestjs-validation-pipeline\u002F16.execution-context",{"title":4544,"path":4545,"stem":4546},"Custom Decorators: власні декоратори","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fcustom-decorators","18.web-development\u002F09.nestjs-validation-pipeline\u002F17.custom-decorators",{"title":4548,"path":4549,"stem":4550},"Global Components: глобальні компоненти","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fglobal-components","18.web-development\u002F09.nestjs-validation-pipeline\u002F18.global-components",{"title":4552,"path":4553,"stem":4554},"Pipeline Best Practices: найкращі практики","\u002Fweb-development\u002Fnestjs-validation-pipeline\u002Fpipeline-best-practices","18.web-development\u002F09.nestjs-validation-pipeline\u002F19.pipeline-best-practices",{"title":4556,"icon":2865,"path":4557,"stem":4558,"children":4559,"page":59},"Інтеграція реляційних баз даних засобами TypeORM","\u002Fweb-development\u002Ftypeorm-integration","18.web-development\u002F10.typeorm-integration",[4560,4564,4568,4572,4576,4580,4584],{"title":4561,"path":4562,"stem":4563},"Робота з базами даних у Node.js через нативні драйвери","\u002Fweb-development\u002Ftypeorm-integration\u002F01-nodejs-database-drivers","18.web-development\u002F10.typeorm-integration\u002F01-nodejs-database-drivers",{"title":4565,"path":4566,"stem":4567},"ORM та знайомство з TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F02-orm-and-typeorm-intro","18.web-development\u002F10.typeorm-integration\u002F02-orm-and-typeorm-intro",{"title":4569,"path":4570,"stem":4571},"Налаштування TypeORM у NestJS проєкті","\u002Fweb-development\u002Ftypeorm-integration\u002F03-typeorm-setup-nestjs","18.web-development\u002F10.typeorm-integration\u002F03-typeorm-setup-nestjs",{"title":4573,"path":4574,"stem":4575},"Entity класи та декоратори TypeORM","\u002Fweb-development\u002Ftypeorm-integration\u002F04-entities-and-decorators","18.web-development\u002F10.typeorm-integration\u002F04-entities-and-decorators",{"title":4577,"path":4578,"stem":4579},"Repository Pattern та CRUD операції","\u002Fweb-development\u002Ftypeorm-integration\u002F05-repository-pattern-crud","18.web-development\u002F10.typeorm-integration\u002F05-repository-pattern-crud",{"title":4581,"path":4582,"stem":4583},"Пагінація та фільтрація даних","\u002Fweb-development\u002Ftypeorm-integration\u002F06-pagination-filtering","18.web-development\u002F10.typeorm-integration\u002F06-pagination-filtering",{"title":4585,"path":4586,"stem":4587},"QueryBuilder для складних запитів","\u002Fweb-development\u002Ftypeorm-integration\u002F07-query-builder","18.web-development\u002F10.typeorm-integration\u002F07-query-builder",{"title":4589,"icon":4590,"path":4591,"stem":4592,"children":4593,"page":59},"Зв'язки між сутностями, міграції та оптимізація запитів","i-lucide-git-branch","\u002Fweb-development\u002Fentity-relations-migrations","18.web-development\u002F11.entity-relations-migrations",[4594,4598,4602,4606,4610],{"title":4595,"path":4596,"stem":4597},"Зв'язки One-to-Many та Many-to-One","\u002Fweb-development\u002Fentity-relations-migrations\u002F01-one-to-many-many-to-one","18.web-development\u002F11.entity-relations-migrations\u002F01-one-to-many-many-to-one",{"title":4599,"path":4600,"stem":4601},"Зв'язки One-to-One та Many-to-Many","\u002Fweb-development\u002Fentity-relations-migrations\u002F02-one-to-one-many-to-many","18.web-development\u002F11.entity-relations-migrations\u002F02-one-to-one-many-to-many",{"title":4603,"path":4604,"stem":4605},"Керування міграціями бази даних","\u002Fweb-development\u002Fentity-relations-migrations\u002F03-migrations-management","18.web-development\u002F11.entity-relations-migrations\u002F03-migrations-management",{"title":4607,"path":4608,"stem":4609},"Транзакції у TypeORM","\u002Fweb-development\u002Fentity-relations-migrations\u002F04-transactions","18.web-development\u002F11.entity-relations-migrations\u002F04-transactions",{"title":4611,"path":4612,"stem":4613,"children":4614},"Індекси та оптимізація запитів","\u002Fweb-development\u002Fentity-relations-migrations\u002F05-indexes-optimization","18.web-development\u002F11.entity-relations-migrations\u002F05-indexes-optimization",[4615],{"title":4611,"path":4612,"stem":4613},{"title":4617,"icon":4618,"path":4619,"stem":4620,"children":4621,"page":59},"Механізми автентифікації у вебзастосунках","i-lucide-key","\u002Fweb-development\u002Fauthentication","18.web-development\u002F12.authentication",[4622,4626,4630,4634,4638,4642,4646,4650,4654],{"title":4623,"path":4624,"stem":4625},"Автентифікація vs Авторизація","\u002Fweb-development\u002Fauthentication\u002F01-authentication-vs-authorization","18.web-development\u002F12.authentication\u002F01-authentication-vs-authorization",{"title":4627,"path":4628,"stem":4629},"Стратегії автентифікації","\u002Fweb-development\u002Fauthentication\u002F02-authentication-strategies","18.web-development\u002F12.authentication\u002F02-authentication-strategies",{"title":4631,"path":4632,"stem":4633},"Автентифікація на основі сесій","\u002Fweb-development\u002Fauthentication\u002F03-session-based-authentication","18.web-development\u002F12.authentication\u002F03-session-based-authentication",{"title":4635,"path":4636,"stem":4637},"Структура JSON Web Token (JWT)","\u002Fweb-development\u002Fauthentication\u002F04-jwt-structure","18.web-development\u002F12.authentication\u002F04-jwt-structure",{"title":4639,"path":4640,"stem":4641},"Інтеграція JWT у NestJS","\u002Fweb-development\u002Fauthentication\u002F05-nestjs-jwt-integration","18.web-development\u002F12.authentication\u002F05-nestjs-jwt-integration",{"title":4643,"path":4644,"stem":4645},"Passport.js стратегії у NestJS","\u002Fweb-development\u002Fauthentication\u002F06-passport-strategies","18.web-development\u002F12.authentication\u002F06-passport-strategies",{"title":4647,"path":4648,"stem":4649},"Безпечне зберігання паролів: хешування та криптографічний захист","\u002Fweb-development\u002Fauthentication\u002F07-password-hashing","18.web-development\u002F12.authentication\u002F07-password-hashing",{"title":4651,"path":4652,"stem":4653},"Refresh Token та безпечне оновлення доступу","\u002Fweb-development\u002Fauthentication\u002F08-refresh-tokens","18.web-development\u002F12.authentication\u002F08-refresh-tokens",{"title":4655,"path":4656,"stem":4657},"OAuth 2.0 та OpenID Connect: делегована автентифікація","\u002Fweb-development\u002Fauthentication\u002F09-oauth2-openid","18.web-development\u002F12.authentication\u002F09-oauth2-openid",{"title":4659,"icon":4660,"path":4661,"stem":4662,"children":4663,"page":59},"Авторизація та безпека серверних застосунків","i-lucide-shield","\u002Fweb-development\u002Fauthorization-security","18.web-development\u002F13.authorization-security",[4664,4668,4672,4676,4680,4684,4688,4692,4696,4700],{"title":4665,"path":4666,"stem":4667},"Моделі авторизації","\u002Fweb-development\u002Fauthorization-security\u002F01-authorization-models","18.web-development\u002F13.authorization-security\u002F01-authorization-models",{"title":4669,"path":4670,"stem":4671},"Реалізація RBAC у NestJS","\u002Fweb-development\u002Fauthorization-security\u002F02-rbac-implementation","18.web-development\u002F13.authorization-security\u002F02-rbac-implementation",{"title":4673,"path":4674,"stem":4675},"Permission-Based Access Control","\u002Fweb-development\u002Fauthorization-security\u002F03-permission-based-access","18.web-development\u002F13.authorization-security\u002F03-permission-based-access",{"title":4677,"path":4678,"stem":4679},"ABAC та бібліотека CASL","\u002Fweb-development\u002Fauthorization-security\u002F04-abac-casl","18.web-development\u002F13.authorization-security\u002F04-abac-casl",{"title":4681,"path":4682,"stem":4683},"Кастомні декоратори та метадані","\u002Fweb-development\u002Fauthorization-security\u002F05-custom-decorators-metadata","18.web-development\u002F13.authorization-security\u002F05-custom-decorators-metadata",{"title":4685,"path":4686,"stem":4687},"Конфігурація CORS","\u002Fweb-development\u002Fauthorization-security\u002F06-cors-configuration","18.web-development\u002F13.authorization-security\u002F06-cors-configuration",{"title":4689,"path":4690,"stem":4691},"Захист через HTTP Security Headers (Helmet)","\u002Fweb-development\u002Fauthorization-security\u002F07-helmet-security-headers","18.web-development\u002F13.authorization-security\u002F07-helmet-security-headers",{"title":4693,"path":4694,"stem":4695},"Rate Limiting та Throttling","\u002Fweb-development\u002Fauthorization-security\u002F08-rate-limiting-throttling","18.web-development\u002F13.authorization-security\u002F08-rate-limiting-throttling",{"title":4697,"path":4698,"stem":4699},"Захист від поширених атак","\u002Fweb-development\u002Fauthorization-security\u002F09-common-attacks-protection","18.web-development\u002F13.authorization-security\u002F09-common-attacks-protection",{"title":4701,"path":4702,"stem":4703},"HTTPS у продакшені","\u002Fweb-development\u002Fauthorization-security\u002F10-https-production","18.web-development\u002F13.authorization-security\u002F10-https-production",{"title":4705,"icon":871,"path":4706,"stem":4707,"children":4708,"page":59},"Комунікація у реальному часі, нотифікації та фонові задачі","\u002Fweb-development\u002Frealtime-notifications-jobs","18.web-development\u002F14.realtime-notifications-jobs",[4709,4713,4717,4721,4725,4729,4732,4735,4739,4743],{"title":4710,"path":4711,"stem":4712},"Методи комунікації у реальному часі","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F01-realtime-communication-methods","18.web-development\u002F14.realtime-notifications-jobs\u002F01-realtime-communication-methods",{"title":4714,"path":4715,"stem":4716},"WebSocket Gateway у NestJS","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F02-websocket-gateway","18.web-development\u002F14.realtime-notifications-jobs\u002F02-websocket-gateway",{"title":4718,"path":4719,"stem":4720},"Lifecycle та Rooms у WebSocket","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F03-websocket-lifecycle-rooms","18.web-development\u002F14.realtime-notifications-jobs\u002F03-websocket-lifecycle-rooms",{"title":4722,"path":4723,"stem":4724},"Server-Sent Events (SSE)","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F04-server-sent-events","18.web-development\u002F14.realtime-notifications-jobs\u002F04-server-sent-events",{"title":4726,"path":4727,"stem":4728},"Архітектура системи нотифікацій","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F05-notification-system","18.web-development\u002F14.realtime-notifications-jobs\u002F05-notification-system",{"title":904,"path":4730,"stem":4731},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F06-email-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F06-email-notifications",{"title":900,"path":4733,"stem":4734},"\u002Fweb-development\u002Frealtime-notifications-jobs\u002F07-web-push-notifications","18.web-development\u002F14.realtime-notifications-jobs\u002F07-web-push-notifications",{"title":4736,"path":4737,"stem":4738},"Фонові задачі та черги","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F08-background-jobs-queues","18.web-development\u002F14.realtime-notifications-jobs\u002F08-background-jobs-queues",{"title":4740,"path":4741,"stem":4742},"Планувальники та Cron jobs","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F09-schedulers-cron","18.web-development\u002F14.realtime-notifications-jobs\u002F09-schedulers-cron",{"title":4744,"path":4745,"stem":4746},"Практичні сценарії застосування","\u002Fweb-development\u002Frealtime-notifications-jobs\u002F10-practical-scenarios","18.web-development\u002F14.realtime-notifications-jobs\u002F10-practical-scenarios",{"title":4748,"icon":4749,"path":4750,"stem":4751,"children":4752,"page":59},"Тестування, документування та розгортання застосунків","i-lucide-rocket","\u002Fweb-development\u002Ftesting-documentation-deployment","18.web-development\u002F15.testing-documentation-deployment",[4753,4757,4761,4765,4769,4773,4777,4781,4785,4789],{"title":4754,"path":4755,"stem":4756},"Піраміда тестування та стратегія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F01-testing-pyramid-strategy","18.web-development\u002F15.testing-documentation-deployment\u002F01-testing-pyramid-strategy",{"title":4758,"path":4759,"stem":4760},"Основи Jest у NestJS","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F02-jest-nestjs-basics","18.web-development\u002F15.testing-documentation-deployment\u002F02-jest-nestjs-basics",{"title":4762,"path":4763,"stem":4764},"Unit-тестування сервісів","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F03-unit-testing-services","18.web-development\u002F15.testing-documentation-deployment\u002F03-unit-testing-services",{"title":4766,"path":4767,"stem":4768},"E2E тестування та покриття коду","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F04-e2e-testing-coverage","18.web-development\u002F15.testing-documentation-deployment\u002F04-e2e-testing-coverage",{"title":4770,"path":4771,"stem":4772},"Swagger, OpenAPI, Scalar та Arazzo","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F05-swagger-openapi","18.web-development\u002F15.testing-documentation-deployment\u002F05-swagger-openapi",{"title":4774,"path":4775,"stem":4776},"Керування конфігурацією","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F06-configuration-management","18.web-development\u002F15.testing-documentation-deployment\u002F06-configuration-management",{"title":4778,"path":4779,"stem":4780},"Docker та контейнеризація","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F07-docker-containerization","18.web-development\u002F15.testing-documentation-deployment\u002F07-docker-containerization",{"title":4782,"path":4783,"stem":4784},"CI\u002FCD Pipelines","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F08-cicd-pipelines","18.web-development\u002F15.testing-documentation-deployment\u002F08-cicd-pipelines",{"title":4786,"path":4787,"stem":4788},"Логування та моніторинг","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F09-logging-monitoring","18.web-development\u002F15.testing-documentation-deployment\u002F09-logging-monitoring",{"title":4790,"path":4791,"stem":4792},"Серіалізація та компресія","\u002Fweb-development\u002Ftesting-documentation-deployment\u002F10-serialization-compression","18.web-development\u002F15.testing-documentation-deployment\u002F10-serialization-compression",{"title":4794,"icon":4795,"path":4796,"stem":4797,"children":4798,"page":59},"AI Core: мислення AI","i-lucide-brain","\u002Fai-core","19.ai-core",[4799,4840,4889,4927],{"title":4800,"icon":4749,"path":4801,"stem":4802,"children":4803,"page":59},"Вхід у професію AI Native Developer","\u002Fai-core\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer",[4804,4808,4812,4816,4820,4824,4828,4832,4836],{"title":4805,"path":4806,"stem":4807},"Вступ до професії розробника цифрових продуктів","\u002Fai-core\u002Fai-native-developer\u002Fdigital-products","19.ai-core\u002F01.ai-native-developer\u002F01.digital-products",{"title":4809,"path":4810,"stem":4811},"Професія розробника програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fsoftware-developer","19.ai-core\u002F01.ai-native-developer\u002F02.software-developer",{"title":4813,"path":4814,"stem":4815},"Професія AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fai-native-developer","19.ai-core\u002F01.ai-native-developer\u002F03.ai-native-developer",{"title":4817,"path":4818,"stem":4819},"Вплив AI на розробку програмного забезпечення","\u002Fai-core\u002Fai-native-developer\u002Fai-impact-on-development","19.ai-core\u002F01.ai-native-developer\u002F04.ai-impact-on-development",{"title":4821,"path":4822,"stem":4823},"Життєвий цикл цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fproduct-lifecycle","19.ai-core\u002F01.ai-native-developer\u002F05.product-lifecycle",{"title":4825,"path":4826,"stem":4827},"Застосування AI на етапах створення цифрового продукту","\u002Fai-core\u002Fai-native-developer\u002Fai-in-product-creation","19.ai-core\u002F01.ai-native-developer\u002F06.ai-in-product-creation",{"title":4829,"path":4830,"stem":4831},"Розподіл завдань між людиною та AI","\u002Fai-core\u002Fai-native-developer\u002Fhuman-vs-ai-tasks","19.ai-core\u002F01.ai-native-developer\u002F07.human-vs-ai-tasks",{"title":4833,"path":4834,"stem":4835},"Компетенції AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcompetencies","19.ai-core\u002F01.ai-native-developer\u002F08.competencies",{"title":4837,"path":4838,"stem":4839},"Карта професійного розвитку AI Native Developer","\u002Fai-core\u002Fai-native-developer\u002Fcareer-roadmap","19.ai-core\u002F01.ai-native-developer\u002F09.career-roadmap",{"title":4841,"icon":255,"path":4842,"stem":4843,"children":4844,"page":59},"Штучний інтелект і машинне навчання","\u002Fai-core\u002Fai-and-machine-learning","19.ai-core\u002F02.ai-and-machine-learning",[4845,4849,4853,4857,4861,4865,4869,4873,4877,4881,4885],{"title":4846,"path":4847,"stem":4848},"Штучний інтелект","\u002Fai-core\u002Fai-and-machine-learning\u002Fwhat-is-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F01.what-is-ai",{"title":4850,"path":4851,"stem":4852},"Відмінність AI від інших програмних систем","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-vs-automation","19.ai-core\u002F02.ai-and-machine-learning\u002F02.ai-vs-automation",{"title":4854,"path":4855,"stem":4856},"Завдання штучного інтелекту","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-tasks","19.ai-core\u002F02.ai-and-machine-learning\u002F03.ai-tasks",{"title":4858,"path":4859,"stem":4860},"Machine Learning","\u002Fai-core\u002Fai-and-machine-learning\u002Fmachine-learning","19.ai-core\u002F02.ai-and-machine-learning\u002F04.machine-learning",{"title":4862,"path":4863,"stem":4864},"Machine Learning Workflow","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-workflow","19.ai-core\u002F02.ai-and-machine-learning\u002F05.ml-workflow",{"title":4866,"path":4867,"stem":4868},"Типи машинного навчання","\u002Fai-core\u002Fai-and-machine-learning\u002Fml-types","19.ai-core\u002F02.ai-and-machine-learning\u002F06.ml-types",{"title":4870,"path":4871,"stem":4872},"Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fgenerative-ai","19.ai-core\u002F02.ai-and-machine-learning\u002F07.generative-ai",{"title":4874,"path":4875,"stem":4876},"Типи контенту, створюваного AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fai-content-types","19.ai-core\u002F02.ai-and-machine-learning\u002F08.ai-content-types",{"title":4878,"path":4879,"stem":4880},"Великі мовні моделі","\u002Fai-core\u002Fai-and-machine-learning\u002Flarge-language-models","19.ai-core\u002F02.ai-and-machine-learning\u002F09.large-language-models",{"title":4882,"path":4883,"stem":4884},"Можливості та обмеження Generative AI","\u002Fai-core\u002Fai-and-machine-learning\u002Fcapabilities-and-limitations","19.ai-core\u002F02.ai-and-machine-learning\u002F10.capabilities-and-limitations",{"title":4886,"path":4887,"stem":4888},"Сучасні AI-асистенти","\u002Fai-core\u002Fai-and-machine-learning\u002Fmodern-ai-assistants","19.ai-core\u002F02.ai-and-machine-learning\u002F11.modern-ai-assistants",{"title":4890,"icon":4891,"path":4892,"stem":4893,"children":4894,"page":59},"Постановка завдань для AI: принципи створення промптів","i-lucide-message-square-text","\u002Fai-core\u002Fprompt-engineering","19.ai-core\u002F03.prompt-engineering",[4895,4899,4903,4907,4911,4915,4919,4923],{"title":4896,"path":4897,"stem":4898},"Промпт як інструмент","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-as-tool","19.ai-core\u002F03.prompt-engineering\u002F01.prompt-as-tool",{"title":4900,"path":4901,"stem":4902},"Принципи створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-principles","19.ai-core\u002F03.prompt-engineering\u002F02.prompt-principles",{"title":4904,"path":4905,"stem":4906},"Структура промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-structure","19.ai-core\u002F03.prompt-engineering\u002F03.prompt-structure",{"title":4908,"path":4909,"stem":4910},"Види промптів за типом задачі","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-types","19.ai-core\u002F03.prompt-engineering\u002F04.prompt-types",{"title":4912,"path":4913,"stem":4914},"Прийоми посилення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-enhancement","19.ai-core\u002F03.prompt-engineering\u002F05.prompt-enhancement",{"title":4916,"path":4917,"stem":4918},"Розбір і покращення промпта","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-analysis","19.ai-core\u002F03.prompt-engineering\u002F06.prompt-analysis",{"title":4920,"path":4921,"stem":4922},"Типові помилки під час створення промптів","\u002Fai-core\u002Fprompt-engineering\u002Fcommon-mistakes","19.ai-core\u002F03.prompt-engineering\u002F07.common-mistakes",{"title":4924,"path":4925,"stem":4926},"Практикум: особиста бібліотека промптів","\u002Fai-core\u002Fprompt-engineering\u002Fprompt-library","19.ai-core\u002F03.prompt-engineering\u002F08.prompt-library",{"title":4928,"icon":793,"path":4929,"stem":4930,"children":4931,"page":59},"Перевірка результатів, безпека та AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow","19.ai-core\u002F04.verification-security-workflow",[4932,4936,4940,4944,4948,4952,4956,4960,4964],{"title":4933,"path":4934,"stem":4935},"Межі можливостей AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-limitations","19.ai-core\u002F04.verification-security-workflow\u002F01.ai-limitations",{"title":4937,"path":4938,"stem":4939},"Галюцинації AI","\u002Fai-core\u002Fverification-security-workflow\u002Fai-hallucinations","19.ai-core\u002F04.verification-security-workflow\u002F02.ai-hallucinations",{"title":4941,"path":4942,"stem":4943},"Критичне мислення під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fcritical-thinking","19.ai-core\u002F04.verification-security-workflow\u002F03.critical-thinking",{"title":4945,"path":4946,"stem":4947},"Перевірка результатів роботи AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresult-verification","19.ai-core\u002F04.verification-security-workflow\u002F04.result-verification",{"title":4949,"path":4950,"stem":4951},"Захист даних під час роботи з AI","\u002Fai-core\u002Fverification-security-workflow\u002Fdata-protection","19.ai-core\u002F04.verification-security-workflow\u002F05.data-protection",{"title":4953,"path":4954,"stem":4955},"Авторське право та навчальна доброчесність","\u002Fai-core\u002Fverification-security-workflow\u002Fcopyright-integrity","19.ai-core\u002F04.verification-security-workflow\u002F06.copyright-integrity",{"title":4957,"path":4958,"stem":4959},"Відповідальне використання AI","\u002Fai-core\u002Fverification-security-workflow\u002Fresponsible-use","19.ai-core\u002F04.verification-security-workflow\u002F07.responsible-use",{"title":4961,"path":4962,"stem":4963},"AI Native Workflow","\u002Fai-core\u002Fverification-security-workflow\u002Fai-native-workflow","19.ai-core\u002F04.verification-security-workflow\u002F08.ai-native-workflow",{"title":4965,"path":4966,"stem":4967},"Застосування AI Native Workflow під час створення цифрового продукту","\u002Fai-core\u002Fverification-security-workflow\u002Fworkflow-in-practice","19.ai-core\u002F04.verification-security-workflow\u002F09.workflow-in-practice",{"title":4969,"icon":4970,"path":4971,"stem":4972,"children":4973,"page":59},"AI Developer: Vibe Coding Sprint","i-lucide-code-xml","\u002Fai-developer","20.ai-developer",[4974,5000,5022,5043],{"title":4975,"icon":4976,"path":4977,"stem":4978,"children":4979,"page":59},"Проєктування і чорнова версія","i-lucide-pencil-ruler","\u002Fai-developer\u002Fdraft-creation","20.ai-developer\u002F01.draft-creation",[4980,4984,4988,4992,4996],{"title":4981,"path":4982,"stem":4983},"Парадигма Vibe Coding Workflow","\u002Fai-developer\u002Fdraft-creation\u002Fvibe-coding-workflow","20.ai-developer\u002F01.draft-creation\u002F01.vibe-coding-workflow",{"title":4985,"path":4986,"stem":4987},"AI-середовище швидкої розробки","\u002Fai-developer\u002Fdraft-creation\u002Fai-ide-environment","20.ai-developer\u002F01.draft-creation\u002F02.ai-ide-environment",{"title":4989,"path":4990,"stem":4991},"Користувацьке завдання та межі першої версії","\u002Fai-developer\u002Fdraft-creation\u002Fproduct-scope-and-mvp","20.ai-developer\u002F01.draft-creation\u002F03.product-scope-and-mvp",{"title":4993,"path":4994,"stem":4995},"Архітектура інтерфейсу та стани застосунку","\u002Fai-developer\u002Fdraft-creation\u002Fapplication-architecture-and-states","20.ai-developer\u002F01.draft-creation\u002F04.application-architecture-and-states",{"title":4997,"path":4998,"stem":4999},"Генерація та фіксація чорнової версії","\u002Fai-developer\u002Fdraft-creation\u002Fgenerating-draft-version","20.ai-developer\u002F01.draft-creation\u002F05.generating-draft-version",{"title":5001,"icon":5002,"path":5003,"stem":5004,"children":5005,"page":59},"Перша робоча версія","i-lucide-play-circle","\u002Fai-developer\u002Ffirst-working-version","20.ai-developer\u002F02.first-working-version",[5006,5010,5014,5018],{"title":5007,"path":5008,"stem":5009},"Уточнення контексту проєкту для AI","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-project-context","20.ai-developer\u002F02.first-working-version\u002F01.refining-project-context",{"title":5011,"path":5012,"stem":5013},"Стратегія завдань для AI-розробки","\u002Fai-developer\u002Ffirst-working-version\u002Fai-prompting-strategy","20.ai-developer\u002F02.first-working-version\u002F02.ai-prompting-strategy",{"title":5015,"path":5016,"stem":5017},"Доопрацювання до першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Frefining-to-working-version","20.ai-developer\u002F02.first-working-version\u002F03.refining-to-working-version",{"title":5019,"path":5020,"stem":5021},"Перевірка першої робочої версії","\u002Fai-developer\u002Ffirst-working-version\u002Ftesting-first-working-version","20.ai-developer\u002F02.first-working-version\u002F04.testing-first-working-version",{"title":5023,"icon":3072,"path":5024,"stem":5025,"children":5026,"page":59},"Ітерації, дебагінг та відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery","20.ai-developer\u002F03.iteration-debugging-recovery",[5027,5031,5035,5039],{"title":5028,"path":5029,"stem":5030},"Управління точковими змінами продукту","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fchange-management","20.ai-developer\u002F03.iteration-debugging-recovery\u002F01.change-management",{"title":5032,"path":5033,"stem":5034},"Надійність інтерфейсу та обробка помилок","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fscenario-reliability-and-errors","20.ai-developer\u002F03.iteration-debugging-recovery\u002F02.scenario-reliability-and-errors",{"title":5036,"path":5037,"stem":5038},"Керування контекстом і збереження версій","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fproject-context-and-versions","20.ai-developer\u002F03.iteration-debugging-recovery\u002F03.project-context-and-versions",{"title":5040,"path":5041,"stem":5042},"Збої AI-розробки, ліміти та аварійне відновлення","\u002Fai-developer\u002Fiteration-debugging-recovery\u002Fai-breakdowns-and-recovery","20.ai-developer\u002F03.iteration-debugging-recovery\u002F04.ai-breakdowns-and-recovery",{"title":5044,"icon":5045,"path":5046,"stem":5047,"children":5048,"page":59},"Перевірка та завершення продукту","i-lucide-check-check","\u002Fai-developer\u002Fverification-and-completion","20.ai-developer\u002F04.verification-and-completion",[5049,5053,5057],{"title":5050,"path":5051,"stem":5052},"Комплексний аудит та підсумкове тестування","\u002Fai-developer\u002Fverification-and-completion\u002Ffinal-product-testing","20.ai-developer\u002F04.verification-and-completion\u002F01.final-product-testing",{"title":5054,"path":5055,"stem":5056},"Підготовка підсумкової версії коду","\u002Fai-developer\u002Fverification-and-completion\u002Fpreparing-release-version","20.ai-developer\u002F04.verification-and-completion\u002F02.preparing-release-version",{"title":5058,"path":5059,"stem":5060},"Демонстрація, публікація та критерії оцінювання","\u002Fai-developer\u002Fverification-and-completion\u002Fproduct-showcase-and-publishing","20.ai-developer\u002F04.verification-and-completion\u002F03.product-showcase-and-publishing",{"title":5062,"path":5063,"stem":5064,"children":5065,"page":59},"Tailwind","\u002Ftailwind","21.tailwind",[5066,5070,5074,5078,5082,5086,5090,5094,5098,5102,5106,5110],{"title":5067,"path":5068,"stem":5069},"Що таке Tailwind CSS і навіщо він потрібен","\u002Ftailwind\u002Ftailwind-intro-philosophy","21.tailwind\u002F01.tailwind-intro-philosophy",{"title":5071,"path":5072,"stem":5073},"Встановлення та налаштування Tailwind CSS v4","\u002Ftailwind\u002Ftailwind-installation-setup","21.tailwind\u002F02.tailwind-installation-setup",{"title":5075,"path":5076,"stem":5077},"Utility-класи: основи та система Tailwind","\u002Ftailwind\u002Ftailwind-utility-classes-core","21.tailwind\u002F03.tailwind-utility-classes-core",{"title":5079,"path":5080,"stem":5081},"Layout: Flexbox та Grid через Tailwind","\u002Ftailwind\u002Ftailwind-flexbox-grid","21.tailwind\u002F04.tailwind-flexbox-grid",{"title":5083,"path":5084,"stem":5085},"Кастомізація теми через @theme у Tailwind v4","\u002Ftailwind\u002Ftailwind-theme-customization","21.tailwind\u002F05.tailwind-theme-customization",{"title":5087,"path":5088,"stem":5089},"Варіанти: hover, focus, responsive, dark mode та нові v4","\u002Ftailwind\u002Ftailwind-variants-states","21.tailwind\u002F06.tailwind-variants-states",{"title":5091,"path":5092,"stem":5093},"Типографіка та система кольорів у Tailwind v4","\u002Ftailwind\u002Ftailwind-typography-colors","21.tailwind\u002F07.tailwind-typography-colors",{"title":5095,"path":5096,"stem":5097},"Компоненти та повторюваність: @apply, @utility та патерни","\u002Ftailwind\u002Ftailwind-components-patterns","21.tailwind\u002F08.tailwind-components-patterns",{"title":5099,"path":5100,"stem":5101},"Темна тема та система дизайн-токенів у Tailwind v4","\u002Ftailwind\u002Ftailwind-dark-mode-theming","21.tailwind\u002F09.tailwind-dark-mode-theming",{"title":5103,"path":5104,"stem":5105},"Довільні значення та контейнерні запити у Tailwind v4","\u002Ftailwind\u002Ftailwind-arbitrary-container-queries","21.tailwind\u002F10.tailwind-arbitrary-container-queries",{"title":5107,"path":5108,"stem":5109},"Анімації, трансформації та 3D у Tailwind v4","\u002Ftailwind\u002Ftailwind-animations-transforms","21.tailwind\u002F11.tailwind-animations-transforms",{"title":5111,"path":5112,"stem":5113},"Tailwind CLI, PostCSS та інтеграція з фреймворками","\u002Ftailwind\u002Ftailwind-cli-tooling","21.tailwind\u002F12.tailwind-cli-tooling",{"title":5115,"path":5116,"stem":5117,"children":5118,"page":59},"React Typescript","\u002Freact-typescript","22.react-typescript",[5119,5144,5148,5152,5156,5160,5164,5168,5172],{"title":5120,"path":5121,"stem":5122,"children":5123,"page":59},"From Html To Project","\u002Freact-typescript\u002Ffrom-html-to-project","22.react-typescript\u002F01.from-html-to-project",[5124,5128,5132,5136,5140],{"title":5125,"path":5126,"stem":5127},"Від одного HTML-файлу до повноцінного проєкту","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fevolution","22.react-typescript\u002F01.from-html-to-project\u002F01.evolution",{"title":5129,"path":5130,"stem":5131},"Що таке React","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fwhat-is-react","22.react-typescript\u002F01.from-html-to-project\u002F02.what-is-react",{"title":5133,"path":5134,"stem":5135},"JSX та TSX — синтаксичний цукор, а не магія","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-tsx-syntax","22.react-typescript\u002F01.from-html-to-project\u002F03.jsx-tsx-syntax",{"title":5137,"path":5138,"stem":5139},"Компоненти — будівельні блоки інтерфейсу","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fcomponents","22.react-typescript\u002F01.from-html-to-project\u002F04.components",{"title":5141,"path":5142,"stem":5143},"JSX — розмітка всередині TypeScript","\u002Freact-typescript\u002Ffrom-html-to-project\u002Fjsx-expressions","22.react-typescript\u002F01.from-html-to-project\u002F05.jsx-expressions",{"title":5145,"path":5146,"stem":5147},"Хук useReducer: структуроване управління складним станом","\u002Freact-typescript\u002Fuse-reducer","22.react-typescript\u002F23.use-reducer",{"title":5149,"path":5150,"stem":5151},"Context API: передавання даних без «пропс-дрілінгу»","\u002Freact-typescript\u002Fcontext-api","22.react-typescript\u002F24.context-api",{"title":5153,"path":5154,"stem":5155},"Синхронізація з ефектами: хук useEffect та функції очищення","\u002Freact-typescript\u002Fuse-effect","22.react-typescript\u002F27.use-effect",{"title":5157,"path":5158,"stem":5159},"Можливо, вам не потрібен ефект: антипатерни та альтернативи","\u002Freact-typescript\u002Fyou-might-not-need-effect","22.react-typescript\u002F28.you-might-not-need-effect",{"title":5161,"path":5162,"stem":5163},"Життєвий цикл реактивних ефектів: мислення процесами синхронізації","\u002Freact-typescript\u002Flifecycle-of-reactive-effects","22.react-typescript\u002F29.lifecycle-of-reactive-effects",{"title":5165,"path":5166,"stem":5167},"Розділення подій та ефектів: реактивна проти нереактивної логіки","\u002Freact-typescript\u002Fseparating-events-from-effects","22.react-typescript\u002F30.separating-events-from-effects",{"title":5169,"path":5170,"stem":5171},"Видалення зайвих залежностей ефектів та оптимізація синхронізації","\u002Freact-typescript\u002Fremoving-effect-dependencies","22.react-typescript\u002F31.removing-effect-dependencies",{"title":5173,"path":5174,"stem":5175},"Кастомні хуки: повторне використання та композиція реактивної логіки","\u002Freact-typescript\u002Fcustom-hooks","22.react-typescript\u002F32.custom-hooks",{"title":5177,"path":5178,"stem":5179},"Тестування компонентів діаграм та пісочниць","\u002Ftest-components","98.test-components",{"id":5181,"title":3735,"body":5182,"description":11796,"extension":11797,"links":11798,"meta":11799,"navigation":5349,"path":3736,"seo":11800,"stem":3737,"__hash__":11801},"docs\u002F16.ai-python\u002F04.statistics-basics\u002F03.variability.md",{"type":5183,"value":5184,"toc":11760},"minimark",[5185,5189,5269,5272,5277,5281,5300,5307,5529,5543,5553,5562,5576,5579,5593,5639,5641,5645,5652,5657,5660,5664,5982,5988,5992,5999,6238,6244,6279,6281,6285,6300,6304,6311,6329,6333,6342,6345,6354,6357,6429,6506,6510,6983,6988,6992,6995,7252,7257,7277,7295,7302,7304,7308,7319,7322,7325,7329,7349,7702,7707,7711,7730,8122,8129,8175,8177,8181,8184,8198,8201,8217,8220,8685,8732,8750,8752,8756,8765,8768,8792,8802,8822,8970,8977,8981,9446,9451,9453,9457,9465,9468,9478,9482,9917,9924,9934,9970,10007,10009,10013,10020,10026,10045,10055,10757,10798,10805,10807,10811,10932,10934,10938,10942,11049,11051,11055,11224,11226,11230,11329,11331,11335,11492,11494,11498,11670,11672,11676,11679,11693,11704,11706,11717,11728,11756],[5186,5187,3735],"h1",{"id":5188},"міри-варіації-розсіювання",[5190,5191,5192,5216],"card-group",{},[5193,5194,5197],"card",{"icon":5195,"title":5196},"i-lucide-target","🎯 Мета підтеми",[5198,5199,5200,5204,5207,5210,5213],"ul",{},[5201,5202,5203],"li",{},"Зрозуміти, що таке варіація (розсіювання) даних",[5201,5205,5206],{},"Навчитися обчислювати дисперсію та стандартне відхилення",[5201,5208,5209],{},"Розпізнавати високо- та низьковаріативні дані",[5201,5211,5212],{},"Опанувати квартилі та міжквартильний розмах (IQR)",[5201,5214,5215],{},"Побачити зв'язок між варіацією та передбачуваністю в ML",[5193,5217,5219],{"icon":4618,"title":5218},"🔑 Ключові терміни",[5198,5220,5221,5233,5242,5251,5260],{},[5201,5222,5223,5227,5228,5232],{},[5224,5225,5226],"strong",{},"Розмах"," (",[5229,5230,5231],"em",{},"range",") — різниця між максимальним та мінімальним значенням",[5201,5234,5235,5227,5238,5241],{},[5224,5236,5237],{},"Дисперсія",[5229,5239,5240],{},"variance",", σ²) — середній квадрат відхилення від середнього",[5201,5243,5244,5227,5247,5250],{},[5224,5245,5246],{},"Стандартне відхилення",[5229,5248,5249],{},"standard deviation",", σ) — квадратний корінь із дисперсії",[5201,5252,5253,5227,5256,5259],{},[5224,5254,5255],{},"Квартилі",[5229,5257,5258],{},"quartiles",") — значення, що поділяють дані на 4 рівні частини",[5201,5261,5262,5227,5265,5268],{},[5224,5263,5264],{},"Міжквартильний розмах",[5229,5266,5267],{},"IQR",") — різниця між Q3 і Q1, стійка до аутлайерів",[5270,5271],"hr",{},[5273,5274,5276],"h2",{"id":5275},"два-стрільці-одна-мішень-задача-про-стабільність","Два стрільці, одна мішень: задача про стабільність",[5278,5279,5280],"p",{},"Уявіть: двоє стрільців — Олексій та Борис — стріляють по мішені. Кожен робить 10 пострілів. Підраховуємо відстань від центру мішені до кожного влучення (у сантиметрах):",[5278,5282,5283,5286,5287,5291,5294,5286,5297],{},[5224,5284,5285],{},"Олексій:"," ",[5288,5289,5290],"code",{},"[8, 7, 9, 8, 8, 7, 9, 8, 8, 8]",[5292,5293],"br",{},[5224,5295,5296],{},"Борис:",[5288,5298,5299],{},"[2, 5, 15, 12, 3, 18, 1, 10, 4, 10]",[5278,5301,5302,5303,5306],{},"Хто кращий стрілець? Давайте порахуємо ",[5224,5304,5305],{},"середню"," відстань від центру:",[5308,5309,5312],"jupyter-notebook",{"kernel":5310,"title":5311},"Python 3 (ipykernel)","shooters_comparison.ipynb",[5313,5314,5316,5518],"jupyter-cell",{"execution-count":5315},"1",[5317,5318,5323],"pre",{"className":5319,"code":5320,"language":5321,"meta":5322,"style":5322},"language-python shiki shiki-themes light-plus dark-plus dark-plus","import numpy as np\n\noleksiy = np.array([8, 7, 9, 8, 8, 7, 9, 8, 8, 8])\nborys = np.array([2, 5, 15, 12, 3, 18, 1, 10, 4, 10])\n\nprint(f\"Олексій - середня відстань: {oleksiy.mean():.1f} см\")\nprint(f\"Борис   - середня відстань: {borys.mean():.1f} см\")\n","python","",[5288,5324,5325,5344,5351,5403,5457,5462,5495],{"__ignoreMap":5322},[5326,5327,5330,5334,5338,5341],"span",{"class":5328,"line":5329},"line",1,[5326,5331,5333],{"class":5332},"s8xlr","import",[5326,5335,5337],{"class":5336},"sHH4Y"," numpy ",[5326,5339,5340],{"class":5332},"as",[5326,5342,5343],{"class":5336}," np\n",[5326,5345,5347],{"class":5328,"line":5346},2,[5326,5348,5350],{"emptyLinePlaceholder":5349},true,"\n",[5326,5352,5354,5357,5361,5364,5367,5369,5372,5374,5376,5378,5380,5382,5384,5386,5388,5390,5392,5394,5396,5398,5400],{"class":5328,"line":5353},3,[5326,5355,5356],{"class":5336},"oleksiy = np.array([",[5326,5358,5360],{"class":5359},"sJj4R","8",[5326,5362,5363],{"class":5336},", ",[5326,5365,5366],{"class":5359},"7",[5326,5368,5363],{"class":5336},[5326,5370,5371],{"class":5359},"9",[5326,5373,5363],{"class":5336},[5326,5375,5360],{"class":5359},[5326,5377,5363],{"class":5336},[5326,5379,5360],{"class":5359},[5326,5381,5363],{"class":5336},[5326,5383,5366],{"class":5359},[5326,5385,5363],{"class":5336},[5326,5387,5371],{"class":5359},[5326,5389,5363],{"class":5336},[5326,5391,5360],{"class":5359},[5326,5393,5363],{"class":5336},[5326,5395,5360],{"class":5359},[5326,5397,5363],{"class":5336},[5326,5399,5360],{"class":5359},[5326,5401,5402],{"class":5336},"])\n",[5326,5404,5406,5409,5412,5414,5417,5419,5422,5424,5427,5429,5432,5434,5437,5439,5441,5443,5446,5448,5451,5453,5455],{"class":5328,"line":5405},4,[5326,5407,5408],{"class":5336},"borys = np.array([",[5326,5410,5411],{"class":5359},"2",[5326,5413,5363],{"class":5336},[5326,5415,5416],{"class":5359},"5",[5326,5418,5363],{"class":5336},[5326,5420,5421],{"class":5359},"15",[5326,5423,5363],{"class":5336},[5326,5425,5426],{"class":5359},"12",[5326,5428,5363],{"class":5336},[5326,5430,5431],{"class":5359},"3",[5326,5433,5363],{"class":5336},[5326,5435,5436],{"class":5359},"18",[5326,5438,5363],{"class":5336},[5326,5440,5315],{"class":5359},[5326,5442,5363],{"class":5336},[5326,5444,5445],{"class":5359},"10",[5326,5447,5363],{"class":5336},[5326,5449,5450],{"class":5359},"4",[5326,5452,5363],{"class":5336},[5326,5454,5445],{"class":5359},[5326,5456,5402],{"class":5336},[5326,5458,5460],{"class":5328,"line":5459},5,[5326,5461,5350],{"emptyLinePlaceholder":5349},[5326,5463,5465,5469,5472,5476,5480,5483,5486,5489,5492],{"class":5328,"line":5464},6,[5326,5466,5468],{"class":5467},"s8Opu","print",[5326,5470,5471],{"class":5336},"(",[5326,5473,5475],{"class":5474},"su1O8","f",[5326,5477,5479],{"class":5478},"sbdoH","\"Олексій - середня відстань: ",[5326,5481,5482],{"class":5474},"{",[5326,5484,5485],{"class":5336},"oleksiy.mean()",[5326,5487,5488],{"class":5474},":.1f}",[5326,5490,5491],{"class":5478}," см\"",[5326,5493,5494],{"class":5336},")\n",[5326,5496,5498,5500,5502,5504,5507,5509,5512,5514,5516],{"class":5328,"line":5497},7,[5326,5499,5468],{"class":5467},[5326,5501,5471],{"class":5336},[5326,5503,5475],{"class":5474},[5326,5505,5506],{"class":5478},"\"Борис   - середня відстань: ",[5326,5508,5482],{"class":5474},[5326,5510,5511],{"class":5336},"borys.mean()",[5326,5513,5488],{"class":5474},[5326,5515,5491],{"class":5478},[5326,5517,5494],{"class":5336},[5519,5520,5521],"template",{"v-slot:output":5322},[5317,5522,5527],{"className":5523,"code":5525,"language":5526},[5524],"language-text","Олексій - середня відстань: 8.0 см\nБорис   - середня відстань: 8.0 см\n","text",[5288,5528,5525],{"__ignoreMap":5322},[5278,5530,5531,5534,5535,5538,5539,5542],{},[5224,5532,5533],{},"Середнє однакове!"," Але інтуїтивно ми розуміємо, що Олексій стріляє ",[5224,5536,5537],{},"стабільніше"," — всі його постріли в діапазоні 7–9 см. Борис «стрибає» від 1 до 18 см — він ",[5224,5540,5541],{},"нестабільний",".",[5544,5545,5546],"blockquote",{},[5278,5547,5548,5549,5552],{},"Аналогія: Уявіть двох водіїв автобуса. Перший їде плавно — пасажири стоять спокійно. Другий постійно різко гальмує та прискорюється — пасажири хитаються. Обидва доїхали за однаковий час (середнє), але ",[5224,5550,5551],{},"комфорт"," (стабільність) зовсім різний.",[5278,5554,5555],{},[5556,5557],"img",{"alt":5558,"className":5559,"src":5561},"Порівняння стабільності двох стрільців: однакове середнє, але різна варіація",[5560],"diagram-img","\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F01.png",[5278,5563,5564,5565,5568,5569,5572,5573,5542],{},"Саме для вимірювання цієї ",[5224,5566,5567],{},"розкиданості"," (варіації, розсіювання) існують спеціальні міри. Середнє показує ",[5224,5570,5571],{},"центр"," даних, а міри варіації показують, наскільки дані ",[5224,5574,5575],{},"розкидані навколо центру",[5278,5577,5578],{},"У Machine Learning варіація критична:",[5198,5580,5581,5587],{},[5201,5582,5583,5586],{},[5224,5584,5585],{},"Низька варіація"," → передбачуваність (ознака стабільна, модель може на неї покластися)",[5201,5588,5589,5592],{},[5224,5590,5591],{},"Висока варіація"," → невизначеність (ознака «шумна», потрібна обережність)",[5594,5595,5596,5601,5604],"note",{},[5278,5597,5598],{},[5224,5599,5600],{},"Інженерна аналогія: Мережевий Ping проти Jitter (тремтіння затримки)",[5278,5602,5603],{},"У комп'ютерних мережах та онлайн-іграх варіація затримок пакета часто критичніша за сам пінг:",[5198,5605,5606,5618],{},[5201,5607,5608,5611,5612,5617],{},[5224,5609,5610],{},"Провайдер A:"," середній пінг = 30 мс, але розкид коливається строго в діапазоні 29–31 мс (стандартне відхилення ",[5613,5614],"math-formula",{"tex":5615,":inline":5616},"\\sigma \\approx 0.5","true"," мс). Пакети надходять монотонно і плавно — онлайн-гра працює без жодних мікро-зависань.",[5201,5619,5620,5623,5624,5627,5628,5227,5631,5634,5635,5638],{},[5224,5621,5622],{},"Провайдер B:"," середній пінг теж = 30 мс! Але пакети надходять хаотично: 5 мс, 60 мс, 12 мс, 90 мс, 1 мс (",[5613,5625],{"tex":5626,":inline":5616},"\\sigma \\approx 35"," мс). Виникає ",[5224,5629,5630],{},"джиттер",[5229,5632,5633],{},"network jitter",") — буфер переповнюється, пакети прибувають поза порядком, гравець спостерігає різкі лаги (",[5229,5636,5637],{},"stuttering","), хоча середнє арифметичне пінгу в обох провайдерів однакове.",[5270,5640],{},[5273,5642,5644],{"id":5643},"розмах-range-найпростіша-міра","Розмах (Range): найпростіша міра",[5278,5646,5647,5227,5649,5651],{},[5224,5648,5226],{},[5229,5650,5231],{},") — це різниця між максимальним та мінімальним значенням у даних.",[5653,5654,5656],"h3",{"id":5655},"формула","Формула",[5613,5658],{"tex":5659},"\\text{Range} = \\text{max}(X) - \\text{min}(X)",[5653,5661,5663],{"id":5662},"обчислення","Обчислення",[5308,5665,5667,5674],{"kernel":5310,"title":5666},"range_calculation.ipynb",[5313,5668,5670],{"type":5669},"markdown",[5653,5671,5673],{"id":5672},"розмах-для-двох-стрільців","Розмах для двох стрільців",[5313,5675,5676,5974],{"execution-count":5315},[5317,5677,5679],{"className":5319,"code":5678,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\noleksiy = np.array([8, 7, 9, 8, 8, 7, 9, 8, 8, 8])\nborys = np.array([2, 5, 15, 12, 3, 18, 1, 10, 4, 10])\n\nrange_oleksiy = oleksiy.max() - oleksiy.min()\nrange_borys = borys.max() - borys.min()\n\nprint(\"Олексій:\")\nprint(f\"  Мінімум: {oleksiy.min()} см\")\nprint(f\"  Максимум: {oleksiy.max()} см\")\nprint(f\"  Розмах: {range_oleksiy} см\")\n\nprint(\"\\nБорис:\")\nprint(f\"  Мінімум: {borys.min()} см\")\nprint(f\"  Максимум: {borys.max()} см\")\nprint(f\"  Розмах: {range_borys} см\")\n",[5288,5680,5681,5691,5695,5739,5783,5787,5792,5797,5802,5814,5838,5861,5884,5889,5908,5930,5952],{"__ignoreMap":5322},[5326,5682,5683,5685,5687,5689],{"class":5328,"line":5329},[5326,5684,5333],{"class":5332},[5326,5686,5337],{"class":5336},[5326,5688,5340],{"class":5332},[5326,5690,5343],{"class":5336},[5326,5692,5693],{"class":5328,"line":5346},[5326,5694,5350],{"emptyLinePlaceholder":5349},[5326,5696,5697,5699,5701,5703,5705,5707,5709,5711,5713,5715,5717,5719,5721,5723,5725,5727,5729,5731,5733,5735,5737],{"class":5328,"line":5353},[5326,5698,5356],{"class":5336},[5326,5700,5360],{"class":5359},[5326,5702,5363],{"class":5336},[5326,5704,5366],{"class":5359},[5326,5706,5363],{"class":5336},[5326,5708,5371],{"class":5359},[5326,5710,5363],{"class":5336},[5326,5712,5360],{"class":5359},[5326,5714,5363],{"class":5336},[5326,5716,5360],{"class":5359},[5326,5718,5363],{"class":5336},[5326,5720,5366],{"class":5359},[5326,5722,5363],{"class":5336},[5326,5724,5371],{"class":5359},[5326,5726,5363],{"class":5336},[5326,5728,5360],{"class":5359},[5326,5730,5363],{"class":5336},[5326,5732,5360],{"class":5359},[5326,5734,5363],{"class":5336},[5326,5736,5360],{"class":5359},[5326,5738,5402],{"class":5336},[5326,5740,5741,5743,5745,5747,5749,5751,5753,5755,5757,5759,5761,5763,5765,5767,5769,5771,5773,5775,5777,5779,5781],{"class":5328,"line":5405},[5326,5742,5408],{"class":5336},[5326,5744,5411],{"class":5359},[5326,5746,5363],{"class":5336},[5326,5748,5416],{"class":5359},[5326,5750,5363],{"class":5336},[5326,5752,5421],{"class":5359},[5326,5754,5363],{"class":5336},[5326,5756,5426],{"class":5359},[5326,5758,5363],{"class":5336},[5326,5760,5431],{"class":5359},[5326,5762,5363],{"class":5336},[5326,5764,5436],{"class":5359},[5326,5766,5363],{"class":5336},[5326,5768,5315],{"class":5359},[5326,5770,5363],{"class":5336},[5326,5772,5445],{"class":5359},[5326,5774,5363],{"class":5336},[5326,5776,5450],{"class":5359},[5326,5778,5363],{"class":5336},[5326,5780,5445],{"class":5359},[5326,5782,5402],{"class":5336},[5326,5784,5785],{"class":5328,"line":5459},[5326,5786,5350],{"emptyLinePlaceholder":5349},[5326,5788,5789],{"class":5328,"line":5464},[5326,5790,5791],{"class":5336},"range_oleksiy = oleksiy.max() - oleksiy.min()\n",[5326,5793,5794],{"class":5328,"line":5497},[5326,5795,5796],{"class":5336},"range_borys = borys.max() - borys.min()\n",[5326,5798,5800],{"class":5328,"line":5799},8,[5326,5801,5350],{"emptyLinePlaceholder":5349},[5326,5803,5805,5807,5809,5812],{"class":5328,"line":5804},9,[5326,5806,5468],{"class":5467},[5326,5808,5471],{"class":5336},[5326,5810,5811],{"class":5478},"\"Олексій:\"",[5326,5813,5494],{"class":5336},[5326,5815,5817,5819,5821,5823,5826,5828,5831,5834,5836],{"class":5328,"line":5816},10,[5326,5818,5468],{"class":5467},[5326,5820,5471],{"class":5336},[5326,5822,5475],{"class":5474},[5326,5824,5825],{"class":5478},"\"  Мінімум: ",[5326,5827,5482],{"class":5474},[5326,5829,5830],{"class":5336},"oleksiy.min()",[5326,5832,5833],{"class":5474},"}",[5326,5835,5491],{"class":5478},[5326,5837,5494],{"class":5336},[5326,5839,5841,5843,5845,5847,5850,5852,5855,5857,5859],{"class":5328,"line":5840},11,[5326,5842,5468],{"class":5467},[5326,5844,5471],{"class":5336},[5326,5846,5475],{"class":5474},[5326,5848,5849],{"class":5478},"\"  Максимум: ",[5326,5851,5482],{"class":5474},[5326,5853,5854],{"class":5336},"oleksiy.max()",[5326,5856,5833],{"class":5474},[5326,5858,5491],{"class":5478},[5326,5860,5494],{"class":5336},[5326,5862,5864,5866,5868,5870,5873,5875,5878,5880,5882],{"class":5328,"line":5863},12,[5326,5865,5468],{"class":5467},[5326,5867,5471],{"class":5336},[5326,5869,5475],{"class":5474},[5326,5871,5872],{"class":5478},"\"  Розмах: ",[5326,5874,5482],{"class":5474},[5326,5876,5877],{"class":5336},"range_oleksiy",[5326,5879,5833],{"class":5474},[5326,5881,5491],{"class":5478},[5326,5883,5494],{"class":5336},[5326,5885,5887],{"class":5328,"line":5886},13,[5326,5888,5350],{"emptyLinePlaceholder":5349},[5326,5890,5892,5894,5896,5899,5903,5906],{"class":5328,"line":5891},14,[5326,5893,5468],{"class":5467},[5326,5895,5471],{"class":5336},[5326,5897,5898],{"class":5478},"\"",[5326,5900,5902],{"class":5901},"sjcCO","\\n",[5326,5904,5905],{"class":5478},"Борис:\"",[5326,5907,5494],{"class":5336},[5326,5909,5911,5913,5915,5917,5919,5921,5924,5926,5928],{"class":5328,"line":5910},15,[5326,5912,5468],{"class":5467},[5326,5914,5471],{"class":5336},[5326,5916,5475],{"class":5474},[5326,5918,5825],{"class":5478},[5326,5920,5482],{"class":5474},[5326,5922,5923],{"class":5336},"borys.min()",[5326,5925,5833],{"class":5474},[5326,5927,5491],{"class":5478},[5326,5929,5494],{"class":5336},[5326,5931,5933,5935,5937,5939,5941,5943,5946,5948,5950],{"class":5328,"line":5932},16,[5326,5934,5468],{"class":5467},[5326,5936,5471],{"class":5336},[5326,5938,5475],{"class":5474},[5326,5940,5849],{"class":5478},[5326,5942,5482],{"class":5474},[5326,5944,5945],{"class":5336},"borys.max()",[5326,5947,5833],{"class":5474},[5326,5949,5491],{"class":5478},[5326,5951,5494],{"class":5336},[5326,5953,5955,5957,5959,5961,5963,5965,5968,5970,5972],{"class":5328,"line":5954},17,[5326,5956,5468],{"class":5467},[5326,5958,5471],{"class":5336},[5326,5960,5475],{"class":5474},[5326,5962,5872],{"class":5478},[5326,5964,5482],{"class":5474},[5326,5966,5967],{"class":5336},"range_borys",[5326,5969,5833],{"class":5474},[5326,5971,5491],{"class":5478},[5326,5973,5494],{"class":5336},[5519,5975,5976],{"v-slot:output":5322},[5317,5977,5980],{"className":5978,"code":5979,"language":5526},[5524],"Олексій:\n  Мінімум: 7 см\n  Максимум: 9 см\n  Розмах: 2 см\n\nБорис:\n  Мінімум: 1 см\n  Максимум: 18 см\n  Розмах: 17 см\n",[5288,5981,5979],{"__ignoreMap":5322},[5278,5983,5984,5987],{},[5224,5985,5986],{},"Тепер бачимо різницю!"," Олексій має розмах 2 см (дуже стабільний), Борис — 17 см (нестабільний).",[5653,5989,5991],{"id":5990},"проблема-розмаху-чутливість-до-аутлайерів","Проблема розмаху: чутливість до аутлайерів",[5278,5993,5994,5995,5998],{},"Розмах використовує ",[5224,5996,5997],{},"лише два значення"," — мінімум та максимум. Все, що між ними, ігнорується. Це робить його дуже чутливим до екстремальних значень:",[5308,6000,6002],{"kernel":5310,"title":6001},"range_outlier_problem.ipynb",[5313,6003,6004,6230],{"execution-count":5315},[5317,6005,6007],{"className":5319,"code":6006,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Оцінки студентів (за 100-бальною шкалою)\ngrades_normal = np.array([82, 85, 88, 84, 86, 87, 83, 85, 86, 84])\ngrades_with_outlier = np.array([82, 85, 88, 84, 86, 87, 83, 85, 86, 15])  # один студент списав і отримав 15\n\nrange_normal = grades_normal.max() - grades_normal.min()\nrange_with_outlier = grades_with_outlier.max() - grades_with_outlier.min()\n\nprint(f\"Розмах БЕЗ аутлайера: {range_normal} балів\")\nprint(f\"Розмах З аутлайером:  {range_with_outlier} балів\")\nprint(f\"Зміна: {range_with_outlier - range_normal} балів ({(range_with_outlier - range_normal) \u002F range_normal * 100:.0f}% збільшення)\")\n",[5288,6008,6009,6019,6023,6029,6081,6130,6134,6139,6144,6148,6171,6193],{"__ignoreMap":5322},[5326,6010,6011,6013,6015,6017],{"class":5328,"line":5329},[5326,6012,5333],{"class":5332},[5326,6014,5337],{"class":5336},[5326,6016,5340],{"class":5332},[5326,6018,5343],{"class":5336},[5326,6020,6021],{"class":5328,"line":5346},[5326,6022,5350],{"emptyLinePlaceholder":5349},[5326,6024,6025],{"class":5328,"line":5353},[5326,6026,6028],{"class":6027},"spJ8K","# Оцінки студентів (за 100-бальною шкалою)\n",[5326,6030,6031,6034,6037,6039,6042,6044,6047,6049,6052,6054,6057,6059,6062,6064,6067,6069,6071,6073,6075,6077,6079],{"class":5328,"line":5405},[5326,6032,6033],{"class":5336},"grades_normal = np.array([",[5326,6035,6036],{"class":5359},"82",[5326,6038,5363],{"class":5336},[5326,6040,6041],{"class":5359},"85",[5326,6043,5363],{"class":5336},[5326,6045,6046],{"class":5359},"88",[5326,6048,5363],{"class":5336},[5326,6050,6051],{"class":5359},"84",[5326,6053,5363],{"class":5336},[5326,6055,6056],{"class":5359},"86",[5326,6058,5363],{"class":5336},[5326,6060,6061],{"class":5359},"87",[5326,6063,5363],{"class":5336},[5326,6065,6066],{"class":5359},"83",[5326,6068,5363],{"class":5336},[5326,6070,6041],{"class":5359},[5326,6072,5363],{"class":5336},[5326,6074,6056],{"class":5359},[5326,6076,5363],{"class":5336},[5326,6078,6051],{"class":5359},[5326,6080,5402],{"class":5336},[5326,6082,6083,6086,6088,6090,6092,6094,6096,6098,6100,6102,6104,6106,6108,6110,6112,6114,6116,6118,6120,6122,6124,6127],{"class":5328,"line":5459},[5326,6084,6085],{"class":5336},"grades_with_outlier = np.array([",[5326,6087,6036],{"class":5359},[5326,6089,5363],{"class":5336},[5326,6091,6041],{"class":5359},[5326,6093,5363],{"class":5336},[5326,6095,6046],{"class":5359},[5326,6097,5363],{"class":5336},[5326,6099,6051],{"class":5359},[5326,6101,5363],{"class":5336},[5326,6103,6056],{"class":5359},[5326,6105,5363],{"class":5336},[5326,6107,6061],{"class":5359},[5326,6109,5363],{"class":5336},[5326,6111,6066],{"class":5359},[5326,6113,5363],{"class":5336},[5326,6115,6041],{"class":5359},[5326,6117,5363],{"class":5336},[5326,6119,6056],{"class":5359},[5326,6121,5363],{"class":5336},[5326,6123,5421],{"class":5359},[5326,6125,6126],{"class":5336},"])  ",[5326,6128,6129],{"class":6027},"# один студент списав і отримав 15\n",[5326,6131,6132],{"class":5328,"line":5464},[5326,6133,5350],{"emptyLinePlaceholder":5349},[5326,6135,6136],{"class":5328,"line":5497},[5326,6137,6138],{"class":5336},"range_normal = grades_normal.max() - grades_normal.min()\n",[5326,6140,6141],{"class":5328,"line":5799},[5326,6142,6143],{"class":5336},"range_with_outlier = grades_with_outlier.max() - grades_with_outlier.min()\n",[5326,6145,6146],{"class":5328,"line":5804},[5326,6147,5350],{"emptyLinePlaceholder":5349},[5326,6149,6150,6152,6154,6156,6159,6161,6164,6166,6169],{"class":5328,"line":5816},[5326,6151,5468],{"class":5467},[5326,6153,5471],{"class":5336},[5326,6155,5475],{"class":5474},[5326,6157,6158],{"class":5478},"\"Розмах БЕЗ аутлайера: ",[5326,6160,5482],{"class":5474},[5326,6162,6163],{"class":5336},"range_normal",[5326,6165,5833],{"class":5474},[5326,6167,6168],{"class":5478}," балів\"",[5326,6170,5494],{"class":5336},[5326,6172,6173,6175,6177,6179,6182,6184,6187,6189,6191],{"class":5328,"line":5840},[5326,6174,5468],{"class":5467},[5326,6176,5471],{"class":5336},[5326,6178,5475],{"class":5474},[5326,6180,6181],{"class":5478},"\"Розмах З аутлайером:  ",[5326,6183,5482],{"class":5474},[5326,6185,6186],{"class":5336},"range_with_outlier",[5326,6188,5833],{"class":5474},[5326,6190,6168],{"class":5478},[5326,6192,5494],{"class":5336},[5326,6194,6195,6197,6199,6201,6204,6206,6209,6211,6214,6216,6219,6222,6225,6228],{"class":5328,"line":5863},[5326,6196,5468],{"class":5467},[5326,6198,5471],{"class":5336},[5326,6200,5475],{"class":5474},[5326,6202,6203],{"class":5478},"\"Зміна: ",[5326,6205,5482],{"class":5474},[5326,6207,6208],{"class":5336},"range_with_outlier - range_normal",[5326,6210,5833],{"class":5474},[5326,6212,6213],{"class":5478}," балів (",[5326,6215,5482],{"class":5474},[5326,6217,6218],{"class":5336},"(range_with_outlier - range_normal) \u002F range_normal * ",[5326,6220,6221],{"class":5359},"100",[5326,6223,6224],{"class":5474},":.0f}",[5326,6226,6227],{"class":5478},"% збільшення)\"",[5326,6229,5494],{"class":5336},[5519,6231,6232],{"v-slot:output":5322},[5317,6233,6236],{"className":6234,"code":6235,"language":5526},[5524],"Розмах БЕЗ аутлайера: 6 балів\nРозмах З аутлайером:  73 балів\nЗміна: 67 балів (1117% збільшення)\n",[5288,6237,6235],{"__ignoreMap":5322},[5278,6239,6240,6243],{},[5224,6241,6242],{},"Один аутлайер збільшив розмах у 12 разів!"," Розмах більше не відображає реальну варіацію основної маси даних.",[6245,6246,6247,6252,6263,6268],"warning",{},[5278,6248,6249],{},[5224,6250,6251],{},"Коли НЕ використовувати розмах:",[5198,6253,6254,6257,6260],{},[5201,6255,6256],{},"Дані містять аутлайери",[5201,6258,6259],{},"Потрібна точна міра варіації (розмах дуже грубий)",[5201,6261,6262],{},"Порівнюються датасети різного розміру (розмах зростає зі збільшенням даних)",[5278,6264,6265],{},[5224,6266,6267],{},"Коли розмах корисний:",[5198,6269,6270,6273,6276],{},[5201,6271,6272],{},"Швидка оцінка діапазону даних (min–max)",[5201,6274,6275],{},"Перевірка на очевидні помилки введення",[5201,6277,6278],{},"Побудова шкал графіків",[5270,6280],{},[5273,6282,6284],{"id":6283},"дисперсія-variance-математично-точна-міра","Дисперсія (Variance): математично точна міра",[5278,6286,6287,5227,6289,6291,6292,6295,6296,6299],{},[5224,6288,5237],{},[5229,6290,5240],{},", позначається σ² або s²) — це ",[5224,6293,6294],{},"середній квадрат відхилення"," кожного значення від середнього. Вона враховує ",[5224,6297,6298],{},"всі дані",", а не тільки крайні значення.",[5653,6301,6303],{"id":6302},"інтуїтивне-пояснення","Інтуїтивне пояснення",[5278,6305,6306,6307,6310],{},"Дисперсія відповідає на запитання: «Наскільки далеко ",[5224,6308,6309],{},"в середньому"," знаходяться дані від їхнього центру (середнього)?»",[6312,6313,6314,6317,6323,6326],"ol",{},[5201,6315,6316],{},"Беремо кожне значення",[5201,6318,6319,6320],{},"Обчислюємо, наскільки воно відхиляється від середнього: ",[5613,6321],{"tex":6322,":inline":5616},"x_i - \\bar{x}",[5201,6324,6325],{},"Возводимо це відхилення в квадрат (щоб негативні та позитивні не анулювали одне одного)",[5201,6327,6328],{},"Обчислюємо середнє цих квадратів",[5653,6330,6332],{"id":6331},"формули","Формули",[5278,6334,6335,5227,6338,6341],{},[5224,6336,6337],{},"Дисперсія генеральної сукупності",[5229,6339,6340],{},"population variance",", σ²):",[5613,6343],{"tex":6344},"\\sigma^2 = \\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\mu)^2",[5278,6346,6347,5227,6350,6353],{},[5224,6348,6349],{},"Дисперсія вибірки",[5229,6351,6352],{},"sample variance",", s²):",[5613,6355],{"tex":6356},"s^2 = \\frac{1}{n-1} \\sum_{i=1}^{n} (x_i - \\bar{x})^2",[5594,6358,6359,6364,6385,6405],{},[5278,6360,6361],{},[5224,6362,6363],{},"Різниця між n та n−1:",[5198,6365,6366,6376],{},[5201,6367,6368,6371,6372,6375],{},[5224,6369,6370],{},"n"," — використовується, коли у вас ",[5224,6373,6374],{},"усі дані"," (генеральна сукупність)",[5201,6377,6378,6371,6381,6384],{},[5224,6379,6380],{},"n−1",[5224,6382,6383],{},"вибірка"," з більшої сукупності (поправка Бесселя для незміщеної оцінки)",[5278,6386,6387,6388,6391,6392,6394,6395,6391,6398,6400,6401,6404],{},"У NumPy за замовчуванням ",[5288,6389,6390],{},"np.var()"," використовує ",[5224,6393,6370],{}," (ddof=0). Pandas ",[5288,6396,6397],{},"df.var()",[5224,6399,6380],{}," (ddof=1). Для узгодженості використовуйте параметр ",[5288,6402,6403],{},"ddof",":",[5317,6406,6408],{"className":5319,"code":6407,"language":5321,"meta":5322,"style":5322},"np.var(data, ddof=1)  # вибіркова дисперсія (як pandas)\n",[5288,6409,6410],{"__ignoreMap":5322},[5326,6411,6412,6415,6418,6421,6423,6426],{"class":5328,"line":5329},[5326,6413,6414],{"class":5336},"np.var(data, ",[5326,6416,6403],{"class":6417},"siwwj",[5326,6419,6420],{"class":5336},"=",[5326,6422,5315],{"class":5359},[5326,6424,6425],{"class":5336},")  ",[5326,6427,6428],{"class":6027},"# вибіркова дисперсія (як pandas)\n",[5594,6430,6431,6439],{},[5278,6432,6433],{},[5224,6434,6435,6436,6404],{},"Анатомія формули вибіркової дисперсії ",[5613,6437],{"tex":6438,":inline":5616},"s^2",[6312,6440,6441,6458,6467,6479,6498],{},[5201,6442,6443,6446,6447,6450,6451,6454,6455,5542],{},[5613,6444],{"tex":6445,":inline":5616},"(x_i - \\bar{x})"," — ",[5224,6448,6449],{},"Центроване відхилення:"," дельта відхилення конкретного ",[5613,6452],{"tex":6453,":inline":5616},"i","-го спостереження від вибіркового центру ",[5613,6456],{"tex":6457,":inline":5616},"\\bar{x}",[5201,6459,6460,6446,6463,6466],{},[5613,6461],{"tex":6462,":inline":5616},"(...)^2",[5224,6464,6465],{},"Квадратичний штраф:"," по-перше, позбавляє від'ємних знаків (без квадрата сума відхилень строго дорівнює нулю), а по-друге, нелінійно штрафує великі відхилення (відхилення 4 дає штраф 16, а відхилення 2 — лише 4).",[5201,6468,6469,6446,6472,6475,6476,6478],{},[5613,6470],{"tex":6471,":inline":5616},"\\sum_{i=1}^{n}",[5224,6473,6474],{},"Акумулятор площ:"," підсумовування квадратів помилок усіх ",[5613,6477],{"tex":6370,":inline":5616}," спостережень у єдиний накопичений обсяг розсіювання.",[5201,6480,6481,6446,6484,6487,6488,6490,6491,6493,6494,6497],{},[5613,6482],{"tex":6483,":inline":5616},"\\frac{1}{n-1}",[5224,6485,6486],{},"Поправка Бесселя (нормалізація):"," оскільки вибіркове середнє ",[5613,6489],{"tex":6457,":inline":5616}," вже підлаштоване під вибірку, ділення на ",[5613,6492],{"tex":6370,":inline":5616}," систематично недооцінювало б справжню дисперсію генеральної сукупності. Ділення на ",[5613,6495],{"tex":6496,":inline":5616},"n-1"," усуває зміщення.",[5201,6499,6500,6446,6502,6505],{},[5613,6501],{"tex":6438,":inline":5616},[5224,6503,6504],{},"Дисперсія:"," середня квадратична площа розсіювання (вимірюється у квадратах вихідних величин: см², грн², мс²).",[5653,6507,6509],{"id":6508},"обчислення-дисперсії","Обчислення дисперсії",[5308,6511,6513,6519,6813],{"kernel":5310,"title":6512},"variance_calculation.ipynb",[5313,6514,6515],{"type":5669},[5653,6516,6518],{"id":6517},"покрокове-обчислення-дисперсії","Покрокове обчислення дисперсії",[5313,6520,6521,6805],{"execution-count":5315},[5317,6522,6524],{"className":5319,"code":6523,"language":5321,"meta":5322,"style":5322},"import numpy as np\nimport pandas as pd\n\noleksiy = np.array([8, 7, 9, 8, 8, 7, 9, 8, 8, 8])\n\n# Крок 1: Обчислюємо середнє\nmean = oleksiy.mean()\nprint(f\"Крок 1. Середнє: {mean:.1f}\")\n\n# Крок 2: Відхилення від середнього\ndeviations = oleksiy - mean\nprint(f\"\\nКрок 2. Відхилення від середнього:\")\nprint(deviations)\n\n# Крок 3: Квадрати відхилень\nsquared_deviations = (oleksiy - mean) ** 2\nprint(f\"\\nКрок 3. Квадрати відхилень:\")\nprint(squared_deviations)\n\n# Крок 4: Середнє квадратів = дисперсія\nvariance = squared_deviations.mean()\nprint(f\"\\nКрок 4. Дисперсія (середнє квадратів): {variance:.2f}\")\n\n# Перевірка за допомогою NumPy\nvariance_numpy = np.var(oleksiy, ddof=0)\nprint(f\"Перевірка (NumPy): {variance_numpy:.2f}\")\n",[5288,6525,6526,6536,6548,6552,6596,6600,6605,6610,6632,6636,6641,6646,6663,6670,6674,6679,6687,6704,6712,6717,6723,6729,6756,6761,6767,6782],{"__ignoreMap":5322},[5326,6527,6528,6530,6532,6534],{"class":5328,"line":5329},[5326,6529,5333],{"class":5332},[5326,6531,5337],{"class":5336},[5326,6533,5340],{"class":5332},[5326,6535,5343],{"class":5336},[5326,6537,6538,6540,6543,6545],{"class":5328,"line":5346},[5326,6539,5333],{"class":5332},[5326,6541,6542],{"class":5336}," pandas ",[5326,6544,5340],{"class":5332},[5326,6546,6547],{"class":5336}," pd\n",[5326,6549,6550],{"class":5328,"line":5353},[5326,6551,5350],{"emptyLinePlaceholder":5349},[5326,6553,6554,6556,6558,6560,6562,6564,6566,6568,6570,6572,6574,6576,6578,6580,6582,6584,6586,6588,6590,6592,6594],{"class":5328,"line":5405},[5326,6555,5356],{"class":5336},[5326,6557,5360],{"class":5359},[5326,6559,5363],{"class":5336},[5326,6561,5366],{"class":5359},[5326,6563,5363],{"class":5336},[5326,6565,5371],{"class":5359},[5326,6567,5363],{"class":5336},[5326,6569,5360],{"class":5359},[5326,6571,5363],{"class":5336},[5326,6573,5360],{"class":5359},[5326,6575,5363],{"class":5336},[5326,6577,5366],{"class":5359},[5326,6579,5363],{"class":5336},[5326,6581,5371],{"class":5359},[5326,6583,5363],{"class":5336},[5326,6585,5360],{"class":5359},[5326,6587,5363],{"class":5336},[5326,6589,5360],{"class":5359},[5326,6591,5363],{"class":5336},[5326,6593,5360],{"class":5359},[5326,6595,5402],{"class":5336},[5326,6597,6598],{"class":5328,"line":5459},[5326,6599,5350],{"emptyLinePlaceholder":5349},[5326,6601,6602],{"class":5328,"line":5464},[5326,6603,6604],{"class":6027},"# Крок 1: Обчислюємо середнє\n",[5326,6606,6607],{"class":5328,"line":5497},[5326,6608,6609],{"class":5336},"mean = oleksiy.mean()\n",[5326,6611,6612,6614,6616,6618,6621,6623,6626,6628,6630],{"class":5328,"line":5799},[5326,6613,5468],{"class":5467},[5326,6615,5471],{"class":5336},[5326,6617,5475],{"class":5474},[5326,6619,6620],{"class":5478},"\"Крок 1. Середнє: ",[5326,6622,5482],{"class":5474},[5326,6624,6625],{"class":5336},"mean",[5326,6627,5488],{"class":5474},[5326,6629,5898],{"class":5478},[5326,6631,5494],{"class":5336},[5326,6633,6634],{"class":5328,"line":5804},[5326,6635,5350],{"emptyLinePlaceholder":5349},[5326,6637,6638],{"class":5328,"line":5816},[5326,6639,6640],{"class":6027},"# Крок 2: Відхилення від середнього\n",[5326,6642,6643],{"class":5328,"line":5840},[5326,6644,6645],{"class":5336},"deviations = oleksiy - mean\n",[5326,6647,6648,6650,6652,6654,6656,6658,6661],{"class":5328,"line":5863},[5326,6649,5468],{"class":5467},[5326,6651,5471],{"class":5336},[5326,6653,5475],{"class":5474},[5326,6655,5898],{"class":5478},[5326,6657,5902],{"class":5901},[5326,6659,6660],{"class":5478},"Крок 2. Відхилення від середнього:\"",[5326,6662,5494],{"class":5336},[5326,6664,6665,6667],{"class":5328,"line":5886},[5326,6666,5468],{"class":5467},[5326,6668,6669],{"class":5336},"(deviations)\n",[5326,6671,6672],{"class":5328,"line":5891},[5326,6673,5350],{"emptyLinePlaceholder":5349},[5326,6675,6676],{"class":5328,"line":5910},[5326,6677,6678],{"class":6027},"# Крок 3: Квадрати відхилень\n",[5326,6680,6681,6684],{"class":5328,"line":5932},[5326,6682,6683],{"class":5336},"squared_deviations = (oleksiy - mean) ** ",[5326,6685,6686],{"class":5359},"2\n",[5326,6688,6689,6691,6693,6695,6697,6699,6702],{"class":5328,"line":5954},[5326,6690,5468],{"class":5467},[5326,6692,5471],{"class":5336},[5326,6694,5475],{"class":5474},[5326,6696,5898],{"class":5478},[5326,6698,5902],{"class":5901},[5326,6700,6701],{"class":5478},"Крок 3. Квадрати відхилень:\"",[5326,6703,5494],{"class":5336},[5326,6705,6707,6709],{"class":5328,"line":6706},18,[5326,6708,5468],{"class":5467},[5326,6710,6711],{"class":5336},"(squared_deviations)\n",[5326,6713,6715],{"class":5328,"line":6714},19,[5326,6716,5350],{"emptyLinePlaceholder":5349},[5326,6718,6720],{"class":5328,"line":6719},20,[5326,6721,6722],{"class":6027},"# Крок 4: Середнє квадратів = дисперсія\n",[5326,6724,6726],{"class":5328,"line":6725},21,[5326,6727,6728],{"class":5336},"variance = squared_deviations.mean()\n",[5326,6730,6732,6734,6736,6738,6740,6742,6745,6747,6749,6752,6754],{"class":5328,"line":6731},22,[5326,6733,5468],{"class":5467},[5326,6735,5471],{"class":5336},[5326,6737,5475],{"class":5474},[5326,6739,5898],{"class":5478},[5326,6741,5902],{"class":5901},[5326,6743,6744],{"class":5478},"Крок 4. Дисперсія (середнє квадратів): ",[5326,6746,5482],{"class":5474},[5326,6748,5240],{"class":5336},[5326,6750,6751],{"class":5474},":.2f}",[5326,6753,5898],{"class":5478},[5326,6755,5494],{"class":5336},[5326,6757,6759],{"class":5328,"line":6758},23,[5326,6760,5350],{"emptyLinePlaceholder":5349},[5326,6762,6764],{"class":5328,"line":6763},24,[5326,6765,6766],{"class":6027},"# Перевірка за допомогою NumPy\n",[5326,6768,6770,6773,6775,6777,6780],{"class":5328,"line":6769},25,[5326,6771,6772],{"class":5336},"variance_numpy = np.var(oleksiy, ",[5326,6774,6403],{"class":6417},[5326,6776,6420],{"class":5336},[5326,6778,6779],{"class":5359},"0",[5326,6781,5494],{"class":5336},[5326,6783,6785,6787,6789,6791,6794,6796,6799,6801,6803],{"class":5328,"line":6784},26,[5326,6786,5468],{"class":5467},[5326,6788,5471],{"class":5336},[5326,6790,5475],{"class":5474},[5326,6792,6793],{"class":5478},"\"Перевірка (NumPy): ",[5326,6795,5482],{"class":5474},[5326,6797,6798],{"class":5336},"variance_numpy",[5326,6800,6751],{"class":5474},[5326,6802,5898],{"class":5478},[5326,6804,5494],{"class":5336},[5519,6806,6807],{"v-slot:output":5322},[5317,6808,6811],{"className":6809,"code":6810,"language":5526},[5524],"Крок 1. Середнє: 8.0\n\nКрок 2. Відхилення від середнього:\n[ 0. -1.  1.  0.  0. -1.  1.  0.  0.  0.]\n\nКрок 3. Квадрати відхилень:\n[0. 1. 1. 0. 0. 1. 1. 0. 0. 0.]\n\nКрок 4. Дисперсія (середнє квадратів): 0.40\n\nПеревірка (NumPy): 0.40\n",[5288,6812,6810],{"__ignoreMap":5322},[5313,6814,6815,6975],{"execution-count":5411},[5317,6816,6818],{"className":5319,"code":6817,"language":5321,"meta":5322,"style":5322},"# Порівняємо дисперсію для обох стрільців\nborys = np.array([2, 5, 15, 12, 3, 18, 1, 10, 4, 10])\n\nvar_oleksiy = np.var(oleksiy, ddof=0)\nvar_borys = np.var(borys, ddof=0)\n\nprint(f\"Дисперсія Олексія: {var_oleksiy:.2f} см²\")\nprint(f\"Дисперсія Бориса:  {var_borys:.2f} см²\")\nprint(f\"\\nБорис має дисперсію в {var_borys \u002F var_oleksiy:.1f} разів більшу!\")\n",[5288,6819,6820,6825,6869,6873,6886,6899,6903,6926,6948],{"__ignoreMap":5322},[5326,6821,6822],{"class":5328,"line":5329},[5326,6823,6824],{"class":6027},"# Порівняємо дисперсію для обох стрільців\n",[5326,6826,6827,6829,6831,6833,6835,6837,6839,6841,6843,6845,6847,6849,6851,6853,6855,6857,6859,6861,6863,6865,6867],{"class":5328,"line":5346},[5326,6828,5408],{"class":5336},[5326,6830,5411],{"class":5359},[5326,6832,5363],{"class":5336},[5326,6834,5416],{"class":5359},[5326,6836,5363],{"class":5336},[5326,6838,5421],{"class":5359},[5326,6840,5363],{"class":5336},[5326,6842,5426],{"class":5359},[5326,6844,5363],{"class":5336},[5326,6846,5431],{"class":5359},[5326,6848,5363],{"class":5336},[5326,6850,5436],{"class":5359},[5326,6852,5363],{"class":5336},[5326,6854,5315],{"class":5359},[5326,6856,5363],{"class":5336},[5326,6858,5445],{"class":5359},[5326,6860,5363],{"class":5336},[5326,6862,5450],{"class":5359},[5326,6864,5363],{"class":5336},[5326,6866,5445],{"class":5359},[5326,6868,5402],{"class":5336},[5326,6870,6871],{"class":5328,"line":5353},[5326,6872,5350],{"emptyLinePlaceholder":5349},[5326,6874,6875,6878,6880,6882,6884],{"class":5328,"line":5405},[5326,6876,6877],{"class":5336},"var_oleksiy = np.var(oleksiy, ",[5326,6879,6403],{"class":6417},[5326,6881,6420],{"class":5336},[5326,6883,6779],{"class":5359},[5326,6885,5494],{"class":5336},[5326,6887,6888,6891,6893,6895,6897],{"class":5328,"line":5459},[5326,6889,6890],{"class":5336},"var_borys = np.var(borys, ",[5326,6892,6403],{"class":6417},[5326,6894,6420],{"class":5336},[5326,6896,6779],{"class":5359},[5326,6898,5494],{"class":5336},[5326,6900,6901],{"class":5328,"line":5464},[5326,6902,5350],{"emptyLinePlaceholder":5349},[5326,6904,6905,6907,6909,6911,6914,6916,6919,6921,6924],{"class":5328,"line":5497},[5326,6906,5468],{"class":5467},[5326,6908,5471],{"class":5336},[5326,6910,5475],{"class":5474},[5326,6912,6913],{"class":5478},"\"Дисперсія Олексія: ",[5326,6915,5482],{"class":5474},[5326,6917,6918],{"class":5336},"var_oleksiy",[5326,6920,6751],{"class":5474},[5326,6922,6923],{"class":5478}," см²\"",[5326,6925,5494],{"class":5336},[5326,6927,6928,6930,6932,6934,6937,6939,6942,6944,6946],{"class":5328,"line":5799},[5326,6929,5468],{"class":5467},[5326,6931,5471],{"class":5336},[5326,6933,5475],{"class":5474},[5326,6935,6936],{"class":5478},"\"Дисперсія Бориса:  ",[5326,6938,5482],{"class":5474},[5326,6940,6941],{"class":5336},"var_borys",[5326,6943,6751],{"class":5474},[5326,6945,6923],{"class":5478},[5326,6947,5494],{"class":5336},[5326,6949,6950,6952,6954,6956,6958,6960,6963,6965,6968,6970,6973],{"class":5328,"line":5804},[5326,6951,5468],{"class":5467},[5326,6953,5471],{"class":5336},[5326,6955,5475],{"class":5474},[5326,6957,5898],{"class":5478},[5326,6959,5902],{"class":5901},[5326,6961,6962],{"class":5478},"Борис має дисперсію в ",[5326,6964,5482],{"class":5474},[5326,6966,6967],{"class":5336},"var_borys \u002F var_oleksiy",[5326,6969,5488],{"class":5474},[5326,6971,6972],{"class":5478}," разів більшу!\"",[5326,6974,5494],{"class":5336},[5519,6976,6977],{"v-slot:output":5322},[5317,6978,6981],{"className":6979,"code":6980,"language":5526},[5524],"Дисперсія Олексія: 0.40 см²\nДисперсія Бориса:  28.00 см²\n\nБорис має дисперсію в 70.0 разів більшу!\n",[5288,6982,6980],{"__ignoreMap":5322},[5544,6984,6985],{},[5278,6986,6987],{},"Аналогія: Дисперсія — це як «середній квадратний радіус» розкиду точок навколо центру. Чим більша дисперсія, тим далі «розлітаються» дані від середнього. Олексій стріляє в коло радіусом √0.4 ≈ 0.6 см. Борис — у коло радіусом √28 ≈ 5.3 см.",[5653,6989,6991],{"id":6990},"чому-квадрат-відхилення","Чому квадрат відхилення?",[5278,6993,6994],{},"Чому ми возводимо відхилення в квадрат, а не просто берем абсолютне значення?",[5308,6996,6998],{"kernel":5310,"title":6997},"why_square.ipynb",[5313,6999,7000,7244],{"execution-count":5315},[5317,7001,7003],{"className":5319,"code":7002,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\ndata = np.array([2, 4, 6, 8, 10])\nmean = data.mean()\n\n# Спроба 1: Просто сума відхилень (не працює!)\nsimple_deviations = data - mean\nprint(f\"Відхилення від середнього: {simple_deviations}\")\nprint(f\"Сума відхилень: {simple_deviations.sum():.10f}\")\nprint(\"→ Завжди дорівнює нулю! (позитивні та негативні анулюються)\\n\")\n\n# Спроба 2: Абсолютні відхилення (працює, але математично незручно)\nabs_deviations = np.abs(data - mean)\nprint(f\"Абсолютні відхилення: {abs_deviations}\")\nprint(f\"Середнє абсолютне відхилення (MAD): {abs_deviations.mean():.2f}\\n\")\n\n# Спроба 3: Квадрати відхилень (ідеально!)\nsquared_deviations = (data - mean) ** 2\nprint(f\"Квадрати відхилень: {squared_deviations}\")\nprint(f\"Дисперсія (середній квадрат): {squared_deviations.mean():.2f}\")\n",[5288,7004,7005,7015,7019,7045,7050,7054,7059,7064,7086,7109,7124,7128,7133,7138,7160,7184,7188,7193,7200,7222],{"__ignoreMap":5322},[5326,7006,7007,7009,7011,7013],{"class":5328,"line":5329},[5326,7008,5333],{"class":5332},[5326,7010,5337],{"class":5336},[5326,7012,5340],{"class":5332},[5326,7014,5343],{"class":5336},[5326,7016,7017],{"class":5328,"line":5346},[5326,7018,5350],{"emptyLinePlaceholder":5349},[5326,7020,7021,7024,7026,7028,7030,7032,7035,7037,7039,7041,7043],{"class":5328,"line":5353},[5326,7022,7023],{"class":5336},"data = np.array([",[5326,7025,5411],{"class":5359},[5326,7027,5363],{"class":5336},[5326,7029,5450],{"class":5359},[5326,7031,5363],{"class":5336},[5326,7033,7034],{"class":5359},"6",[5326,7036,5363],{"class":5336},[5326,7038,5360],{"class":5359},[5326,7040,5363],{"class":5336},[5326,7042,5445],{"class":5359},[5326,7044,5402],{"class":5336},[5326,7046,7047],{"class":5328,"line":5405},[5326,7048,7049],{"class":5336},"mean = data.mean()\n",[5326,7051,7052],{"class":5328,"line":5459},[5326,7053,5350],{"emptyLinePlaceholder":5349},[5326,7055,7056],{"class":5328,"line":5464},[5326,7057,7058],{"class":6027},"# Спроба 1: Просто сума відхилень (не працює!)\n",[5326,7060,7061],{"class":5328,"line":5497},[5326,7062,7063],{"class":5336},"simple_deviations = data - mean\n",[5326,7065,7066,7068,7070,7072,7075,7077,7080,7082,7084],{"class":5328,"line":5799},[5326,7067,5468],{"class":5467},[5326,7069,5471],{"class":5336},[5326,7071,5475],{"class":5474},[5326,7073,7074],{"class":5478},"\"Відхилення від середнього: ",[5326,7076,5482],{"class":5474},[5326,7078,7079],{"class":5336},"simple_deviations",[5326,7081,5833],{"class":5474},[5326,7083,5898],{"class":5478},[5326,7085,5494],{"class":5336},[5326,7087,7088,7090,7092,7094,7097,7099,7102,7105,7107],{"class":5328,"line":5804},[5326,7089,5468],{"class":5467},[5326,7091,5471],{"class":5336},[5326,7093,5475],{"class":5474},[5326,7095,7096],{"class":5478},"\"Сума відхилень: ",[5326,7098,5482],{"class":5474},[5326,7100,7101],{"class":5336},"simple_deviations.sum()",[5326,7103,7104],{"class":5474},":.10f}",[5326,7106,5898],{"class":5478},[5326,7108,5494],{"class":5336},[5326,7110,7111,7113,7115,7118,7120,7122],{"class":5328,"line":5816},[5326,7112,5468],{"class":5467},[5326,7114,5471],{"class":5336},[5326,7116,7117],{"class":5478},"\"→ Завжди дорівнює нулю! (позитивні та негативні анулюються)",[5326,7119,5902],{"class":5901},[5326,7121,5898],{"class":5478},[5326,7123,5494],{"class":5336},[5326,7125,7126],{"class":5328,"line":5840},[5326,7127,5350],{"emptyLinePlaceholder":5349},[5326,7129,7130],{"class":5328,"line":5863},[5326,7131,7132],{"class":6027},"# Спроба 2: Абсолютні відхилення (працює, але математично незручно)\n",[5326,7134,7135],{"class":5328,"line":5886},[5326,7136,7137],{"class":5336},"abs_deviations = np.abs(data - mean)\n",[5326,7139,7140,7142,7144,7146,7149,7151,7154,7156,7158],{"class":5328,"line":5891},[5326,7141,5468],{"class":5467},[5326,7143,5471],{"class":5336},[5326,7145,5475],{"class":5474},[5326,7147,7148],{"class":5478},"\"Абсолютні відхилення: ",[5326,7150,5482],{"class":5474},[5326,7152,7153],{"class":5336},"abs_deviations",[5326,7155,5833],{"class":5474},[5326,7157,5898],{"class":5478},[5326,7159,5494],{"class":5336},[5326,7161,7162,7164,7166,7168,7171,7173,7176,7178,7180,7182],{"class":5328,"line":5910},[5326,7163,5468],{"class":5467},[5326,7165,5471],{"class":5336},[5326,7167,5475],{"class":5474},[5326,7169,7170],{"class":5478},"\"Середнє абсолютне відхилення (MAD): ",[5326,7172,5482],{"class":5474},[5326,7174,7175],{"class":5336},"abs_deviations.mean()",[5326,7177,6751],{"class":5474},[5326,7179,5902],{"class":5901},[5326,7181,5898],{"class":5478},[5326,7183,5494],{"class":5336},[5326,7185,7186],{"class":5328,"line":5932},[5326,7187,5350],{"emptyLinePlaceholder":5349},[5326,7189,7190],{"class":5328,"line":5954},[5326,7191,7192],{"class":6027},"# Спроба 3: Квадрати відхилень (ідеально!)\n",[5326,7194,7195,7198],{"class":5328,"line":6706},[5326,7196,7197],{"class":5336},"squared_deviations = (data - mean) ** ",[5326,7199,6686],{"class":5359},[5326,7201,7202,7204,7206,7208,7211,7213,7216,7218,7220],{"class":5328,"line":6714},[5326,7203,5468],{"class":5467},[5326,7205,5471],{"class":5336},[5326,7207,5475],{"class":5474},[5326,7209,7210],{"class":5478},"\"Квадрати відхилень: ",[5326,7212,5482],{"class":5474},[5326,7214,7215],{"class":5336},"squared_deviations",[5326,7217,5833],{"class":5474},[5326,7219,5898],{"class":5478},[5326,7221,5494],{"class":5336},[5326,7223,7224,7226,7228,7230,7233,7235,7238,7240,7242],{"class":5328,"line":6719},[5326,7225,5468],{"class":5467},[5326,7227,5471],{"class":5336},[5326,7229,5475],{"class":5474},[5326,7231,7232],{"class":5478},"\"Дисперсія (середній квадрат): ",[5326,7234,5482],{"class":5474},[5326,7236,7237],{"class":5336},"squared_deviations.mean()",[5326,7239,6751],{"class":5474},[5326,7241,5898],{"class":5478},[5326,7243,5494],{"class":5336},[5519,7245,7246],{"v-slot:output":5322},[5317,7247,7250],{"className":7248,"code":7249,"language":5526},[5524],"Відхилення від середнього: [-4. -2.  0.  2.  4.]\nСума відхилень: 0.0000000000\n→ Завжди дорівнює нулю! (позитивні та негативні анулюються)\n\nАбсолютні відхилення: [4. 2. 0. 2. 4.]\nСереднє абсолютне відхилення (MAD): 2.40\n\nКвадрати відхилень: [16.  4.  0.  4. 16.]\nДисперсія (середній квадрат): 8.00\n",[5288,7251,7249],{"__ignoreMap":5322},[5278,7253,7254],{},[5224,7255,7256],{},"Причини використання квадрату:",[6312,7258,7259,7265,7271],{},[5201,7260,7261,7264],{},[5224,7262,7263],{},"Усуває знаки"," — негативні та позитивні відхилення не анулюються",[5201,7266,7267,7270],{},[5224,7268,7269],{},"Математично зручно"," — диференційовно, добре поводиться в теоремах",[5201,7272,7273,7276],{},[5224,7274,7275],{},"Більше штрафує великі відхилення"," — квадрат 4 = 16, а квадрат 2 = 4 (різниця 12 vs 2 для абсолюту)",[5594,7278,7279,7282,7283,7286,7287,7290,7291,7294],{},[5224,7280,7281],{},"Важливо:"," Дисперсія ",[5224,7284,7285],{},"не має інтуїтивних одиниць"," виміру. Якщо дані в сантиметрах, то дисперсія в ",[5224,7288,7289],{},"см²"," (квадратних сантиметрах). Що це означає? Важко сказати. Тому в практиці частіше використовують ",[5224,7292,7293],{},"стандартне відхилення"," (квадратний корінь із дисперсії), яке повертає одиниці виміру до оригінальних.",[5278,7296,7297],{},[5556,7298],{"alt":7299,"className":7300,"src":7301},"Геометрична інтуїція дисперсії: сума площ квадратів відхилень",[5560],"\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F02.png",[5270,7303],{},[5273,7305,7307],{"id":7306},"стандартне-відхилення-standard-deviation","Стандартне відхилення (Standard Deviation)",[5278,7309,7310,5227,7312,7314,7315,7318],{},[5224,7311,5246],{},[5229,7313,5249],{},", позначається σ або s) — це ",[5224,7316,7317],{},"квадратний корінь із дисперсії",". Це найпопулярніша міра варіації.",[5653,7320,5656],{"id":7321},"формула-1",[5613,7323],{"tex":7324},"\\sigma = \\sqrt{\\sigma^2} = \\sqrt{\\frac{1}{n} \\sum_{i=1}^{n} (x_i - \\mu)^2}",[5653,7326,7328],{"id":7327},"переваги-над-дисперсією","Переваги над дисперсією",[6312,7330,7331,7337,7343],{},[5201,7332,7333,7336],{},[5224,7334,7335],{},"Одиниці виміру такі ж, як у даних"," — якщо дані в см, то σ теж у см",[5201,7338,7339,7342],{},[5224,7340,7341],{},"Інтуїтивна інтерпретація"," — «типове відхилення від середнього»",[5201,7344,7345,7348],{},[5224,7346,7347],{},"Правило 68-95-99.7"," для нормального розподілу (побачимо в наступній статті)",[5308,7350,7352,7358],{"kernel":5310,"title":7351},"std_calculation.ipynb",[5313,7353,7354],{"type":5669},[5653,7355,7357],{"id":7356},"стандартне-відхилення-звязок-із-дисперсією","Стандартне відхилення: зв'язок із дисперсією",[5313,7359,7360,7694],{"execution-count":5315},[5317,7361,7363],{"className":5319,"code":7362,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\noleksiy = np.array([8, 7, 9, 8, 8, 7, 9, 8, 8, 8])\nborys = np.array([2, 5, 15, 12, 3, 18, 1, 10, 4, 10])\n\n# Дисперсія (variance)\nvar_oleksiy = np.var(oleksiy, ddof=0)\nvar_borys = np.var(borys, ddof=0)\n\n# Стандартне відхилення (standard deviation)\nstd_oleksiy = np.std(oleksiy, ddof=0)\nstd_borys = np.std(borys, ddof=0)\n\nprint(\"Олексій:\")\nprint(f\"  Дисперсія:           {var_oleksiy:.2f} см²\")\nprint(f\"  Стандартне відхилення: {std_oleksiy:.2f} см\")\nprint(f\"  Перевірка (√дисперсія): {np.sqrt(var_oleksiy):.2f} см\")\n\nprint(\"\\nБорис:\")\nprint(f\"  Дисперсія:           {var_borys:.2f} см²\")\nprint(f\"  Стандартне відхилення: {std_borys:.2f} см\")\nprint(f\"  Перевірка (√дисперсія): {np.sqrt(var_borys):.2f} см\")\n",[5288,7364,7365,7375,7379,7423,7467,7471,7476,7488,7500,7504,7509,7522,7535,7539,7549,7570,7592,7614,7618,7632,7652,7673],{"__ignoreMap":5322},[5326,7366,7367,7369,7371,7373],{"class":5328,"line":5329},[5326,7368,5333],{"class":5332},[5326,7370,5337],{"class":5336},[5326,7372,5340],{"class":5332},[5326,7374,5343],{"class":5336},[5326,7376,7377],{"class":5328,"line":5346},[5326,7378,5350],{"emptyLinePlaceholder":5349},[5326,7380,7381,7383,7385,7387,7389,7391,7393,7395,7397,7399,7401,7403,7405,7407,7409,7411,7413,7415,7417,7419,7421],{"class":5328,"line":5353},[5326,7382,5356],{"class":5336},[5326,7384,5360],{"class":5359},[5326,7386,5363],{"class":5336},[5326,7388,5366],{"class":5359},[5326,7390,5363],{"class":5336},[5326,7392,5371],{"class":5359},[5326,7394,5363],{"class":5336},[5326,7396,5360],{"class":5359},[5326,7398,5363],{"class":5336},[5326,7400,5360],{"class":5359},[5326,7402,5363],{"class":5336},[5326,7404,5366],{"class":5359},[5326,7406,5363],{"class":5336},[5326,7408,5371],{"class":5359},[5326,7410,5363],{"class":5336},[5326,7412,5360],{"class":5359},[5326,7414,5363],{"class":5336},[5326,7416,5360],{"class":5359},[5326,7418,5363],{"class":5336},[5326,7420,5360],{"class":5359},[5326,7422,5402],{"class":5336},[5326,7424,7425,7427,7429,7431,7433,7435,7437,7439,7441,7443,7445,7447,7449,7451,7453,7455,7457,7459,7461,7463,7465],{"class":5328,"line":5405},[5326,7426,5408],{"class":5336},[5326,7428,5411],{"class":5359},[5326,7430,5363],{"class":5336},[5326,7432,5416],{"class":5359},[5326,7434,5363],{"class":5336},[5326,7436,5421],{"class":5359},[5326,7438,5363],{"class":5336},[5326,7440,5426],{"class":5359},[5326,7442,5363],{"class":5336},[5326,7444,5431],{"class":5359},[5326,7446,5363],{"class":5336},[5326,7448,5436],{"class":5359},[5326,7450,5363],{"class":5336},[5326,7452,5315],{"class":5359},[5326,7454,5363],{"class":5336},[5326,7456,5445],{"class":5359},[5326,7458,5363],{"class":5336},[5326,7460,5450],{"class":5359},[5326,7462,5363],{"class":5336},[5326,7464,5445],{"class":5359},[5326,7466,5402],{"class":5336},[5326,7468,7469],{"class":5328,"line":5459},[5326,7470,5350],{"emptyLinePlaceholder":5349},[5326,7472,7473],{"class":5328,"line":5464},[5326,7474,7475],{"class":6027},"# Дисперсія (variance)\n",[5326,7477,7478,7480,7482,7484,7486],{"class":5328,"line":5497},[5326,7479,6877],{"class":5336},[5326,7481,6403],{"class":6417},[5326,7483,6420],{"class":5336},[5326,7485,6779],{"class":5359},[5326,7487,5494],{"class":5336},[5326,7489,7490,7492,7494,7496,7498],{"class":5328,"line":5799},[5326,7491,6890],{"class":5336},[5326,7493,6403],{"class":6417},[5326,7495,6420],{"class":5336},[5326,7497,6779],{"class":5359},[5326,7499,5494],{"class":5336},[5326,7501,7502],{"class":5328,"line":5804},[5326,7503,5350],{"emptyLinePlaceholder":5349},[5326,7505,7506],{"class":5328,"line":5816},[5326,7507,7508],{"class":6027},"# Стандартне відхилення (standard deviation)\n",[5326,7510,7511,7514,7516,7518,7520],{"class":5328,"line":5840},[5326,7512,7513],{"class":5336},"std_oleksiy = np.std(oleksiy, ",[5326,7515,6403],{"class":6417},[5326,7517,6420],{"class":5336},[5326,7519,6779],{"class":5359},[5326,7521,5494],{"class":5336},[5326,7523,7524,7527,7529,7531,7533],{"class":5328,"line":5863},[5326,7525,7526],{"class":5336},"std_borys = np.std(borys, ",[5326,7528,6403],{"class":6417},[5326,7530,6420],{"class":5336},[5326,7532,6779],{"class":5359},[5326,7534,5494],{"class":5336},[5326,7536,7537],{"class":5328,"line":5886},[5326,7538,5350],{"emptyLinePlaceholder":5349},[5326,7540,7541,7543,7545,7547],{"class":5328,"line":5891},[5326,7542,5468],{"class":5467},[5326,7544,5471],{"class":5336},[5326,7546,5811],{"class":5478},[5326,7548,5494],{"class":5336},[5326,7550,7551,7553,7555,7557,7560,7562,7564,7566,7568],{"class":5328,"line":5910},[5326,7552,5468],{"class":5467},[5326,7554,5471],{"class":5336},[5326,7556,5475],{"class":5474},[5326,7558,7559],{"class":5478},"\"  Дисперсія:           ",[5326,7561,5482],{"class":5474},[5326,7563,6918],{"class":5336},[5326,7565,6751],{"class":5474},[5326,7567,6923],{"class":5478},[5326,7569,5494],{"class":5336},[5326,7571,7572,7574,7576,7578,7581,7583,7586,7588,7590],{"class":5328,"line":5932},[5326,7573,5468],{"class":5467},[5326,7575,5471],{"class":5336},[5326,7577,5475],{"class":5474},[5326,7579,7580],{"class":5478},"\"  Стандартне відхилення: ",[5326,7582,5482],{"class":5474},[5326,7584,7585],{"class":5336},"std_oleksiy",[5326,7587,6751],{"class":5474},[5326,7589,5491],{"class":5478},[5326,7591,5494],{"class":5336},[5326,7593,7594,7596,7598,7600,7603,7605,7608,7610,7612],{"class":5328,"line":5954},[5326,7595,5468],{"class":5467},[5326,7597,5471],{"class":5336},[5326,7599,5475],{"class":5474},[5326,7601,7602],{"class":5478},"\"  Перевірка (√дисперсія): ",[5326,7604,5482],{"class":5474},[5326,7606,7607],{"class":5336},"np.sqrt(var_oleksiy)",[5326,7609,6751],{"class":5474},[5326,7611,5491],{"class":5478},[5326,7613,5494],{"class":5336},[5326,7615,7616],{"class":5328,"line":6706},[5326,7617,5350],{"emptyLinePlaceholder":5349},[5326,7619,7620,7622,7624,7626,7628,7630],{"class":5328,"line":6714},[5326,7621,5468],{"class":5467},[5326,7623,5471],{"class":5336},[5326,7625,5898],{"class":5478},[5326,7627,5902],{"class":5901},[5326,7629,5905],{"class":5478},[5326,7631,5494],{"class":5336},[5326,7633,7634,7636,7638,7640,7642,7644,7646,7648,7650],{"class":5328,"line":6719},[5326,7635,5468],{"class":5467},[5326,7637,5471],{"class":5336},[5326,7639,5475],{"class":5474},[5326,7641,7559],{"class":5478},[5326,7643,5482],{"class":5474},[5326,7645,6941],{"class":5336},[5326,7647,6751],{"class":5474},[5326,7649,6923],{"class":5478},[5326,7651,5494],{"class":5336},[5326,7653,7654,7656,7658,7660,7662,7664,7667,7669,7671],{"class":5328,"line":6725},[5326,7655,5468],{"class":5467},[5326,7657,5471],{"class":5336},[5326,7659,5475],{"class":5474},[5326,7661,7580],{"class":5478},[5326,7663,5482],{"class":5474},[5326,7665,7666],{"class":5336},"std_borys",[5326,7668,6751],{"class":5474},[5326,7670,5491],{"class":5478},[5326,7672,5494],{"class":5336},[5326,7674,7675,7677,7679,7681,7683,7685,7688,7690,7692],{"class":5328,"line":6731},[5326,7676,5468],{"class":5467},[5326,7678,5471],{"class":5336},[5326,7680,5475],{"class":5474},[5326,7682,7602],{"class":5478},[5326,7684,5482],{"class":5474},[5326,7686,7687],{"class":5336},"np.sqrt(var_borys)",[5326,7689,6751],{"class":5474},[5326,7691,5491],{"class":5478},[5326,7693,5494],{"class":5336},[5519,7695,7696],{"v-slot:output":5322},[5317,7697,7700],{"className":7698,"code":7699,"language":5526},[5524],"Олексій:\n  Дисперсія:           0.40 см²\n  Стандартне відхилення: 0.63 см\n  Перевірка (√дисперсія): 0.63 см\n\nБорис:\n  Дисперсія:           28.00 см²\n  Стандартне відхилення: 5.29 см\n  Перевірка (√дисперсія): 5.29 см\n",[5288,7701,7699],{"__ignoreMap":5322},[5544,7703,7704],{},[5278,7705,7706],{},"Аналогія: Якщо дисперсія — це «площа» розкиду, то стандартне відхилення — це «радіус» розкиду. Для Олексія: результати зазвичай у межах 8 ± 0.63 см. Для Бориса: 8 ± 5.29 см (майже в 10 разів більший «радіус невизначеності»).",[5653,7708,7710],{"id":7709},"інтерпретація-стандартного-відхилення","Інтерпретація стандартного відхилення",[5278,7712,7713,7716,7717,7720,7721,7723,7716,7726,7729],{},[5224,7714,7715],{},"Низьке стандартне відхилення"," → дані ",[5224,7718,7719],{},"згруповані"," навколо середнього (передбачувані, стабільні)",[5292,7722],{},[5224,7724,7725],{},"Високе стандартне відхилення",[5224,7727,7728],{},"розкидані"," (непередбачувані, мінливі)",[5308,7731,7733],{"kernel":5310,"title":7732},"std_interpretation.ipynb",[5313,7734,7735,8114],{"execution-count":5315},[5317,7736,7738],{"className":5319,"code":7737,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Три випадки з однаковим середнім, але різною варіацією\nlow_var = np.array([50, 49, 51, 50, 50, 49, 51, 50, 50, 50])\nmedium_var = np.array([45, 48, 52, 47, 53, 46, 54, 48, 52, 50])\nhigh_var = np.array([30, 40, 60, 35, 65, 45, 55, 50, 60, 55])\n\ndatasets = [\n    (\"Низька варіація\", low_var),\n    (\"Середня варіація\", medium_var),\n    (\"Висока варіація\", high_var)\n]\n\nfor name, data in datasets:\n    mean = data.mean()\n    std = data.std(ddof=0)\n    print(f\"{name}:\")\n    print(f\"  Дані: {data}\")\n    print(f\"  Середнє: {mean:.1f}\")\n    print(f\"  Стандартне відхилення: {std:.2f}\")\n    print(f\"  Діапазон (Mean ± 1×Std): [{mean - std:.1f}, {mean + std:.1f}]\\n\")\n",[5288,7739,7740,7750,7754,7759,7807,7859,7910,7914,7919,7930,7940,7950,7955,7959,7973,7978,7991,8014,8036,8057,8078],{"__ignoreMap":5322},[5326,7741,7742,7744,7746,7748],{"class":5328,"line":5329},[5326,7743,5333],{"class":5332},[5326,7745,5337],{"class":5336},[5326,7747,5340],{"class":5332},[5326,7749,5343],{"class":5336},[5326,7751,7752],{"class":5328,"line":5346},[5326,7753,5350],{"emptyLinePlaceholder":5349},[5326,7755,7756],{"class":5328,"line":5353},[5326,7757,7758],{"class":6027},"# Три випадки з однаковим середнім, але різною варіацією\n",[5326,7760,7761,7764,7767,7769,7772,7774,7777,7779,7781,7783,7785,7787,7789,7791,7793,7795,7797,7799,7801,7803,7805],{"class":5328,"line":5405},[5326,7762,7763],{"class":5336},"low_var = np.array([",[5326,7765,7766],{"class":5359},"50",[5326,7768,5363],{"class":5336},[5326,7770,7771],{"class":5359},"49",[5326,7773,5363],{"class":5336},[5326,7775,7776],{"class":5359},"51",[5326,7778,5363],{"class":5336},[5326,7780,7766],{"class":5359},[5326,7782,5363],{"class":5336},[5326,7784,7766],{"class":5359},[5326,7786,5363],{"class":5336},[5326,7788,7771],{"class":5359},[5326,7790,5363],{"class":5336},[5326,7792,7776],{"class":5359},[5326,7794,5363],{"class":5336},[5326,7796,7766],{"class":5359},[5326,7798,5363],{"class":5336},[5326,7800,7766],{"class":5359},[5326,7802,5363],{"class":5336},[5326,7804,7766],{"class":5359},[5326,7806,5402],{"class":5336},[5326,7808,7809,7812,7815,7817,7820,7822,7825,7827,7830,7832,7835,7837,7840,7842,7845,7847,7849,7851,7853,7855,7857],{"class":5328,"line":5459},[5326,7810,7811],{"class":5336},"medium_var = np.array([",[5326,7813,7814],{"class":5359},"45",[5326,7816,5363],{"class":5336},[5326,7818,7819],{"class":5359},"48",[5326,7821,5363],{"class":5336},[5326,7823,7824],{"class":5359},"52",[5326,7826,5363],{"class":5336},[5326,7828,7829],{"class":5359},"47",[5326,7831,5363],{"class":5336},[5326,7833,7834],{"class":5359},"53",[5326,7836,5363],{"class":5336},[5326,7838,7839],{"class":5359},"46",[5326,7841,5363],{"class":5336},[5326,7843,7844],{"class":5359},"54",[5326,7846,5363],{"class":5336},[5326,7848,7819],{"class":5359},[5326,7850,5363],{"class":5336},[5326,7852,7824],{"class":5359},[5326,7854,5363],{"class":5336},[5326,7856,7766],{"class":5359},[5326,7858,5402],{"class":5336},[5326,7860,7861,7864,7867,7869,7872,7874,7877,7879,7882,7884,7887,7889,7891,7893,7896,7898,7900,7902,7904,7906,7908],{"class":5328,"line":5464},[5326,7862,7863],{"class":5336},"high_var = np.array([",[5326,7865,7866],{"class":5359},"30",[5326,7868,5363],{"class":5336},[5326,7870,7871],{"class":5359},"40",[5326,7873,5363],{"class":5336},[5326,7875,7876],{"class":5359},"60",[5326,7878,5363],{"class":5336},[5326,7880,7881],{"class":5359},"35",[5326,7883,5363],{"class":5336},[5326,7885,7886],{"class":5359},"65",[5326,7888,5363],{"class":5336},[5326,7890,7814],{"class":5359},[5326,7892,5363],{"class":5336},[5326,7894,7895],{"class":5359},"55",[5326,7897,5363],{"class":5336},[5326,7899,7766],{"class":5359},[5326,7901,5363],{"class":5336},[5326,7903,7876],{"class":5359},[5326,7905,5363],{"class":5336},[5326,7907,7895],{"class":5359},[5326,7909,5402],{"class":5336},[5326,7911,7912],{"class":5328,"line":5497},[5326,7913,5350],{"emptyLinePlaceholder":5349},[5326,7915,7916],{"class":5328,"line":5799},[5326,7917,7918],{"class":5336},"datasets = [\n",[5326,7920,7921,7924,7927],{"class":5328,"line":5804},[5326,7922,7923],{"class":5336},"    (",[5326,7925,7926],{"class":5478},"\"Низька варіація\"",[5326,7928,7929],{"class":5336},", low_var),\n",[5326,7931,7932,7934,7937],{"class":5328,"line":5816},[5326,7933,7923],{"class":5336},[5326,7935,7936],{"class":5478},"\"Середня варіація\"",[5326,7938,7939],{"class":5336},", medium_var),\n",[5326,7941,7942,7944,7947],{"class":5328,"line":5840},[5326,7943,7923],{"class":5336},[5326,7945,7946],{"class":5478},"\"Висока варіація\"",[5326,7948,7949],{"class":5336},", high_var)\n",[5326,7951,7952],{"class":5328,"line":5863},[5326,7953,7954],{"class":5336},"]\n",[5326,7956,7957],{"class":5328,"line":5886},[5326,7958,5350],{"emptyLinePlaceholder":5349},[5326,7960,7961,7964,7967,7970],{"class":5328,"line":5891},[5326,7962,7963],{"class":5332},"for",[5326,7965,7966],{"class":5336}," name, data ",[5326,7968,7969],{"class":5332},"in",[5326,7971,7972],{"class":5336}," datasets:\n",[5326,7974,7975],{"class":5328,"line":5910},[5326,7976,7977],{"class":5336},"    mean = data.mean()\n",[5326,7979,7980,7983,7985,7987,7989],{"class":5328,"line":5932},[5326,7981,7982],{"class":5336},"    std = data.std(",[5326,7984,6403],{"class":6417},[5326,7986,6420],{"class":5336},[5326,7988,6779],{"class":5359},[5326,7990,5494],{"class":5336},[5326,7992,7993,7996,7998,8000,8002,8004,8007,8009,8012],{"class":5328,"line":5954},[5326,7994,7995],{"class":5467},"    print",[5326,7997,5471],{"class":5336},[5326,7999,5475],{"class":5474},[5326,8001,5898],{"class":5478},[5326,8003,5482],{"class":5474},[5326,8005,8006],{"class":5336},"name",[5326,8008,5833],{"class":5474},[5326,8010,8011],{"class":5478},":\"",[5326,8013,5494],{"class":5336},[5326,8015,8016,8018,8020,8022,8025,8027,8030,8032,8034],{"class":5328,"line":6706},[5326,8017,7995],{"class":5467},[5326,8019,5471],{"class":5336},[5326,8021,5475],{"class":5474},[5326,8023,8024],{"class":5478},"\"  Дані: ",[5326,8026,5482],{"class":5474},[5326,8028,8029],{"class":5336},"data",[5326,8031,5833],{"class":5474},[5326,8033,5898],{"class":5478},[5326,8035,5494],{"class":5336},[5326,8037,8038,8040,8042,8044,8047,8049,8051,8053,8055],{"class":5328,"line":6714},[5326,8039,7995],{"class":5467},[5326,8041,5471],{"class":5336},[5326,8043,5475],{"class":5474},[5326,8045,8046],{"class":5478},"\"  Середнє: ",[5326,8048,5482],{"class":5474},[5326,8050,6625],{"class":5336},[5326,8052,5488],{"class":5474},[5326,8054,5898],{"class":5478},[5326,8056,5494],{"class":5336},[5326,8058,8059,8061,8063,8065,8067,8069,8072,8074,8076],{"class":5328,"line":6719},[5326,8060,7995],{"class":5467},[5326,8062,5471],{"class":5336},[5326,8064,5475],{"class":5474},[5326,8066,7580],{"class":5478},[5326,8068,5482],{"class":5474},[5326,8070,8071],{"class":5336},"std",[5326,8073,6751],{"class":5474},[5326,8075,5898],{"class":5478},[5326,8077,5494],{"class":5336},[5326,8079,8080,8082,8084,8086,8089,8091,8094,8096,8098,8100,8103,8105,8108,8110,8112],{"class":5328,"line":6725},[5326,8081,7995],{"class":5467},[5326,8083,5471],{"class":5336},[5326,8085,5475],{"class":5474},[5326,8087,8088],{"class":5478},"\"  Діапазон (Mean ± 1×Std): [",[5326,8090,5482],{"class":5474},[5326,8092,8093],{"class":5336},"mean - std",[5326,8095,5488],{"class":5474},[5326,8097,5363],{"class":5478},[5326,8099,5482],{"class":5474},[5326,8101,8102],{"class":5336},"mean + std",[5326,8104,5488],{"class":5474},[5326,8106,8107],{"class":5478},"]",[5326,8109,5902],{"class":5901},[5326,8111,5898],{"class":5478},[5326,8113,5494],{"class":5336},[5519,8115,8116],{"v-slot:output":5322},[5317,8117,8120],{"className":8118,"code":8119,"language":5526},[5524],"Низька варіація:\n  Дані: [50 49 51 50 50 49 51 50 50 50]\n  Середнє: 50.0\n  Стандартне відхилення: 0.63\n  Діапазон (Mean ± 1×Std): [49.4, 50.6]\n\nСередня варіація:\n  Дані: [45 48 52 47 53 46 54 48 52 50]\n  Середнє: 49.5\n  Стандартне відхилення: 3.02\n  Діапазон (Mean ± 1×Std): [46.5, 52.5]\n\nВисока варіація:\n  Дані: [30 40 60 35 65 45 55 50 60 55]\n  Середнє: 49.5\n  Стандартне відхилення: 11.34\n  Діапазон (Mean ± 1×Std): [38.2, 60.8]\n",[5288,8121,8119],{"__ignoreMap":5322},[5278,8123,8124],{},[5556,8125],{"alt":8126,"className":8127,"src":8128},"Три ступені варіації при однаковому середньому: низька, середня та висока мінливість",[5560],"\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F03.png",[8130,8131,8132,8137,8164],"tip",{},[5278,8133,8134],{},[5224,8135,8136],{},"Практичне правило для нормального розподілу:",[5198,8138,8139,8148,8156],{},[5201,8140,8141,8144,8145],{},[5224,8142,8143],{},"68%"," даних лежать у межах ",[5613,8146],{"tex":8147,":inline":5616},"\\mu \\pm 1\\sigma",[5201,8149,8150,8144,8153],{},[5224,8151,8152],{},"95%",[5613,8154],{"tex":8155,":inline":5616},"\\mu \\pm 2\\sigma",[5201,8157,8158,8144,8161],{},[5224,8159,8160],{},"99.7%",[5613,8162],{"tex":8163,":inline":5616},"\\mu \\pm 3\\sigma",[5278,8165,8166,8167,8170,8171,8174],{},"Це правило називається ",[5224,8168,8169],{},"емпіричним правилом"," або ",[5224,8172,8173],{},"правилом трьох сигм",". Детальніше розглянемо в статті про нормальний розподіл.",[5270,8176],{},[5273,8178,8180],{"id":8179},"коефіцієнт-варіації-coefficient-of-variation","Коефіцієнт варіації (Coefficient of Variation)",[5278,8182,8183],{},"Уявіть, що ви порівнюєте:",[5198,8185,8186,8192],{},[5201,8187,8188,8191],{},[5224,8189,8190],{},"Зарплати"," (середнє 30 000 грн, стандартне відхилення 5 000 грн)",[5201,8193,8194,8197],{},[5224,8195,8196],{},"Ціни на автомобілі"," (середнє 500 000 грн, стандартне відхилення 100 000 грн)",[5278,8199,8200],{},"У другому випадку стандартне відхилення в 20 разів більше. Але чи означає це, що ціни на автомобілі більш мінливі? Не обов'язково — адже і саме середнє у 16 разів більше!",[5278,8202,8203,5227,8206,8209,8210,8213,8214,6404],{},[5224,8204,8205],{},"Коефіцієнт варіації",[5229,8207,8208],{},"coefficient of variation",", CV) — це ",[5224,8211,8212],{},"нормалізована"," міра варіації, яка показує відхилення ",[5224,8215,8216],{},"відносно середнього",[5613,8218],{"tex":8219},"CV = \\frac{\\sigma}{\\mu} \\times 100\\%",[5308,8221,8223],{"kernel":5310,"title":8222},"cv_comparison.ipynb",[5313,8224,8225,8677],{"execution-count":5315},[5317,8226,8228],{"className":5319,"code":8227,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Зарплати (тис. грн)\nsalaries = np.array([25, 28, 30, 32, 35, 30, 28, 33, 31, 29])\nmean_salary = salaries.mean()\nstd_salary = salaries.std(ddof=0)\ncv_salary = (std_salary \u002F mean_salary) * 100\n\n# Ціни на автомобілі (тис. грн)\ncars = np.array([400, 450, 500, 550, 600, 500, 480, 520, 510, 490])\nmean_car = cars.mean()\nstd_car = cars.std(ddof=0)\ncv_car = (std_car \u002F mean_car) * 100\n\nprint(\"Зарплати:\")\nprint(f\"  Середнє: {mean_salary:.1f} тис. грн\")\nprint(f\"  Стандартне відхилення: {std_salary:.2f} тис. грн\")\nprint(f\"  Коефіцієнт варіації: {cv_salary:.1f}%\")\n\nprint(\"\\nЦіни на автомобілі:\")\nprint(f\"  Середнє: {mean_car:.1f} тис. грн\")\nprint(f\"  Стандартне відхилення: {std_car:.2f} тис. грн\")\nprint(f\"  Коефіцієнт варіації: {cv_car:.1f}%\")\n\nprint(f\"\\nВисновок:\")\nif cv_salary > cv_car:\n    print(f\"  Зарплати більш мінливі відносно їхнього середнього ({cv_salary:.1f}% vs {cv_car:.1f}%)\")\nelse:\n    print(f\"  Ціни на авто більш мінливі відносно їхнього середнього ({cv_car:.1f}% vs {cv_salary:.1f}%)\")\n",[5288,8229,8230,8240,8244,8249,8300,8305,8318,8326,8330,8335,8389,8394,8407,8414,8418,8429,8451,8472,8495,8499,8514,8535,8556,8577,8581,8598,8606,8638,8647],{"__ignoreMap":5322},[5326,8231,8232,8234,8236,8238],{"class":5328,"line":5329},[5326,8233,5333],{"class":5332},[5326,8235,5337],{"class":5336},[5326,8237,5340],{"class":5332},[5326,8239,5343],{"class":5336},[5326,8241,8242],{"class":5328,"line":5346},[5326,8243,5350],{"emptyLinePlaceholder":5349},[5326,8245,8246],{"class":5328,"line":5353},[5326,8247,8248],{"class":6027},"# Зарплати (тис. грн)\n",[5326,8250,8251,8254,8257,8259,8262,8264,8266,8268,8271,8273,8275,8277,8279,8281,8283,8285,8288,8290,8293,8295,8298],{"class":5328,"line":5405},[5326,8252,8253],{"class":5336},"salaries = np.array([",[5326,8255,8256],{"class":5359},"25",[5326,8258,5363],{"class":5336},[5326,8260,8261],{"class":5359},"28",[5326,8263,5363],{"class":5336},[5326,8265,7866],{"class":5359},[5326,8267,5363],{"class":5336},[5326,8269,8270],{"class":5359},"32",[5326,8272,5363],{"class":5336},[5326,8274,7881],{"class":5359},[5326,8276,5363],{"class":5336},[5326,8278,7866],{"class":5359},[5326,8280,5363],{"class":5336},[5326,8282,8261],{"class":5359},[5326,8284,5363],{"class":5336},[5326,8286,8287],{"class":5359},"33",[5326,8289,5363],{"class":5336},[5326,8291,8292],{"class":5359},"31",[5326,8294,5363],{"class":5336},[5326,8296,8297],{"class":5359},"29",[5326,8299,5402],{"class":5336},[5326,8301,8302],{"class":5328,"line":5459},[5326,8303,8304],{"class":5336},"mean_salary = salaries.mean()\n",[5326,8306,8307,8310,8312,8314,8316],{"class":5328,"line":5464},[5326,8308,8309],{"class":5336},"std_salary = salaries.std(",[5326,8311,6403],{"class":6417},[5326,8313,6420],{"class":5336},[5326,8315,6779],{"class":5359},[5326,8317,5494],{"class":5336},[5326,8319,8320,8323],{"class":5328,"line":5497},[5326,8321,8322],{"class":5336},"cv_salary = (std_salary \u002F mean_salary) * ",[5326,8324,8325],{"class":5359},"100\n",[5326,8327,8328],{"class":5328,"line":5799},[5326,8329,5350],{"emptyLinePlaceholder":5349},[5326,8331,8332],{"class":5328,"line":5804},[5326,8333,8334],{"class":6027},"# Ціни на автомобілі (тис. грн)\n",[5326,8336,8337,8340,8343,8345,8348,8350,8353,8355,8358,8360,8363,8365,8367,8369,8372,8374,8377,8379,8382,8384,8387],{"class":5328,"line":5816},[5326,8338,8339],{"class":5336},"cars = np.array([",[5326,8341,8342],{"class":5359},"400",[5326,8344,5363],{"class":5336},[5326,8346,8347],{"class":5359},"450",[5326,8349,5363],{"class":5336},[5326,8351,8352],{"class":5359},"500",[5326,8354,5363],{"class":5336},[5326,8356,8357],{"class":5359},"550",[5326,8359,5363],{"class":5336},[5326,8361,8362],{"class":5359},"600",[5326,8364,5363],{"class":5336},[5326,8366,8352],{"class":5359},[5326,8368,5363],{"class":5336},[5326,8370,8371],{"class":5359},"480",[5326,8373,5363],{"class":5336},[5326,8375,8376],{"class":5359},"520",[5326,8378,5363],{"class":5336},[5326,8380,8381],{"class":5359},"510",[5326,8383,5363],{"class":5336},[5326,8385,8386],{"class":5359},"490",[5326,8388,5402],{"class":5336},[5326,8390,8391],{"class":5328,"line":5840},[5326,8392,8393],{"class":5336},"mean_car = cars.mean()\n",[5326,8395,8396,8399,8401,8403,8405],{"class":5328,"line":5863},[5326,8397,8398],{"class":5336},"std_car = cars.std(",[5326,8400,6403],{"class":6417},[5326,8402,6420],{"class":5336},[5326,8404,6779],{"class":5359},[5326,8406,5494],{"class":5336},[5326,8408,8409,8412],{"class":5328,"line":5886},[5326,8410,8411],{"class":5336},"cv_car = (std_car \u002F mean_car) * ",[5326,8413,8325],{"class":5359},[5326,8415,8416],{"class":5328,"line":5891},[5326,8417,5350],{"emptyLinePlaceholder":5349},[5326,8419,8420,8422,8424,8427],{"class":5328,"line":5910},[5326,8421,5468],{"class":5467},[5326,8423,5471],{"class":5336},[5326,8425,8426],{"class":5478},"\"Зарплати:\"",[5326,8428,5494],{"class":5336},[5326,8430,8431,8433,8435,8437,8439,8441,8444,8446,8449],{"class":5328,"line":5932},[5326,8432,5468],{"class":5467},[5326,8434,5471],{"class":5336},[5326,8436,5475],{"class":5474},[5326,8438,8046],{"class":5478},[5326,8440,5482],{"class":5474},[5326,8442,8443],{"class":5336},"mean_salary",[5326,8445,5488],{"class":5474},[5326,8447,8448],{"class":5478}," тис. грн\"",[5326,8450,5494],{"class":5336},[5326,8452,8453,8455,8457,8459,8461,8463,8466,8468,8470],{"class":5328,"line":5954},[5326,8454,5468],{"class":5467},[5326,8456,5471],{"class":5336},[5326,8458,5475],{"class":5474},[5326,8460,7580],{"class":5478},[5326,8462,5482],{"class":5474},[5326,8464,8465],{"class":5336},"std_salary",[5326,8467,6751],{"class":5474},[5326,8469,8448],{"class":5478},[5326,8471,5494],{"class":5336},[5326,8473,8474,8476,8478,8480,8483,8485,8488,8490,8493],{"class":5328,"line":6706},[5326,8475,5468],{"class":5467},[5326,8477,5471],{"class":5336},[5326,8479,5475],{"class":5474},[5326,8481,8482],{"class":5478},"\"  Коефіцієнт варіації: ",[5326,8484,5482],{"class":5474},[5326,8486,8487],{"class":5336},"cv_salary",[5326,8489,5488],{"class":5474},[5326,8491,8492],{"class":5478},"%\"",[5326,8494,5494],{"class":5336},[5326,8496,8497],{"class":5328,"line":6714},[5326,8498,5350],{"emptyLinePlaceholder":5349},[5326,8500,8501,8503,8505,8507,8509,8512],{"class":5328,"line":6719},[5326,8502,5468],{"class":5467},[5326,8504,5471],{"class":5336},[5326,8506,5898],{"class":5478},[5326,8508,5902],{"class":5901},[5326,8510,8511],{"class":5478},"Ціни на автомобілі:\"",[5326,8513,5494],{"class":5336},[5326,8515,8516,8518,8520,8522,8524,8526,8529,8531,8533],{"class":5328,"line":6725},[5326,8517,5468],{"class":5467},[5326,8519,5471],{"class":5336},[5326,8521,5475],{"class":5474},[5326,8523,8046],{"class":5478},[5326,8525,5482],{"class":5474},[5326,8527,8528],{"class":5336},"mean_car",[5326,8530,5488],{"class":5474},[5326,8532,8448],{"class":5478},[5326,8534,5494],{"class":5336},[5326,8536,8537,8539,8541,8543,8545,8547,8550,8552,8554],{"class":5328,"line":6731},[5326,8538,5468],{"class":5467},[5326,8540,5471],{"class":5336},[5326,8542,5475],{"class":5474},[5326,8544,7580],{"class":5478},[5326,8546,5482],{"class":5474},[5326,8548,8549],{"class":5336},"std_car",[5326,8551,6751],{"class":5474},[5326,8553,8448],{"class":5478},[5326,8555,5494],{"class":5336},[5326,8557,8558,8560,8562,8564,8566,8568,8571,8573,8575],{"class":5328,"line":6758},[5326,8559,5468],{"class":5467},[5326,8561,5471],{"class":5336},[5326,8563,5475],{"class":5474},[5326,8565,8482],{"class":5478},[5326,8567,5482],{"class":5474},[5326,8569,8570],{"class":5336},"cv_car",[5326,8572,5488],{"class":5474},[5326,8574,8492],{"class":5478},[5326,8576,5494],{"class":5336},[5326,8578,8579],{"class":5328,"line":6763},[5326,8580,5350],{"emptyLinePlaceholder":5349},[5326,8582,8583,8585,8587,8589,8591,8593,8596],{"class":5328,"line":6769},[5326,8584,5468],{"class":5467},[5326,8586,5471],{"class":5336},[5326,8588,5475],{"class":5474},[5326,8590,5898],{"class":5478},[5326,8592,5902],{"class":5901},[5326,8594,8595],{"class":5478},"Висновок:\"",[5326,8597,5494],{"class":5336},[5326,8599,8600,8603],{"class":5328,"line":6784},[5326,8601,8602],{"class":5332},"if",[5326,8604,8605],{"class":5336}," cv_salary > cv_car:\n",[5326,8607,8609,8611,8613,8615,8618,8620,8622,8624,8627,8629,8631,8633,8636],{"class":5328,"line":8608},27,[5326,8610,7995],{"class":5467},[5326,8612,5471],{"class":5336},[5326,8614,5475],{"class":5474},[5326,8616,8617],{"class":5478},"\"  Зарплати більш мінливі відносно їхнього середнього (",[5326,8619,5482],{"class":5474},[5326,8621,8487],{"class":5336},[5326,8623,5488],{"class":5474},[5326,8625,8626],{"class":5478},"% vs ",[5326,8628,5482],{"class":5474},[5326,8630,8570],{"class":5336},[5326,8632,5488],{"class":5474},[5326,8634,8635],{"class":5478},"%)\"",[5326,8637,5494],{"class":5336},[5326,8639,8641,8644],{"class":5328,"line":8640},28,[5326,8642,8643],{"class":5332},"else",[5326,8645,8646],{"class":5336},":\n",[5326,8648,8650,8652,8654,8656,8659,8661,8663,8665,8667,8669,8671,8673,8675],{"class":5328,"line":8649},29,[5326,8651,7995],{"class":5467},[5326,8653,5471],{"class":5336},[5326,8655,5475],{"class":5474},[5326,8657,8658],{"class":5478},"\"  Ціни на авто більш мінливі відносно їхнього середнього (",[5326,8660,5482],{"class":5474},[5326,8662,8570],{"class":5336},[5326,8664,5488],{"class":5474},[5326,8666,8626],{"class":5478},[5326,8668,5482],{"class":5474},[5326,8670,8487],{"class":5336},[5326,8672,5488],{"class":5474},[5326,8674,8635],{"class":5478},[5326,8676,5494],{"class":5336},[5519,8678,8679],{"v-slot:output":5322},[5317,8680,8683],{"className":8681,"code":8682,"language":5526},[5524],"Зарплати:\n  Середнє: 30.1 тис. грн\n  Стандартне відхилення: 2.73 тис. грн\n  Коефіцієнт варіації: 9.1%\n\nЦіни на автомобілі:\n  Середнє: 500.0 тис. грн\n  Стандартне відхилення: 54.77 тис. грн\n  Коефіцієнт варіації: 11.0%\n\nВисновок:\n  Ціни на авто більш мінливі відносно їхнього середнього (11.0% vs 9.1%)\n",[5288,8684,8682],{"__ignoreMap":5322},[5594,8686,8687,8692,8718,8721],{},[5278,8688,8689],{},[5224,8690,8691],{},"Інтерпретація CV:",[5198,8693,8694,8700,8706,8712],{},[5201,8695,8696,8699],{},[5224,8697,8698],{},"CV \u003C 10%"," — низька варіація (дані дуже стабільні)",[5201,8701,8702,8705],{},[5224,8703,8704],{},"10% ≤ CV ≤ 25%"," — помірна варіація",[5201,8707,8708,8711],{},[5224,8709,8710],{},"CV > 25%"," — висока варіація (дані дуже мінливі)",[5201,8713,8714,8717],{},[5224,8715,8716],{},"CV > 50%"," — екстремальна варіація",[5278,8719,8720],{},"CV особливо корисний для:",[5198,8722,8723,8726,8729],{},[5201,8724,8725],{},"Порівняння варіації між різними змінними (зарплати vs ціни)",[5201,8727,8728],{},"Порівняння варіації в різних одиницях виміру",[5201,8730,8731],{},"Оцінки якості вимірювальних приладів (менший CV = більша точність)",[6245,8733,8734,8739],{},[5278,8735,8736],{},[5224,8737,8738],{},"Обмеження CV:",[5198,8740,8741,8744,8747],{},[5201,8742,8743],{},"Не працює, якщо середнє близьке до нуля (ділення на маленьке число)",[5201,8745,8746],{},"Не має сенсу для даних без природного нуля (температура в Цельсіях — 0°C не означає «відсутність тепла»)",[5201,8748,8749],{},"Чутливий до аутлайерів (як і std)",[5270,8751],{},[5273,8753,8755],{"id":8754},"квартилі-та-персентилі","Квартилі та персентилі",[5278,8757,8758,5227,8761,8764],{},[5224,8759,8760],{},"Персентиль",[5229,8762,8763],{},"percentile",") — це значення, нижче якого знаходиться певний відсоток даних.",[5278,8766,8767],{},"Наприклад:",[5198,8769,8770,8776,8786],{},[5201,8771,8772,8775],{},[5224,8773,8774],{},"25-й персентиль"," (P25) — 25% даних менші за це значення",[5201,8777,8778,8781,8782,8785],{},[5224,8779,8780],{},"50-й персентиль"," (P50) — це ",[5224,8783,8784],{},"медіана"," (50% менші, 50% більші)",[5201,8787,8788,8791],{},[5224,8789,8790],{},"75-й персентиль"," (P75) — 75% даних менші за це значення",[5278,8793,8794,5227,8796,8798,8799,6404],{},[5224,8795,5255],{},[5229,8797,5258],{},") — це спеціальні персентилі, що поділяють дані на ",[5224,8800,8801],{},"4 рівні частини",[5198,8803,8804,8810,8816],{},[5201,8805,8806,8809],{},[5224,8807,8808],{},"Q1"," (перший квартиль) = P25 — 25-й персентиль",[5201,8811,8812,8815],{},[5224,8813,8814],{},"Q2"," (другий квартиль) = P50 — медіана",[5201,8817,8818,8821],{},[5224,8819,8820],{},"Q3"," (третій квартиль) = P75 — 75-й персентиль",[8823,8824,8826],"plant-uml",{"alt":8825},"П'ятичислове зведення та квартилі",[5317,8827,8831],{"className":8828,"code":8829,"language":8830,"meta":5322,"style":5322},"language-plantuml shiki shiki-themes light-plus dark-plus dark-plus","@startuml\nskinparam style plain\nskinparam backgroundColor #FFFFFF\n\nrectangle \"Мінімум\" as min #lightblue\nrectangle \"Q1 (25%)\" as q1 #lightgreen\nrectangle \"Q2 (50%)\\nМедіана\" as q2 #lightyellow\nrectangle \"Q3 (75%)\" as q3 #lightcoral\nrectangle \"Максимум\" as max #lavender\n\nmin -right-> q1 : \"25% даних\"\nq1 -right-> q2 : \"25% даних\"\nq2 -right-> q3 : \"25% даних\"\nq3 -right-> max : \"25% даних\"\n\nnote bottom of min\n  Найменше значення\nend note\n\nnote bottom of q2\n  Центральне значення\n  (медіана)\nend note\n\nnote bottom of max\n  Найбільше значення\nend note\n\n@enduml\n","plantuml",[5288,8832,8833,8838,8843,8848,8852,8857,8862,8867,8872,8877,8881,8886,8891,8896,8901,8905,8910,8915,8920,8924,8929,8934,8939,8943,8947,8952,8957,8961,8965],{"__ignoreMap":5322},[5326,8834,8835],{"class":5328,"line":5329},[5326,8836,8837],{},"@startuml\n",[5326,8839,8840],{"class":5328,"line":5346},[5326,8841,8842],{},"skinparam style plain\n",[5326,8844,8845],{"class":5328,"line":5353},[5326,8846,8847],{},"skinparam backgroundColor #FFFFFF\n",[5326,8849,8850],{"class":5328,"line":5405},[5326,8851,5350],{"emptyLinePlaceholder":5349},[5326,8853,8854],{"class":5328,"line":5459},[5326,8855,8856],{},"rectangle \"Мінімум\" as min #lightblue\n",[5326,8858,8859],{"class":5328,"line":5464},[5326,8860,8861],{},"rectangle \"Q1 (25%)\" as q1 #lightgreen\n",[5326,8863,8864],{"class":5328,"line":5497},[5326,8865,8866],{},"rectangle \"Q2 (50%)\\nМедіана\" as q2 #lightyellow\n",[5326,8868,8869],{"class":5328,"line":5799},[5326,8870,8871],{},"rectangle \"Q3 (75%)\" as q3 #lightcoral\n",[5326,8873,8874],{"class":5328,"line":5804},[5326,8875,8876],{},"rectangle \"Максимум\" as max #lavender\n",[5326,8878,8879],{"class":5328,"line":5816},[5326,8880,5350],{"emptyLinePlaceholder":5349},[5326,8882,8883],{"class":5328,"line":5840},[5326,8884,8885],{},"min -right-> q1 : \"25% даних\"\n",[5326,8887,8888],{"class":5328,"line":5863},[5326,8889,8890],{},"q1 -right-> q2 : \"25% даних\"\n",[5326,8892,8893],{"class":5328,"line":5886},[5326,8894,8895],{},"q2 -right-> q3 : \"25% даних\"\n",[5326,8897,8898],{"class":5328,"line":5891},[5326,8899,8900],{},"q3 -right-> max : \"25% даних\"\n",[5326,8902,8903],{"class":5328,"line":5910},[5326,8904,5350],{"emptyLinePlaceholder":5349},[5326,8906,8907],{"class":5328,"line":5932},[5326,8908,8909],{},"note bottom of min\n",[5326,8911,8912],{"class":5328,"line":5954},[5326,8913,8914],{},"  Найменше значення\n",[5326,8916,8917],{"class":5328,"line":6706},[5326,8918,8919],{},"end note\n",[5326,8921,8922],{"class":5328,"line":6714},[5326,8923,5350],{"emptyLinePlaceholder":5349},[5326,8925,8926],{"class":5328,"line":6719},[5326,8927,8928],{},"note bottom of q2\n",[5326,8930,8931],{"class":5328,"line":6725},[5326,8932,8933],{},"  Центральне значення\n",[5326,8935,8936],{"class":5328,"line":6731},[5326,8937,8938],{},"  (медіана)\n",[5326,8940,8941],{"class":5328,"line":6758},[5326,8942,8919],{},[5326,8944,8945],{"class":5328,"line":6763},[5326,8946,5350],{"emptyLinePlaceholder":5349},[5326,8948,8949],{"class":5328,"line":6769},[5326,8950,8951],{},"note bottom of max\n",[5326,8953,8954],{"class":5328,"line":6784},[5326,8955,8956],{},"  Найбільше значення\n",[5326,8958,8959],{"class":5328,"line":8608},[5326,8960,8919],{},[5326,8962,8963],{"class":5328,"line":8640},[5326,8964,5350],{"emptyLinePlaceholder":5349},[5326,8966,8967],{"class":5328,"line":8649},[5326,8968,8969],{},"@enduml\n",[5278,8971,8972],{},[5556,8973],{"alt":8974,"className":8975,"src":8976},"Розподіл 20 оцінок студентів на 4 квартилі (по 25% даних у кожному)",[5560],"\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F04.png",[5653,8978,8980],{"id":8979},"обчислення-квартилів","Обчислення квартилів",[5308,8982,8984,8990,9389],{"kernel":5310,"title":8983},"quartiles_calculation.ipynb",[5313,8985,8986],{"type":5669},[5653,8987,8989],{"id":8988},"обчислення-квартилів-для-оцінок-студентів","Обчислення квартилів для оцінок студентів",[5313,8991,8992,9381],{"execution-count":5315},[5317,8993,8995],{"className":5319,"code":8994,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Оцінки 20 студентів (за 100-бальною шкалою)\ngrades = np.array([62, 65, 68, 70, 72, 74, 76, 78, 80, 82, \n                   84, 85, 86, 88, 90, 91, 92, 94, 96, 98])\n\n# Обчислення квартилів\nq1 = np.percentile(grades, 25)\nq2 = np.percentile(grades, 50)  # медіана\nq3 = np.percentile(grades, 75)\n\nminimum = grades.min()\nmaximum = grades.max()\n\nprint(\"П'ятичисловий підсумок (Five-Number Summary):\")\nprint(f\"  Мінімум:  {minimum}\")\nprint(f\"  Q1 (25%): {q1}\")\nprint(f\"  Q2 (50%): {q2} ← Медіана\")\nprint(f\"  Q3 (75%): {q3}\")\nprint(f\"  Максимум: {maximum}\")\n\nprint(\"\\nІнтерпретація:\")\nprint(f\"  25% студентів отримали менше {q1:.0f} балів\")\nprint(f\"  50% студентів отримали менше {q2:.0f} балів (медіана)\")\nprint(f\"  75% студентів отримали менше {q3:.0f} балів\")\n",[5288,8996,8997,9007,9011,9016,9070,9119,9123,9128,9137,9149,9159,9163,9168,9173,9177,9188,9210,9232,9255,9277,9298,9302,9317,9338,9360],{"__ignoreMap":5322},[5326,8998,8999,9001,9003,9005],{"class":5328,"line":5329},[5326,9000,5333],{"class":5332},[5326,9002,5337],{"class":5336},[5326,9004,5340],{"class":5332},[5326,9006,5343],{"class":5336},[5326,9008,9009],{"class":5328,"line":5346},[5326,9010,5350],{"emptyLinePlaceholder":5349},[5326,9012,9013],{"class":5328,"line":5353},[5326,9014,9015],{"class":6027},"# Оцінки 20 студентів (за 100-бальною шкалою)\n",[5326,9017,9018,9021,9024,9026,9028,9030,9033,9035,9038,9040,9043,9045,9048,9050,9053,9055,9058,9060,9063,9065,9067],{"class":5328,"line":5405},[5326,9019,9020],{"class":5336},"grades = np.array([",[5326,9022,9023],{"class":5359},"62",[5326,9025,5363],{"class":5336},[5326,9027,7886],{"class":5359},[5326,9029,5363],{"class":5336},[5326,9031,9032],{"class":5359},"68",[5326,9034,5363],{"class":5336},[5326,9036,9037],{"class":5359},"70",[5326,9039,5363],{"class":5336},[5326,9041,9042],{"class":5359},"72",[5326,9044,5363],{"class":5336},[5326,9046,9047],{"class":5359},"74",[5326,9049,5363],{"class":5336},[5326,9051,9052],{"class":5359},"76",[5326,9054,5363],{"class":5336},[5326,9056,9057],{"class":5359},"78",[5326,9059,5363],{"class":5336},[5326,9061,9062],{"class":5359},"80",[5326,9064,5363],{"class":5336},[5326,9066,6036],{"class":5359},[5326,9068,9069],{"class":5336},", \n",[5326,9071,9072,9075,9077,9079,9081,9083,9085,9087,9089,9092,9094,9097,9099,9102,9104,9107,9109,9112,9114,9117],{"class":5328,"line":5459},[5326,9073,9074],{"class":5359},"                   84",[5326,9076,5363],{"class":5336},[5326,9078,6041],{"class":5359},[5326,9080,5363],{"class":5336},[5326,9082,6056],{"class":5359},[5326,9084,5363],{"class":5336},[5326,9086,6046],{"class":5359},[5326,9088,5363],{"class":5336},[5326,9090,9091],{"class":5359},"90",[5326,9093,5363],{"class":5336},[5326,9095,9096],{"class":5359},"91",[5326,9098,5363],{"class":5336},[5326,9100,9101],{"class":5359},"92",[5326,9103,5363],{"class":5336},[5326,9105,9106],{"class":5359},"94",[5326,9108,5363],{"class":5336},[5326,9110,9111],{"class":5359},"96",[5326,9113,5363],{"class":5336},[5326,9115,9116],{"class":5359},"98",[5326,9118,5402],{"class":5336},[5326,9120,9121],{"class":5328,"line":5464},[5326,9122,5350],{"emptyLinePlaceholder":5349},[5326,9124,9125],{"class":5328,"line":5497},[5326,9126,9127],{"class":6027},"# Обчислення квартилів\n",[5326,9129,9130,9133,9135],{"class":5328,"line":5799},[5326,9131,9132],{"class":5336},"q1 = np.percentile(grades, ",[5326,9134,8256],{"class":5359},[5326,9136,5494],{"class":5336},[5326,9138,9139,9142,9144,9146],{"class":5328,"line":5804},[5326,9140,9141],{"class":5336},"q2 = np.percentile(grades, ",[5326,9143,7766],{"class":5359},[5326,9145,6425],{"class":5336},[5326,9147,9148],{"class":6027},"# медіана\n",[5326,9150,9151,9154,9157],{"class":5328,"line":5816},[5326,9152,9153],{"class":5336},"q3 = np.percentile(grades, ",[5326,9155,9156],{"class":5359},"75",[5326,9158,5494],{"class":5336},[5326,9160,9161],{"class":5328,"line":5840},[5326,9162,5350],{"emptyLinePlaceholder":5349},[5326,9164,9165],{"class":5328,"line":5863},[5326,9166,9167],{"class":5336},"minimum = grades.min()\n",[5326,9169,9170],{"class":5328,"line":5886},[5326,9171,9172],{"class":5336},"maximum = grades.max()\n",[5326,9174,9175],{"class":5328,"line":5891},[5326,9176,5350],{"emptyLinePlaceholder":5349},[5326,9178,9179,9181,9183,9186],{"class":5328,"line":5910},[5326,9180,5468],{"class":5467},[5326,9182,5471],{"class":5336},[5326,9184,9185],{"class":5478},"\"П'ятичисловий підсумок (Five-Number Summary):\"",[5326,9187,5494],{"class":5336},[5326,9189,9190,9192,9194,9196,9199,9201,9204,9206,9208],{"class":5328,"line":5932},[5326,9191,5468],{"class":5467},[5326,9193,5471],{"class":5336},[5326,9195,5475],{"class":5474},[5326,9197,9198],{"class":5478},"\"  Мінімум:  ",[5326,9200,5482],{"class":5474},[5326,9202,9203],{"class":5336},"minimum",[5326,9205,5833],{"class":5474},[5326,9207,5898],{"class":5478},[5326,9209,5494],{"class":5336},[5326,9211,9212,9214,9216,9218,9221,9223,9226,9228,9230],{"class":5328,"line":5954},[5326,9213,5468],{"class":5467},[5326,9215,5471],{"class":5336},[5326,9217,5475],{"class":5474},[5326,9219,9220],{"class":5478},"\"  Q1 (25%): ",[5326,9222,5482],{"class":5474},[5326,9224,9225],{"class":5336},"q1",[5326,9227,5833],{"class":5474},[5326,9229,5898],{"class":5478},[5326,9231,5494],{"class":5336},[5326,9233,9234,9236,9238,9240,9243,9245,9248,9250,9253],{"class":5328,"line":6706},[5326,9235,5468],{"class":5467},[5326,9237,5471],{"class":5336},[5326,9239,5475],{"class":5474},[5326,9241,9242],{"class":5478},"\"  Q2 (50%): ",[5326,9244,5482],{"class":5474},[5326,9246,9247],{"class":5336},"q2",[5326,9249,5833],{"class":5474},[5326,9251,9252],{"class":5478}," ← Медіана\"",[5326,9254,5494],{"class":5336},[5326,9256,9257,9259,9261,9263,9266,9268,9271,9273,9275],{"class":5328,"line":6714},[5326,9258,5468],{"class":5467},[5326,9260,5471],{"class":5336},[5326,9262,5475],{"class":5474},[5326,9264,9265],{"class":5478},"\"  Q3 (75%): ",[5326,9267,5482],{"class":5474},[5326,9269,9270],{"class":5336},"q3",[5326,9272,5833],{"class":5474},[5326,9274,5898],{"class":5478},[5326,9276,5494],{"class":5336},[5326,9278,9279,9281,9283,9285,9287,9289,9292,9294,9296],{"class":5328,"line":6719},[5326,9280,5468],{"class":5467},[5326,9282,5471],{"class":5336},[5326,9284,5475],{"class":5474},[5326,9286,5849],{"class":5478},[5326,9288,5482],{"class":5474},[5326,9290,9291],{"class":5336},"maximum",[5326,9293,5833],{"class":5474},[5326,9295,5898],{"class":5478},[5326,9297,5494],{"class":5336},[5326,9299,9300],{"class":5328,"line":6725},[5326,9301,5350],{"emptyLinePlaceholder":5349},[5326,9303,9304,9306,9308,9310,9312,9315],{"class":5328,"line":6731},[5326,9305,5468],{"class":5467},[5326,9307,5471],{"class":5336},[5326,9309,5898],{"class":5478},[5326,9311,5902],{"class":5901},[5326,9313,9314],{"class":5478},"Інтерпретація:\"",[5326,9316,5494],{"class":5336},[5326,9318,9319,9321,9323,9325,9328,9330,9332,9334,9336],{"class":5328,"line":6758},[5326,9320,5468],{"class":5467},[5326,9322,5471],{"class":5336},[5326,9324,5475],{"class":5474},[5326,9326,9327],{"class":5478},"\"  25% студентів отримали менше ",[5326,9329,5482],{"class":5474},[5326,9331,9225],{"class":5336},[5326,9333,6224],{"class":5474},[5326,9335,6168],{"class":5478},[5326,9337,5494],{"class":5336},[5326,9339,9340,9342,9344,9346,9349,9351,9353,9355,9358],{"class":5328,"line":6763},[5326,9341,5468],{"class":5467},[5326,9343,5471],{"class":5336},[5326,9345,5475],{"class":5474},[5326,9347,9348],{"class":5478},"\"  50% студентів отримали менше ",[5326,9350,5482],{"class":5474},[5326,9352,9247],{"class":5336},[5326,9354,6224],{"class":5474},[5326,9356,9357],{"class":5478}," балів (медіана)\"",[5326,9359,5494],{"class":5336},[5326,9361,9362,9364,9366,9368,9371,9373,9375,9377,9379],{"class":5328,"line":6769},[5326,9363,5468],{"class":5467},[5326,9365,5471],{"class":5336},[5326,9367,5475],{"class":5474},[5326,9369,9370],{"class":5478},"\"  75% студентів отримали менше ",[5326,9372,5482],{"class":5474},[5326,9374,9270],{"class":5336},[5326,9376,6224],{"class":5474},[5326,9378,6168],{"class":5478},[5326,9380,5494],{"class":5336},[5519,9382,9383],{"v-slot:output":5322},[5317,9384,9387],{"className":9385,"code":9386,"language":5526},[5524],"П'ятичисловий підсумок (Five-Number Summary):\n  Мінімум:  62\n  Q1 (25%): 73.0\n  Q2 (50%): 83.0 ← Медіана\n  Q3 (75%): 90.25\n  Максимум: 98\n\nІнтерпретація:\n  25% студентів отримали менше 73 балів\n  50% студентів отримали менше 83 балів (медіана)\n  75% студентів отримали менше 90 балів\n",[5288,9388,9386],{"__ignoreMap":5322},[5313,9390,9391,9438],{"execution-count":5411},[5317,9392,9394],{"className":5319,"code":9393,"language":5321,"meta":5322,"style":5322},"# Pandas автоматично обчислює квартилі в методі describe()\nimport pandas as pd\n\ngrades_series = pd.Series(grades)\nprint(\"Статистика pandas (з квартилями):\")\nprint(grades_series.describe())\n",[5288,9395,9396,9401,9411,9415,9420,9431],{"__ignoreMap":5322},[5326,9397,9398],{"class":5328,"line":5329},[5326,9399,9400],{"class":6027},"# Pandas автоматично обчислює квартилі в методі describe()\n",[5326,9402,9403,9405,9407,9409],{"class":5328,"line":5346},[5326,9404,5333],{"class":5332},[5326,9406,6542],{"class":5336},[5326,9408,5340],{"class":5332},[5326,9410,6547],{"class":5336},[5326,9412,9413],{"class":5328,"line":5353},[5326,9414,5350],{"emptyLinePlaceholder":5349},[5326,9416,9417],{"class":5328,"line":5405},[5326,9418,9419],{"class":5336},"grades_series = pd.Series(grades)\n",[5326,9421,9422,9424,9426,9429],{"class":5328,"line":5459},[5326,9423,5468],{"class":5467},[5326,9425,5471],{"class":5336},[5326,9427,9428],{"class":5478},"\"Статистика pandas (з квартилями):\"",[5326,9430,5494],{"class":5336},[5326,9432,9433,9435],{"class":5328,"line":5464},[5326,9434,5468],{"class":5467},[5326,9436,9437],{"class":5336},"(grades_series.describe())\n",[5519,9439,9440],{"v-slot:output":5322},[5317,9441,9444],{"className":9442,"code":9443,"language":5526},[5524],"Статистика pandas (з квартилями):\ncount    20.000000\nmean     81.900000\nstd      10.857321\nmin      62.000000\n25%      73.000000  ← Q1\n50%      83.000000  ← Q2 (медіана)\n75%      90.250000  ← Q3\nmax      98.000000\ndtype: float64\n",[5288,9445,9443],{"__ignoreMap":5322},[5544,9447,9448],{},[5278,9449,9450],{},"Аналогія: Квартилі — це як розрізати торт на 4 рівні частини. Q1 — перший надріз (¼ торта), Q2 — посередині (½ торта), Q3 — третій надріз (¾ торта). Кожна частина містить однакову кількість даних (25%).",[5270,9452],{},[5273,9454,9456],{"id":9455},"міжквартильний-розмах-interquartile-range-iqr","Міжквартильний розмах (Interquartile Range, IQR)",[5278,9458,9459,5227,9461,9464],{},[5224,9460,5264],{},[5229,9462,9463],{},"interquartile range",", IQR) — це різниця між третім та першим квартилями:",[5613,9466],{"tex":9467},"IQR = Q3 - Q1",[5278,9469,9470,9471,9474,9475,5542],{},"IQR показує ",[5224,9472,9473],{},"розмах середніх 50% даних",", ігноруючи крайні 25% з кожного боку. Це робить його ",[5224,9476,9477],{},"стійким до аутлайерів",[5653,9479,9481],{"id":9480},"порівняння-range-та-iqr","Порівняння Range та IQR",[5308,9483,9485,9491],{"kernel":5310,"title":9484},"range_vs_iqr.ipynb",[5313,9486,9487],{"type":5669},[5653,9488,9490],{"id":9489},"стійкість-iqr-до-аутлайерів","Стійкість IQR до аутлайерів",[5313,9492,9493,9909],{"execution-count":5315},[5317,9494,9496],{"className":5319,"code":9495,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Дані без аутлайерів\ndata_clean = np.array([10, 12, 13, 14, 15, 16, 17, 18, 20])\n\n# Дані з аутлайером\ndata_outlier = np.array([10, 12, 13, 14, 15, 16, 17, 18, 100])\n\ndef analyze_spread(data, name):\n    q1 = np.percentile(data, 25)\n    q3 = np.percentile(data, 75)\n    iqr = q3 - q1\n    range_val = data.max() - data.min()\n    \n    print(f\"{name}:\")\n    print(f\"  Range (max - min): {range_val:.0f}\")\n    print(f\"  IQR (Q3 - Q1):     {iqr:.1f}\")\n    print()\n\nanalyze_spread(data_clean, \"Без аутлайера\")\nanalyze_spread(data_outlier, \"З аутлайером (100)\")\n\n# Порівняння зміни\nrange_clean = data_clean.max() - data_clean.min()\nrange_outlier = data_outlier.max() - data_outlier.min()\niqr_clean = np.percentile(data_clean, 75) - np.percentile(data_clean, 25)\niqr_outlier = np.percentile(data_outlier, 75) - np.percentile(data_outlier, 25)\n\nprint(f\"Вплив аутлайера:\")\nprint(f\"  Range змінився на {range_outlier - range_clean:.0f} ({(range_outlier\u002Frange_clean - 1)*100:.0f}% збільшення)\")\nprint(f\"  IQR змінився на {iqr_outlier - iqr_clean:.1f} ({abs(iqr_outlier\u002Fiqr_clean - 1)*100:.0f}% зміна)\")\n",[5288,9497,9498,9508,9512,9517,9563,9567,9572,9613,9617,9636,9645,9654,9659,9664,9669,9689,9711,9733,9740,9744,9754,9764,9768,9773,9778,9783,9797,9811,9815,9828,9867],{"__ignoreMap":5322},[5326,9499,9500,9502,9504,9506],{"class":5328,"line":5329},[5326,9501,5333],{"class":5332},[5326,9503,5337],{"class":5336},[5326,9505,5340],{"class":5332},[5326,9507,5343],{"class":5336},[5326,9509,9510],{"class":5328,"line":5346},[5326,9511,5350],{"emptyLinePlaceholder":5349},[5326,9513,9514],{"class":5328,"line":5353},[5326,9515,9516],{"class":6027},"# Дані без аутлайерів\n",[5326,9518,9519,9522,9524,9526,9528,9530,9533,9535,9538,9540,9542,9544,9547,9549,9552,9554,9556,9558,9561],{"class":5328,"line":5405},[5326,9520,9521],{"class":5336},"data_clean = np.array([",[5326,9523,5445],{"class":5359},[5326,9525,5363],{"class":5336},[5326,9527,5426],{"class":5359},[5326,9529,5363],{"class":5336},[5326,9531,9532],{"class":5359},"13",[5326,9534,5363],{"class":5336},[5326,9536,9537],{"class":5359},"14",[5326,9539,5363],{"class":5336},[5326,9541,5421],{"class":5359},[5326,9543,5363],{"class":5336},[5326,9545,9546],{"class":5359},"16",[5326,9548,5363],{"class":5336},[5326,9550,9551],{"class":5359},"17",[5326,9553,5363],{"class":5336},[5326,9555,5436],{"class":5359},[5326,9557,5363],{"class":5336},[5326,9559,9560],{"class":5359},"20",[5326,9562,5402],{"class":5336},[5326,9564,9565],{"class":5328,"line":5459},[5326,9566,5350],{"emptyLinePlaceholder":5349},[5326,9568,9569],{"class":5328,"line":5464},[5326,9570,9571],{"class":6027},"# Дані з аутлайером\n",[5326,9573,9574,9577,9579,9581,9583,9585,9587,9589,9591,9593,9595,9597,9599,9601,9603,9605,9607,9609,9611],{"class":5328,"line":5497},[5326,9575,9576],{"class":5336},"data_outlier = np.array([",[5326,9578,5445],{"class":5359},[5326,9580,5363],{"class":5336},[5326,9582,5426],{"class":5359},[5326,9584,5363],{"class":5336},[5326,9586,9532],{"class":5359},[5326,9588,5363],{"class":5336},[5326,9590,9537],{"class":5359},[5326,9592,5363],{"class":5336},[5326,9594,5421],{"class":5359},[5326,9596,5363],{"class":5336},[5326,9598,9546],{"class":5359},[5326,9600,5363],{"class":5336},[5326,9602,9551],{"class":5359},[5326,9604,5363],{"class":5336},[5326,9606,5436],{"class":5359},[5326,9608,5363],{"class":5336},[5326,9610,6221],{"class":5359},[5326,9612,5402],{"class":5336},[5326,9614,9615],{"class":5328,"line":5799},[5326,9616,5350],{"emptyLinePlaceholder":5349},[5326,9618,9619,9622,9625,9627,9629,9631,9633],{"class":5328,"line":5804},[5326,9620,9621],{"class":5474},"def",[5326,9623,9624],{"class":5467}," analyze_spread",[5326,9626,5471],{"class":5336},[5326,9628,8029],{"class":6417},[5326,9630,5363],{"class":5336},[5326,9632,8006],{"class":6417},[5326,9634,9635],{"class":5336},"):\n",[5326,9637,9638,9641,9643],{"class":5328,"line":5816},[5326,9639,9640],{"class":5336},"    q1 = np.percentile(data, ",[5326,9642,8256],{"class":5359},[5326,9644,5494],{"class":5336},[5326,9646,9647,9650,9652],{"class":5328,"line":5840},[5326,9648,9649],{"class":5336},"    q3 = np.percentile(data, ",[5326,9651,9156],{"class":5359},[5326,9653,5494],{"class":5336},[5326,9655,9656],{"class":5328,"line":5863},[5326,9657,9658],{"class":5336},"    iqr = q3 - q1\n",[5326,9660,9661],{"class":5328,"line":5886},[5326,9662,9663],{"class":5336},"    range_val = data.max() - data.min()\n",[5326,9665,9666],{"class":5328,"line":5891},[5326,9667,9668],{"class":5336},"    \n",[5326,9670,9671,9673,9675,9677,9679,9681,9683,9685,9687],{"class":5328,"line":5910},[5326,9672,7995],{"class":5467},[5326,9674,5471],{"class":5336},[5326,9676,5475],{"class":5474},[5326,9678,5898],{"class":5478},[5326,9680,5482],{"class":5474},[5326,9682,8006],{"class":5336},[5326,9684,5833],{"class":5474},[5326,9686,8011],{"class":5478},[5326,9688,5494],{"class":5336},[5326,9690,9691,9693,9695,9697,9700,9702,9705,9707,9709],{"class":5328,"line":5932},[5326,9692,7995],{"class":5467},[5326,9694,5471],{"class":5336},[5326,9696,5475],{"class":5474},[5326,9698,9699],{"class":5478},"\"  Range (max - min): ",[5326,9701,5482],{"class":5474},[5326,9703,9704],{"class":5336},"range_val",[5326,9706,6224],{"class":5474},[5326,9708,5898],{"class":5478},[5326,9710,5494],{"class":5336},[5326,9712,9713,9715,9717,9719,9722,9724,9727,9729,9731],{"class":5328,"line":5954},[5326,9714,7995],{"class":5467},[5326,9716,5471],{"class":5336},[5326,9718,5475],{"class":5474},[5326,9720,9721],{"class":5478},"\"  IQR (Q3 - Q1):     ",[5326,9723,5482],{"class":5474},[5326,9725,9726],{"class":5336},"iqr",[5326,9728,5488],{"class":5474},[5326,9730,5898],{"class":5478},[5326,9732,5494],{"class":5336},[5326,9734,9735,9737],{"class":5328,"line":6706},[5326,9736,7995],{"class":5467},[5326,9738,9739],{"class":5336},"()\n",[5326,9741,9742],{"class":5328,"line":6714},[5326,9743,5350],{"emptyLinePlaceholder":5349},[5326,9745,9746,9749,9752],{"class":5328,"line":6719},[5326,9747,9748],{"class":5336},"analyze_spread(data_clean, ",[5326,9750,9751],{"class":5478},"\"Без аутлайера\"",[5326,9753,5494],{"class":5336},[5326,9755,9756,9759,9762],{"class":5328,"line":6725},[5326,9757,9758],{"class":5336},"analyze_spread(data_outlier, ",[5326,9760,9761],{"class":5478},"\"З аутлайером (100)\"",[5326,9763,5494],{"class":5336},[5326,9765,9766],{"class":5328,"line":6731},[5326,9767,5350],{"emptyLinePlaceholder":5349},[5326,9769,9770],{"class":5328,"line":6758},[5326,9771,9772],{"class":6027},"# Порівняння зміни\n",[5326,9774,9775],{"class":5328,"line":6763},[5326,9776,9777],{"class":5336},"range_clean = data_clean.max() - data_clean.min()\n",[5326,9779,9780],{"class":5328,"line":6769},[5326,9781,9782],{"class":5336},"range_outlier = data_outlier.max() - data_outlier.min()\n",[5326,9784,9785,9788,9790,9793,9795],{"class":5328,"line":6784},[5326,9786,9787],{"class":5336},"iqr_clean = np.percentile(data_clean, ",[5326,9789,9156],{"class":5359},[5326,9791,9792],{"class":5336},") - np.percentile(data_clean, ",[5326,9794,8256],{"class":5359},[5326,9796,5494],{"class":5336},[5326,9798,9799,9802,9804,9807,9809],{"class":5328,"line":8608},[5326,9800,9801],{"class":5336},"iqr_outlier = np.percentile(data_outlier, ",[5326,9803,9156],{"class":5359},[5326,9805,9806],{"class":5336},") - np.percentile(data_outlier, ",[5326,9808,8256],{"class":5359},[5326,9810,5494],{"class":5336},[5326,9812,9813],{"class":5328,"line":8640},[5326,9814,5350],{"emptyLinePlaceholder":5349},[5326,9816,9817,9819,9821,9823,9826],{"class":5328,"line":8649},[5326,9818,5468],{"class":5467},[5326,9820,5471],{"class":5336},[5326,9822,5475],{"class":5474},[5326,9824,9825],{"class":5478},"\"Вплив аутлайера:\"",[5326,9827,5494],{"class":5336},[5326,9829,9831,9833,9835,9837,9840,9842,9845,9847,9849,9851,9854,9856,9859,9861,9863,9865],{"class":5328,"line":9830},30,[5326,9832,5468],{"class":5467},[5326,9834,5471],{"class":5336},[5326,9836,5475],{"class":5474},[5326,9838,9839],{"class":5478},"\"  Range змінився на ",[5326,9841,5482],{"class":5474},[5326,9843,9844],{"class":5336},"range_outlier - range_clean",[5326,9846,6224],{"class":5474},[5326,9848,5227],{"class":5478},[5326,9850,5482],{"class":5474},[5326,9852,9853],{"class":5336},"(range_outlier\u002Frange_clean - ",[5326,9855,5315],{"class":5359},[5326,9857,9858],{"class":5336},")*",[5326,9860,6221],{"class":5359},[5326,9862,6224],{"class":5474},[5326,9864,6227],{"class":5478},[5326,9866,5494],{"class":5336},[5326,9868,9870,9872,9874,9876,9879,9881,9884,9886,9888,9890,9893,9896,9898,9900,9902,9904,9907],{"class":5328,"line":9869},31,[5326,9871,5468],{"class":5467},[5326,9873,5471],{"class":5336},[5326,9875,5475],{"class":5474},[5326,9877,9878],{"class":5478},"\"  IQR змінився на ",[5326,9880,5482],{"class":5474},[5326,9882,9883],{"class":5336},"iqr_outlier - iqr_clean",[5326,9885,5488],{"class":5474},[5326,9887,5227],{"class":5478},[5326,9889,5482],{"class":5474},[5326,9891,9892],{"class":5467},"abs",[5326,9894,9895],{"class":5336},"(iqr_outlier\u002Fiqr_clean - ",[5326,9897,5315],{"class":5359},[5326,9899,9858],{"class":5336},[5326,9901,6221],{"class":5359},[5326,9903,6224],{"class":5474},[5326,9905,9906],{"class":5478},"% зміна)\"",[5326,9908,5494],{"class":5336},[5519,9910,9911],{"v-slot:output":5322},[5317,9912,9915],{"className":9913,"code":9914,"language":5526},[5524],"Без аутлайера:\n  Range (max - min): 10\n  IQR (Q3 - Q1):     5.0\n\nЗ аутлайером (100):\n  Range (max - min): 90\n  IQR (Q3 - Q1):     5.0\n\nВплив аутлайера:\n  Range змінився на 80 (800% збільшення)\n  IQR змінився на 0.0 (0% зміна)\n",[5288,9916,9914],{"__ignoreMap":5322},[5278,9918,9919],{},[5556,9920],{"alt":9921,"className":9922,"src":9923},"Порівняння чутливості до аутлайерів: Розмах (Range) vs Міжквартильний розмах (IQR)",[5560],"\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F05.png",[5278,9925,9926,9929,9930,9933],{},[5224,9927,9928],{},"IQR не змінився взагалі!"," Він показує розкид ",[5224,9931,9932],{},"основної маси"," даних, ігноруючи екстремальні значення.",[5594,9935,9936,9941,9944],{},[5278,9937,9938],{},[5224,9939,9940],{},"Інженерна аналогія: Range проти IQR у моніторингу навантаження CPU \u002F RAM",[5278,9942,9943],{},"Уявіть метрики використання оперативної пам'яті бекенд-сервісом у Docker-контейнері:",[5198,9945,9946,9949,9952,9961],{},[5201,9947,9948],{},"Під час старту та прогріву середовища виконання (наприклад, JVM, Node.js чи ініціалізація ML-моделей) пам'ять на 3 секунди стрибає до пікових 950 МБ.",[5201,9950,9951],{},"Після виходу на робочий режим сервіс стабільно споживає від 180 до 220 МБ упродовж 24 годин.",[5201,9953,9954,5286,9957,9960],{},[5224,9955,9956],{},"Розмах (Range):",[5613,9958],{"tex":9959,":inline":5616},"\\text{Max} - \\text{Min} = 950 - 180 = 770"," МБ. Він покаже гігантську нестабільність, хоча 99.9% часу сервіс працює спокійно.",[5201,9962,9963,5286,9966,9969],{},[5224,9964,9965],{},"IQR (Q3 − Q1):",[5613,9967],{"tex":9968,":inline":5616},"220 - 180 = 40"," МБ. Він повністю відсікає короткочасний сплеск ініціалізації та повідомляє DevOps-інженеру реальний робочий коридор споживання пам'яті.",[8130,9971,9972,9977,9991,9996],{},[5278,9973,9974],{},[5224,9975,9976],{},"Коли використовувати IQR замість стандартного відхилення:",[5198,9978,9979,9982,9985,9988],{},[5201,9980,9981],{},"✅ Дані містять аутлайери",[5201,9983,9984],{},"✅ Розподіл сильно асиметричний",[5201,9986,9987],{},"✅ Потрібна робастна (стійка) міра варіації",[5201,9989,9990],{},"✅ Для побудови box-plot діаграм",[5278,9992,9993],{},[5224,9994,9995],{},"Коли використовувати стандартне відхилення:",[5198,9997,9998,10001,10004],{},[5201,9999,10000],{},"✅ Дані приблизно симетричні (нормальний розподіл)",[5201,10002,10003],{},"✅ Немає значних аутлайерів",[5201,10005,10006],{},"✅ Потрібна математично зручна міра (для формул та теорем)",[5270,10008],{},[5273,10010,10012],{"id":10011},"правило-виявлення-аутлайерів-за-допомогою-iqr","Правило виявлення аутлайерів за допомогою IQR",[5278,10014,10015,10016,10019],{},"IQR не тільки міра варіації — він також використовується для ",[5224,10017,10018],{},"автоматичного виявлення аутлайерів",". Класичне правило:",[5278,10021,10022,10025],{},[5224,10023,10024],{},"Аутлайер"," — це значення, яке лежить:",[5198,10027,10028,10037],{},[5201,10029,10030,5286,10033,10036],{},[5224,10031,10032],{},"нижче",[5613,10034],{"tex":10035,":inline":5616},"Q_1 - 1.5 \\times \\text{IQR}",", або",[5201,10038,10039,5286,10042],{},[5224,10040,10041],{},"вище",[5613,10043],{"tex":10044,":inline":5616},"Q_3 + 1.5 \\times \\text{IQR}",[5278,10046,10047,10048,5227,10051,10054],{},"Це називається ",[5224,10049,10050],{},"правилом Тьюкі",[5229,10052,10053],{},"Tukey's fences",").",[5308,10056,10058,10064,10455],{"kernel":5310,"title":10057},"outlier_detection_iqr.ipynb",[5313,10059,10060],{"type":5669},[5653,10061,10063],{"id":10062},"виявлення-аутлайерів-за-правилом-iqr","Виявлення аутлайерів за правилом IQR",[5313,10065,10066,10447],{"execution-count":5315},[5317,10067,10069],{"className":5319,"code":10068,"language":5321,"meta":5322,"style":5322},"import numpy as np\n\n# Дані про вартість квартир (млн грн)\nprices = np.array([1.2, 1.5, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.2, 8.5])\n\n# Обчислюємо квартилі та IQR\nq1 = np.percentile(prices, 25)\nq3 = np.percentile(prices, 75)\niqr = q3 - q1\n\n# Межі для аутлайерів\nlower_fence = q1 - 1.5 * iqr\nupper_fence = q3 + 1.5 * iqr\n\nprint(f\"Q1:  {q1:.2f} млн грн\")\nprint(f\"Q3:  {q3:.2f} млн грн\")\nprint(f\"IQR: {iqr:.2f} млн грн\")\nprint(f\"\\nМежі для нормальних значень:\")\nprint(f\"  Нижня межа: {lower_fence:.2f} млн грн\")\nprint(f\"  Верхня межа: {upper_fence:.2f} млн грн\")\n\n# Виявлення аутлайерів\noutliers = prices[(prices \u003C lower_fence) | (prices > upper_fence)]\nnormal = prices[(prices >= lower_fence) & (prices \u003C= upper_fence)]\n\nprint(f\"\\nАутлайери: {outliers}\")\nprint(f\"Нормальні значення: {normal}\")\nprint(f\"\\nЗнайдено {len(outliers)} аутлайерів із {len(prices)} значень\")\n",[5288,10070,10071,10081,10085,10090,10145,10149,10154,10163,10172,10177,10181,10186,10196,10205,10209,10231,10252,10273,10290,10312,10334,10338,10343,10348,10353,10357,10383,10405],{"__ignoreMap":5322},[5326,10072,10073,10075,10077,10079],{"class":5328,"line":5329},[5326,10074,5333],{"class":5332},[5326,10076,5337],{"class":5336},[5326,10078,5340],{"class":5332},[5326,10080,5343],{"class":5336},[5326,10082,10083],{"class":5328,"line":5346},[5326,10084,5350],{"emptyLinePlaceholder":5349},[5326,10086,10087],{"class":5328,"line":5353},[5326,10088,10089],{"class":6027},"# Дані про вартість квартир (млн грн)\n",[5326,10091,10092,10095,10098,10100,10103,10105,10108,10110,10113,10115,10118,10120,10123,10125,10128,10130,10133,10135,10138,10140,10143],{"class":5328,"line":5405},[5326,10093,10094],{"class":5336},"prices = np.array([",[5326,10096,10097],{"class":5359},"1.2",[5326,10099,5363],{"class":5336},[5326,10101,10102],{"class":5359},"1.5",[5326,10104,5363],{"class":5336},[5326,10106,10107],{"class":5359},"1.8",[5326,10109,5363],{"class":5336},[5326,10111,10112],{"class":5359},"2.0",[5326,10114,5363],{"class":5336},[5326,10116,10117],{"class":5359},"2.2",[5326,10119,5363],{"class":5336},[5326,10121,10122],{"class":5359},"2.5",[5326,10124,5363],{"class":5336},[5326,10126,10127],{"class":5359},"2.8",[5326,10129,5363],{"class":5336},[5326,10131,10132],{"class":5359},"3.0",[5326,10134,5363],{"class":5336},[5326,10136,10137],{"class":5359},"3.2",[5326,10139,5363],{"class":5336},[5326,10141,10142],{"class":5359},"8.5",[5326,10144,5402],{"class":5336},[5326,10146,10147],{"class":5328,"line":5459},[5326,10148,5350],{"emptyLinePlaceholder":5349},[5326,10150,10151],{"class":5328,"line":5464},[5326,10152,10153],{"class":6027},"# Обчислюємо квартилі та IQR\n",[5326,10155,10156,10159,10161],{"class":5328,"line":5497},[5326,10157,10158],{"class":5336},"q1 = np.percentile(prices, ",[5326,10160,8256],{"class":5359},[5326,10162,5494],{"class":5336},[5326,10164,10165,10168,10170],{"class":5328,"line":5799},[5326,10166,10167],{"class":5336},"q3 = np.percentile(prices, ",[5326,10169,9156],{"class":5359},[5326,10171,5494],{"class":5336},[5326,10173,10174],{"class":5328,"line":5804},[5326,10175,10176],{"class":5336},"iqr = q3 - q1\n",[5326,10178,10179],{"class":5328,"line":5816},[5326,10180,5350],{"emptyLinePlaceholder":5349},[5326,10182,10183],{"class":5328,"line":5840},[5326,10184,10185],{"class":6027},"# Межі для аутлайерів\n",[5326,10187,10188,10191,10193],{"class":5328,"line":5863},[5326,10189,10190],{"class":5336},"lower_fence = q1 - ",[5326,10192,10102],{"class":5359},[5326,10194,10195],{"class":5336}," * iqr\n",[5326,10197,10198,10201,10203],{"class":5328,"line":5886},[5326,10199,10200],{"class":5336},"upper_fence = q3 + ",[5326,10202,10102],{"class":5359},[5326,10204,10195],{"class":5336},[5326,10206,10207],{"class":5328,"line":5891},[5326,10208,5350],{"emptyLinePlaceholder":5349},[5326,10210,10211,10213,10215,10217,10220,10222,10224,10226,10229],{"class":5328,"line":5910},[5326,10212,5468],{"class":5467},[5326,10214,5471],{"class":5336},[5326,10216,5475],{"class":5474},[5326,10218,10219],{"class":5478},"\"Q1:  ",[5326,10221,5482],{"class":5474},[5326,10223,9225],{"class":5336},[5326,10225,6751],{"class":5474},[5326,10227,10228],{"class":5478}," млн грн\"",[5326,10230,5494],{"class":5336},[5326,10232,10233,10235,10237,10239,10242,10244,10246,10248,10250],{"class":5328,"line":5932},[5326,10234,5468],{"class":5467},[5326,10236,5471],{"class":5336},[5326,10238,5475],{"class":5474},[5326,10240,10241],{"class":5478},"\"Q3:  ",[5326,10243,5482],{"class":5474},[5326,10245,9270],{"class":5336},[5326,10247,6751],{"class":5474},[5326,10249,10228],{"class":5478},[5326,10251,5494],{"class":5336},[5326,10253,10254,10256,10258,10260,10263,10265,10267,10269,10271],{"class":5328,"line":5954},[5326,10255,5468],{"class":5467},[5326,10257,5471],{"class":5336},[5326,10259,5475],{"class":5474},[5326,10261,10262],{"class":5478},"\"IQR: ",[5326,10264,5482],{"class":5474},[5326,10266,9726],{"class":5336},[5326,10268,6751],{"class":5474},[5326,10270,10228],{"class":5478},[5326,10272,5494],{"class":5336},[5326,10274,10275,10277,10279,10281,10283,10285,10288],{"class":5328,"line":6706},[5326,10276,5468],{"class":5467},[5326,10278,5471],{"class":5336},[5326,10280,5475],{"class":5474},[5326,10282,5898],{"class":5478},[5326,10284,5902],{"class":5901},[5326,10286,10287],{"class":5478},"Межі для нормальних значень:\"",[5326,10289,5494],{"class":5336},[5326,10291,10292,10294,10296,10298,10301,10303,10306,10308,10310],{"class":5328,"line":6714},[5326,10293,5468],{"class":5467},[5326,10295,5471],{"class":5336},[5326,10297,5475],{"class":5474},[5326,10299,10300],{"class":5478},"\"  Нижня межа: ",[5326,10302,5482],{"class":5474},[5326,10304,10305],{"class":5336},"lower_fence",[5326,10307,6751],{"class":5474},[5326,10309,10228],{"class":5478},[5326,10311,5494],{"class":5336},[5326,10313,10314,10316,10318,10320,10323,10325,10328,10330,10332],{"class":5328,"line":6719},[5326,10315,5468],{"class":5467},[5326,10317,5471],{"class":5336},[5326,10319,5475],{"class":5474},[5326,10321,10322],{"class":5478},"\"  Верхня межа: ",[5326,10324,5482],{"class":5474},[5326,10326,10327],{"class":5336},"upper_fence",[5326,10329,6751],{"class":5474},[5326,10331,10228],{"class":5478},[5326,10333,5494],{"class":5336},[5326,10335,10336],{"class":5328,"line":6725},[5326,10337,5350],{"emptyLinePlaceholder":5349},[5326,10339,10340],{"class":5328,"line":6731},[5326,10341,10342],{"class":6027},"# Виявлення аутлайерів\n",[5326,10344,10345],{"class":5328,"line":6758},[5326,10346,10347],{"class":5336},"outliers = prices[(prices \u003C lower_fence) | (prices > upper_fence)]\n",[5326,10349,10350],{"class":5328,"line":6763},[5326,10351,10352],{"class":5336},"normal = prices[(prices >= lower_fence) & (prices \u003C= upper_fence)]\n",[5326,10354,10355],{"class":5328,"line":6769},[5326,10356,5350],{"emptyLinePlaceholder":5349},[5326,10358,10359,10361,10363,10365,10367,10369,10372,10374,10377,10379,10381],{"class":5328,"line":6784},[5326,10360,5468],{"class":5467},[5326,10362,5471],{"class":5336},[5326,10364,5475],{"class":5474},[5326,10366,5898],{"class":5478},[5326,10368,5902],{"class":5901},[5326,10370,10371],{"class":5478},"Аутлайери: ",[5326,10373,5482],{"class":5474},[5326,10375,10376],{"class":5336},"outliers",[5326,10378,5833],{"class":5474},[5326,10380,5898],{"class":5478},[5326,10382,5494],{"class":5336},[5326,10384,10385,10387,10389,10391,10394,10396,10399,10401,10403],{"class":5328,"line":8608},[5326,10386,5468],{"class":5467},[5326,10388,5471],{"class":5336},[5326,10390,5475],{"class":5474},[5326,10392,10393],{"class":5478},"\"Нормальні значення: ",[5326,10395,5482],{"class":5474},[5326,10397,10398],{"class":5336},"normal",[5326,10400,5833],{"class":5474},[5326,10402,5898],{"class":5478},[5326,10404,5494],{"class":5336},[5326,10406,10407,10409,10411,10413,10415,10417,10420,10422,10425,10428,10430,10433,10435,10437,10440,10442,10445],{"class":5328,"line":8640},[5326,10408,5468],{"class":5467},[5326,10410,5471],{"class":5336},[5326,10412,5475],{"class":5474},[5326,10414,5898],{"class":5478},[5326,10416,5902],{"class":5901},[5326,10418,10419],{"class":5478},"Знайдено ",[5326,10421,5482],{"class":5474},[5326,10423,10424],{"class":5467},"len",[5326,10426,10427],{"class":5336},"(outliers)",[5326,10429,5833],{"class":5474},[5326,10431,10432],{"class":5478}," аутлайерів із ",[5326,10434,5482],{"class":5474},[5326,10436,10424],{"class":5467},[5326,10438,10439],{"class":5336},"(prices)",[5326,10441,5833],{"class":5474},[5326,10443,10444],{"class":5478}," значень\"",[5326,10446,5494],{"class":5336},[5519,10448,10449],{"v-slot:output":5322},[5317,10450,10453],{"className":10451,"code":10452,"language":5526},[5524],"Q1:  1.80 млн грн\nQ3:  3.00 млн грн\nIQR: 1.20 млн грн\n\nМежі для нормальних значень:\n  Нижня межа: 0.00 млн грн\n  Верхня межа: 4.80 млн грн\n\nАутлайери: [8.5]\nНормальні значення: [1.2 1.5 1.8 2.  2.2 2.5 2.8 3.  3.2]\n\nЗнайдено 1 аутлайерів із 10 значень\n",[5288,10454,10452],{"__ignoreMap":5322},[5313,10456,10457,10749],{"execution-count":5411},[5317,10458,10460],{"className":5319,"code":10459,"language":5321,"meta":5322,"style":5322},"# Функція для виявлення аутлайерів (багаторазове використання)\ndef detect_outliers_iqr(data):\n    q1 = np.percentile(data, 25)\n    q3 = np.percentile(data, 75)\n    iqr = q3 - q1\n    \n    lower_fence = q1 - 1.5 * iqr\n    upper_fence = q3 + 1.5 * iqr\n    \n    outliers_mask = (data \u003C lower_fence) | (data > upper_fence)\n    \n    return {\n        'outliers': data[outliers_mask],\n        'outliers_indices': np.where(outliers_mask)[0],\n        'normal': data[~outliers_mask],\n        'lower_fence': lower_fence,\n        'upper_fence': upper_fence\n    }\n\n# Тестуємо на даних про зарплати\nsalaries = np.array([25, 28, 30, 32, 35, 30, 28, 33, 31, 200])\nresult = detect_outliers_iqr(salaries)\n\nprint(\"Аналіз зарплат:\")\nprint(f\"  Виявлено аутлайерів: {len(result['outliers'])}\")\nprint(f\"  Аутлайери: {result['outliers']} тис. грн\")\nprint(f\"  Індекси аутлайерів: {result['outliers_indices']}\")\n",[5288,10461,10462,10467,10480,10488,10496,10500,10504,10513,10522,10526,10531,10535,10543,10551,10564,10572,10580,10588,10593,10597,10602,10647,10652,10656,10667,10697,10723],{"__ignoreMap":5322},[5326,10463,10464],{"class":5328,"line":5329},[5326,10465,10466],{"class":6027},"# Функція для виявлення аутлайерів (багаторазове використання)\n",[5326,10468,10469,10471,10474,10476,10478],{"class":5328,"line":5346},[5326,10470,9621],{"class":5474},[5326,10472,10473],{"class":5467}," detect_outliers_iqr",[5326,10475,5471],{"class":5336},[5326,10477,8029],{"class":6417},[5326,10479,9635],{"class":5336},[5326,10481,10482,10484,10486],{"class":5328,"line":5353},[5326,10483,9640],{"class":5336},[5326,10485,8256],{"class":5359},[5326,10487,5494],{"class":5336},[5326,10489,10490,10492,10494],{"class":5328,"line":5405},[5326,10491,9649],{"class":5336},[5326,10493,9156],{"class":5359},[5326,10495,5494],{"class":5336},[5326,10497,10498],{"class":5328,"line":5459},[5326,10499,9658],{"class":5336},[5326,10501,10502],{"class":5328,"line":5464},[5326,10503,9668],{"class":5336},[5326,10505,10506,10509,10511],{"class":5328,"line":5497},[5326,10507,10508],{"class":5336},"    lower_fence = q1 - ",[5326,10510,10102],{"class":5359},[5326,10512,10195],{"class":5336},[5326,10514,10515,10518,10520],{"class":5328,"line":5799},[5326,10516,10517],{"class":5336},"    upper_fence = q3 + ",[5326,10519,10102],{"class":5359},[5326,10521,10195],{"class":5336},[5326,10523,10524],{"class":5328,"line":5804},[5326,10525,9668],{"class":5336},[5326,10527,10528],{"class":5328,"line":5816},[5326,10529,10530],{"class":5336},"    outliers_mask = (data \u003C lower_fence) | (data > upper_fence)\n",[5326,10532,10533],{"class":5328,"line":5840},[5326,10534,9668],{"class":5336},[5326,10536,10537,10540],{"class":5328,"line":5863},[5326,10538,10539],{"class":5332},"    return",[5326,10541,10542],{"class":5336}," {\n",[5326,10544,10545,10548],{"class":5328,"line":5886},[5326,10546,10547],{"class":5478},"        'outliers'",[5326,10549,10550],{"class":5336},": data[outliers_mask],\n",[5326,10552,10553,10556,10559,10561],{"class":5328,"line":5891},[5326,10554,10555],{"class":5478},"        'outliers_indices'",[5326,10557,10558],{"class":5336},": np.where(outliers_mask)[",[5326,10560,6779],{"class":5359},[5326,10562,10563],{"class":5336},"],\n",[5326,10565,10566,10569],{"class":5328,"line":5910},[5326,10567,10568],{"class":5478},"        'normal'",[5326,10570,10571],{"class":5336},": data[~outliers_mask],\n",[5326,10573,10574,10577],{"class":5328,"line":5932},[5326,10575,10576],{"class":5478},"        'lower_fence'",[5326,10578,10579],{"class":5336},": lower_fence,\n",[5326,10581,10582,10585],{"class":5328,"line":5954},[5326,10583,10584],{"class":5478},"        'upper_fence'",[5326,10586,10587],{"class":5336},": upper_fence\n",[5326,10589,10590],{"class":5328,"line":6706},[5326,10591,10592],{"class":5336},"    }\n",[5326,10594,10595],{"class":5328,"line":6714},[5326,10596,5350],{"emptyLinePlaceholder":5349},[5326,10598,10599],{"class":5328,"line":6719},[5326,10600,10601],{"class":6027},"# Тестуємо на даних про зарплати\n",[5326,10603,10604,10606,10608,10610,10612,10614,10616,10618,10620,10622,10624,10626,10628,10630,10632,10634,10636,10638,10640,10642,10645],{"class":5328,"line":6725},[5326,10605,8253],{"class":5336},[5326,10607,8256],{"class":5359},[5326,10609,5363],{"class":5336},[5326,10611,8261],{"class":5359},[5326,10613,5363],{"class":5336},[5326,10615,7866],{"class":5359},[5326,10617,5363],{"class":5336},[5326,10619,8270],{"class":5359},[5326,10621,5363],{"class":5336},[5326,10623,7881],{"class":5359},[5326,10625,5363],{"class":5336},[5326,10627,7866],{"class":5359},[5326,10629,5363],{"class":5336},[5326,10631,8261],{"class":5359},[5326,10633,5363],{"class":5336},[5326,10635,8287],{"class":5359},[5326,10637,5363],{"class":5336},[5326,10639,8292],{"class":5359},[5326,10641,5363],{"class":5336},[5326,10643,10644],{"class":5359},"200",[5326,10646,5402],{"class":5336},[5326,10648,10649],{"class":5328,"line":6731},[5326,10650,10651],{"class":5336},"result = detect_outliers_iqr(salaries)\n",[5326,10653,10654],{"class":5328,"line":6758},[5326,10655,5350],{"emptyLinePlaceholder":5349},[5326,10657,10658,10660,10662,10665],{"class":5328,"line":6763},[5326,10659,5468],{"class":5467},[5326,10661,5471],{"class":5336},[5326,10663,10664],{"class":5478},"\"Аналіз зарплат:\"",[5326,10666,5494],{"class":5336},[5326,10668,10669,10671,10673,10675,10678,10680,10682,10685,10688,10691,10693,10695],{"class":5328,"line":6769},[5326,10670,5468],{"class":5467},[5326,10672,5471],{"class":5336},[5326,10674,5475],{"class":5474},[5326,10676,10677],{"class":5478},"\"  Виявлено аутлайерів: ",[5326,10679,5482],{"class":5474},[5326,10681,10424],{"class":5467},[5326,10683,10684],{"class":5336},"(result[",[5326,10686,10687],{"class":5478},"'outliers'",[5326,10689,10690],{"class":5336},"])",[5326,10692,5833],{"class":5474},[5326,10694,5898],{"class":5478},[5326,10696,5494],{"class":5336},[5326,10698,10699,10701,10703,10705,10708,10710,10713,10715,10717,10719,10721],{"class":5328,"line":6784},[5326,10700,5468],{"class":5467},[5326,10702,5471],{"class":5336},[5326,10704,5475],{"class":5474},[5326,10706,10707],{"class":5478},"\"  Аутлайери: ",[5326,10709,5482],{"class":5474},[5326,10711,10712],{"class":5336},"result[",[5326,10714,10687],{"class":5478},[5326,10716,8107],{"class":5336},[5326,10718,5833],{"class":5474},[5326,10720,8448],{"class":5478},[5326,10722,5494],{"class":5336},[5326,10724,10725,10727,10729,10731,10734,10736,10738,10741,10743,10745,10747],{"class":5328,"line":8608},[5326,10726,5468],{"class":5467},[5326,10728,5471],{"class":5336},[5326,10730,5475],{"class":5474},[5326,10732,10733],{"class":5478},"\"  Індекси аутлайерів: ",[5326,10735,5482],{"class":5474},[5326,10737,10712],{"class":5336},[5326,10739,10740],{"class":5478},"'outliers_indices'",[5326,10742,8107],{"class":5336},[5326,10744,5833],{"class":5474},[5326,10746,5898],{"class":5478},[5326,10748,5494],{"class":5336},[5519,10750,10751],{"v-slot:output":5322},[5317,10752,10755],{"className":10753,"code":10754,"language":5526},[5524],"Аналіз зарплат:\n  Виявлено аутлайерів: 1\n  Аутлайери: [200] тис. грн\n  Індекси аутлайерів: [9]\n",[5288,10756,10754],{"__ignoreMap":5322},[5594,10758,10759,10764,10767,10781,10784],{},[5278,10760,10761],{},[5224,10762,10763],{},"Чому саме 1.5?",[5278,10765,10766],{},"Коефіцієнт 1.5 — це емпірично підібране значення Джоном Тьюкі. Воно добре працює для більшості розподілів:",[5198,10768,10769,10775],{},[5201,10770,10771,10774],{},[5224,10772,10773],{},"Не надто жорстке"," (не помічає як аутлайери звичайні коливання)",[5201,10776,10777,10780],{},[5224,10778,10779],{},"Не надто м'яке"," (не пропускає справжні аномалії)",[5278,10782,10783],{},"Іноді використовують інші коефіцієнти:",[5198,10785,10786,10791],{},[5201,10787,10788,10790],{},[5224,10789,10132],{}," — для більш консервативного підходу (менше хибних спрацьовувань)",[5201,10792,10793,8170,10795,10797],{},[5224,10794,10117],{},[5224,10796,10112],{}," — для більш чутливого виявлення",[5278,10799,10800],{},[5556,10801],{"alt":10802,"className":10803,"src":10804},"Анатомія Box Plot та правило 1.5 IQR для виявлення аутлайерів",[5560],"\u002Fimages\u002Fai-python\u002Fstatistics-basics\u002Fvariability\u002F06.png",[5270,10806],{},[5273,10808,10810],{"id":10809},"порівняльна-таблиця-мір-варіації","Порівняльна таблиця мір варіації",[10812,10813,10814,10837],"table",{},[10815,10816,10817],"thead",{},[10818,10819,10820,10825,10827,10831,10834],"tr",{},[10821,10822,10824],"th",{"align":10823},"left","Міра",[10821,10826,5656],{"align":10823},[10821,10828,10830],{"align":10829},"center","Стійкість до аутлайерів",[10821,10832,10833],{"align":10823},"Одиниці виміру",[10821,10835,10836],{"align":10823},"Коли використовувати",[10838,10839,10840,10859,10878,10896,10913],"tbody",{},[10818,10841,10842,10847,10850,10853,10856],{},[10843,10844,10845],"td",{"align":10823},[5224,10846,5226],{},[10843,10848,10849],{"align":10823},"max − min",[10843,10851,10852],{"align":10829},"❌",[10843,10854,10855],{"align":10823},"Такі ж, як дані",[10843,10857,10858],{"align":10823},"Швидка оцінка діапазону",[10818,10860,10861,10865,10870,10872,10875],{},[10843,10862,10863],{"align":10823},[5224,10864,5237],{},[10843,10866,10867],{"align":10823},[5613,10868],{"tex":10869,":inline":5616},"\\frac{1}{n}\\sum(x_i - \\bar{x})^2",[10843,10871,10852],{"align":10829},[10843,10873,10874],{"align":10823},"Квадрат одиниць",[10843,10876,10877],{"align":10823},"Математичні обчислення, теореми",[10818,10879,10880,10884,10889,10891,10893],{},[10843,10881,10882],{"align":10823},[5224,10883,5246],{},[10843,10885,10886],{"align":10823},[5613,10887],{"tex":10888,":inline":5616},"\\sqrt{\\text{дисперсія}}",[10843,10890,10852],{"align":10829},[10843,10892,10855],{"align":10823},[10843,10894,10895],{"align":10823},"Найпопулярніша міра варіації",[10818,10897,10898,10902,10905,10908,10910],{},[10843,10899,10900],{"align":10823},[5224,10901,5267],{},[10843,10903,10904],{"align":10823},"Q3 − Q1",[10843,10906,10907],{"align":10829},"✅",[10843,10909,10855],{"align":10823},[10843,10911,10912],{"align":10823},"Дані з аутлайерами, box-plots",[10818,10914,10915,10919,10924,10926,10929],{},[10843,10916,10917],{"align":10823},[5224,10918,8205],{},[10843,10920,10921],{"align":10823},[5613,10922],{"tex":10923,":inline":5616},"\\frac{\\sigma}{\\mu} \\times 100\\%",[10843,10925,10852],{"align":10829},[10843,10927,10928],{"align":10823},"Безрозмірний (%)",[10843,10930,10931],{"align":10823},"Порівняння різних змінних",[5270,10933],{},[5273,10935,10937],{"id":10936},"практичні-завдання","Практичні завдання",[5653,10939,10941],{"id":10940},"рівень-1-базові-вправи","Рівень 1: Базові вправи",[10943,10944,10945,10987,11014],"accordion",{},[10946,10947,10949,10952,10958,10961,10978],"accordion-item",{"icon":2990,"label":10948},"Завдання 1.1: Обчислення дисперсії вручну",[5278,10950,10951],{},"Дано температури повітря за тиждень (°C):",[5317,10953,10956],{"className":10954,"code":10955,"language":5526},[5524],"18, 20, 19, 21, 22, 20, 19\n",[5288,10957,10955],{"__ignoreMap":5322},[5278,10959,10960],{},"Без використання NumPy\u002Fpandas:",[6312,10962,10963,10966,10969,10972,10975],{},[5201,10964,10965],{},"Обчисліть середнє",[5201,10967,10968],{},"Знайдіть відхилення кожного значення від середнього",[5201,10970,10971],{},"Зведіть відхилення в квадрат",[5201,10973,10974],{},"Обчисліть дисперсію (середнє квадратів)",[5201,10976,10977],{},"Обчисліть стандартне відхилення (√дисперсія)",[5278,10979,10980,10981,10983,10984,5542],{},"Перевірте результат за допомогою ",[5288,10982,6390],{}," та ",[5288,10985,10986],{},"np.std()",[10946,10988,10991,10994,11000],{"icon":10989,"label":10990},"i-lucide-bar-chart-4","Завдання 1.2: Квартилі та IQR",[5278,10992,10993],{},"Дано оцінки 15 студентів:",[5317,10995,10998],{"className":10996,"code":10997,"language":5526},[5524],"65, 70, 72, 75, 78, 80, 82, 85, 87, 90, 92, 95, 98, 100, 55\n",[5288,10999,10997],{"__ignoreMap":5322},[6312,11001,11002,11005,11008,11011],{},[5201,11003,11004],{},"Обчисліть Q1, Q2 (медіану), Q3",[5201,11006,11007],{},"Обчисліть IQR",[5201,11009,11010],{},"Знайдіть межі для виявлення аутлайерів (Q1 - 1.5×IQR, Q3 + 1.5×IQR)",[5201,11012,11013],{},"Визначте, які оцінки є аутлайерами",[10946,11015,11018,11021,11035,11038],{"icon":11016,"label":11017},"i-lucide-git-compare","Завдання 1.3: Порівняння двох груп",[5278,11019,11020],{},"Згенеруйте дві групи студентів:",[5198,11022,11023,11029],{},[5201,11024,11025,11028],{},[5224,11026,11027],{},"Група A:"," 20 студентів, нормальний розподіл (mean=75, std=5)",[5201,11030,11031,11034],{},[5224,11032,11033],{},"Група B:"," 20 студентів, нормальний розподіл (mean=75, std=15)",[5278,11036,11037],{},"Обчисліть для кожної групи:",[6312,11039,11040,11043,11046],{},[5201,11041,11042],{},"Середнє та стандартне відхилення",[5201,11044,11045],{},"Розмах та IQR",[5201,11047,11048],{},"Зробіть висновок: яка група більш стабільна?",[5270,11050],{},[5653,11052,11054],{"id":11053},"рівень-2-алгоритмічні-задачі","Рівень 2: Алгоритмічні задачі",[10943,11056,11057,11097,11184],{},[10946,11058,11061,11064,11084,11087],{"icon":11059,"label":11060},"i-lucide-percent","Завдання 2.1: Коефіцієнт варіації для різних змінних",[5278,11062,11063],{},"Створіть DataFrame із синтетичними даними про студентів:",[5198,11065,11066,11072,11078],{},[5201,11067,11068,11071],{},[5224,11069,11070],{},"Зріст"," (см): нормальний розподіл, mean=170, std=10",[5201,11073,11074,11077],{},[5224,11075,11076],{},"Вага"," (кг): нормальний розподіл, mean=65, std=12",[5201,11079,11080,11083],{},[5224,11081,11082],{},"Оцінка"," (0–100): нормальний розподіл, mean=75, std=15",[5278,11085,11086],{},"Для кожного стовпця обчисліть:",[6312,11088,11089,11091,11094],{},[5201,11090,11042],{},[5201,11092,11093],{},"Коефіцієнт варіації (CV)",[5201,11095,11096],{},"Визначте, яка змінна найбільш мінлива відносно свого середнього",[10946,11098,11100,11107,11118,11121,11181],{"icon":4475,"label":11099},"Завдання 2.2: Очищення даних від аутлайерів",[5278,11101,11102,11103,11106],{},"Напишіть функцію ",[5288,11104,11105],{},"remove_outliers_iqr(data)",", яка:",[6312,11108,11109,11112,11115],{},[5201,11110,11111],{},"Виявляє аутлайери за правилом IQR",[5201,11113,11114],{},"Видаляє їх із масиву",[5201,11116,11117],{},"Повертає очищений масив та кількість видалених значень",[5278,11119,11120],{},"Протестуйте на даних:",[5317,11122,11124],{"className":5319,"code":11123,"language":5321,"meta":5322,"style":5322},"prices = [1.2, 1.5, 1.8, 2.0, 2.2, 2.5, 2.8, 3.0, 3.2, 8.5, 15.0, 0.5]\n",[5288,11125,11126],{"__ignoreMap":5322},[5326,11127,11128,11131,11133,11135,11137,11139,11141,11143,11145,11147,11149,11151,11153,11155,11157,11159,11161,11163,11165,11167,11169,11171,11174,11176,11179],{"class":5328,"line":5329},[5326,11129,11130],{"class":5336},"prices = [",[5326,11132,10097],{"class":5359},[5326,11134,5363],{"class":5336},[5326,11136,10102],{"class":5359},[5326,11138,5363],{"class":5336},[5326,11140,10107],{"class":5359},[5326,11142,5363],{"class":5336},[5326,11144,10112],{"class":5359},[5326,11146,5363],{"class":5336},[5326,11148,10117],{"class":5359},[5326,11150,5363],{"class":5336},[5326,11152,10122],{"class":5359},[5326,11154,5363],{"class":5336},[5326,11156,10127],{"class":5359},[5326,11158,5363],{"class":5336},[5326,11160,10132],{"class":5359},[5326,11162,5363],{"class":5336},[5326,11164,10137],{"class":5359},[5326,11166,5363],{"class":5336},[5326,11168,10142],{"class":5359},[5326,11170,5363],{"class":5336},[5326,11172,11173],{"class":5359},"15.0",[5326,11175,5363],{"class":5336},[5326,11177,11178],{"class":5359},"0.5",[5326,11180,7954],{"class":5336},[5278,11182,11183],{},"Порівняйте mean та std до та після очищення.",[10946,11185,11188,11191,11205,11208,11221],{"icon":11186,"label":11187},"i-lucide-trending-up","Завдання 2.3: Симуляція стабільності інвестицій",[5278,11189,11190],{},"Змоделюйте два інвестиційні портфелі протягом 365 днів:",[5198,11192,11193,11199],{},[5201,11194,11195,11198],{},[5224,11196,11197],{},"Портфель A (стабільний):"," щоденна дохідність = norm(0.05%, 0.5%)",[5201,11200,11201,11204],{},[5224,11202,11203],{},"Портфель B (ризиковий):"," щоденна дохідність = norm(0.05%, 2.5%)",[5278,11206,11207],{},"Для кожного портфеля обчисліть:",[6312,11209,11210,11213,11216,11218],{},[5201,11211,11212],{},"Середню дохідність",[5201,11214,11215],{},"Стандартне відхилення дохідності (міра ризику)",[5201,11217,8205],{},[5201,11219,11220],{},"Кінцеву вартість (початковий капітал 100 000 грн)",[5278,11222,11223],{},"Зробіть висновок: який портфель краще для консервативного інвестора?",[5270,11225],{},[5653,11227,11229],{"id":11228},"рівень-3-проєктні-завдання","Рівень 3: Проєктні завдання",[10943,11231,11232,11259,11279],{},[10946,11233,11236,11242],{"icon":11234,"label":11235},"i-lucide-flower-2","Завдання 3.1: Аналіз датасету Iris з фокусом на варіацію",[5278,11237,11238,11239,6404],{},"Завантажте датасет Iris (доступний у sklearn або seaborn). Для стовпця ",[5288,11240,11241],{},"sepal_length",[6312,11243,11244,11247,11250,11253,11256],{},[5201,11245,11246],{},"Обчисліть усі міри варіації: Range, Variance, Std, IQR, CV",[5201,11248,11249],{},"Побудуйте гістограму з позначенням mean ± 1×std",[5201,11251,11252],{},"Виявіть аутлайери за правилом IQR",[5201,11254,11255],{},"Порівняйте варіацію для трьох видів квітів (setosa, versicolor, virginica)",[5201,11257,11258],{},"Визначте, який вид має найбільшу варіацію довжини чашолистка",[10946,11260,11263,11270,11276],{"icon":11261,"label":11262},"i-lucide-file-bar-chart","Завдання 3.2: Побудова функції для автоматичного звіту",[5278,11264,11265,11266,11269],{},"Створіть функцію ",[5288,11267,11268],{},"variability_report(data, column_name)",", яка генерує детальний текстовий звіт:",[5317,11271,11274],{"className":11272,"code":11273,"language":5526},[5524],"Звіт про варіацію стовпця 'Salary'\n════════════════════════════════════\nКількість значень: 100\n\nМіри центральної тенденції:\n  Середнє:    42,340 грн\n  Медіана:    40,200 грн\n\nМіри варіації:\n  Розмах:                12,800 грн\n  Дисперсія:             8,456,290 грн²\n  Стандартне відхилення: 2,908 грн (6.9% від середнього)\n  IQR:                   4,200 грн\n  Коефіцієнт варіації:   6.9%\n\nКвартилі:\n  Q1 (25%): 38,100 грн\n  Q2 (50%): 40,200 грн\n  Q3 (75%): 42,300 грн\n\nАутлайери (за правилом IQR):\n  Виявлено: 3 значення\n  Індекси: [5, 23, 87]\n  Значення: [55000, 58000, 60000] грн\n\nВисновок:\n  Низька варіація (CV = 6.9% \u003C 10%).\n  Дані стабільні та передбачувані.\n  Виявлено 3 аутлайери — рекомендується перевірити їх коректність.\n",[5288,11275,11273],{"__ignoreMap":5322},[5278,11277,11278],{},"Функція має автоматично визначати рівень варіації та давати рекомендації.",[10946,11280,11282,11285,11305,11308,11322],{"icon":221,"label":11281},"Завдання 3.3: Порівняння стабільності роботи серверів",[5278,11283,11284],{},"Змоделюйте час відповіді трьох серверів (1000 запитів до кожного):",[5198,11286,11287,11293,11299],{},[5201,11288,11289,11292],{},[5224,11290,11291],{},"Сервер A:"," norm(200 ms, 20 ms)",[5201,11294,11295,11298],{},[5224,11296,11297],{},"Сервер B:"," norm(180 ms, 50 ms) — швидший, але менш стабільний",[5201,11300,11301,11304],{},[5224,11302,11303],{},"Сервер C:"," 95% запитів norm(150 ms, 10 ms) + 5% запитів norm(2000 ms, 500 ms) — швидкий, але іноді зависає",[5278,11306,11307],{},"Для кожного сервера обчисліть:",[6312,11309,11310,11313,11316,11319],{},[5201,11311,11312],{},"Mean, Median, Std, IQR",[5201,11314,11315],{},"Кількість аутлайерів (запити > Q3 + 1.5×IQR)",[5201,11317,11318],{},"95-й персентиль (P95) — метрика SLA",[5201,11320,11321],{},"CV",[5278,11323,11324,11325,11328],{},"Побудуйте три box-plot поруч для порівняння. Зробіть висновок: який сервер обрати для продакшн-системи, де важлива ",[5224,11326,11327],{},"передбачуваність","?",[5270,11330],{},[5273,11332,11334],{"id":11333},"часті-запитання-та-типові-пастки-faq","Часті запитання та типові пастки (FAQ)",[10943,11336,11337,11372,11446,11471],{},[10946,11338,11341,11348],{"icon":11339,"label":11340},"i-lucide-help-circle","❓ Чому у формулі дисперсії відхилення підносять саме до 2-го степеня, а не беруть модуль чи 4-й ступінь?",[5278,11342,11343,11344,11347],{},"У математичній статистиці та оптимізації функція квадрата ",[5613,11345],{"tex":11346,":inline":5616},"f(u) = u^2"," має виняткові аналітичні переваги:",[6312,11349,11350,11364,11369],{},[5201,11351,11352,11355,11356,11359,11360,11363],{},[5224,11353,11354],{},"Гладкість та диференційовність:"," Графік квадрата — це плавна парабола. Її похідна в кожній точці неперервна (",[5613,11357],{"tex":11358,":inline":5616},"\\frac{d}{du}(u^2) = 2u","). Це основа методу найменших квадратів (OLS) та градієнтного спуску в нейромережах. Натомість модуль ",[5613,11361],{"tex":11362,":inline":5616},"|u|"," має гострий злам у нулі, де похідна невизначена, що ускладнює аналітичні доведення.",[5201,11365,11366,11368],{},[5224,11367,6465],{}," Квадрат набагато суворіше карає серйозні промахи. Відхилення на 10 одиниць дає внесок у 100, тоді як відхилення на 2 — лише 4. Для інженерних систем поодинокі гігантські збої є набагато небезпечнішими за масу мікроколивань.",[5201,11370,11371],{},"Степені вище 2 (наприклад, 4-й) надмірно гіперболізують випадковий шум, роблячи оцінку нестабільною.",[10946,11373,11375,11391,11415,11425],{"icon":11339,"label":11374},"❓ Що таке поправка Бесселя і чому в NumPy треба писати ddof=1?",[5278,11376,11377,11378,11381,11382,11384,11385,11388,11389,5542],{},"Коли ми аналізуємо не весь всесвіт (генеральну сукупність), а обмежену ",[5224,11379,11380],{},"вибірку"," з ",[5613,11383],{"tex":6370,":inline":5616}," спостережень, ми не знаємо справжнього середнього ",[5613,11386],{"tex":11387,":inline":5616},"\\mu",". Ми вимушені оцінювати його через вибіркове середнє ",[5613,11390],{"tex":6457,":inline":5616},[5278,11392,11393,11394,11397,11398,11400,11401,11404,11405,11408,11409,11411,11412,11414],{},"Проте вибіркове середнє математично завжди розташоване ",[5224,11395,11396],{},"ближче"," до точок нашої конкретної вибірки, ніж істинне невідоме ",[5613,11399],{"tex":11387,":inline":5616},". Через це сума квадратів ",[5613,11402],{"tex":11403,":inline":5616},"\\sum (x_i - \\bar{x})^2"," завжди виходить систематично ",[5224,11406,11407],{},"меншою",", ніж сума відносно ",[5613,11410],{"tex":11387,":inline":5616},". Якщо поділити її на ",[5613,11413],{"tex":6370,":inline":5616},", ми отримаємо занижену (зміщену) дисперсію.",[5278,11416,11417,11418,11421,11422,11424],{},"Англійський астроном Фрідріх Бессель довів, що ділення на ",[5613,11419],{"tex":11420,":inline":5616},"n - 1"," (де 1 віднімається за \"втрачений\" ступінь свободи, витрачений на обчислення ",[5613,11423],{"tex":6457,":inline":5616},") строго виправляє це зміщення:",[5198,11426,11427,11436],{},[5201,11428,11429,11432,11433,11435],{},[5288,11430,11431],{},"np.var(data, ddof=0)"," — ділить на ",[5613,11434],{"tex":6370,":inline":5616}," (для генеральної сукупності).",[5201,11437,11438,11432,11441,11443,11444,10054],{},[5288,11439,11440],{},"np.var(data, ddof=1)",[5613,11442],{"tex":11420,":inline":5616}," (для вибірок, узгоджено з pandas ",[5288,11445,6397],{},[10946,11447,11449,11460],{"icon":11339,"label":11448},"❓ Чому інженери віддають перевагу стандартному відхиленню (σ) над дисперсією (σ²)?",[5278,11450,11451,11452,11455,11456,11459],{},"Дисперсія вимірюється в штучних ",[5224,11453,11454],{},"квадратах одиниць виміру",". Якщо ви аналізуєте затримку бекенду в мілісекундах (мс), дисперсія вийде в \"мілісекундах у квадраті\" (",[5613,11457],{"tex":11458,":inline":5616},"\\text{мс}^2","), що позбавлене фізичного відчуття.",[5278,11461,11462,11463,11466,11467,11470],{},"Стандартне відхилення ",[5613,11464],{"tex":11465,":inline":5616},"\\sigma = \\sqrt{\\sigma^2}"," повертає масштаб назад до початкових одиниць виміру даних (мс, грн, см). Вираз: ",[5229,11468,11469],{},"«Середній час відповіді становить 50 мс зі стандартним відхиленням ±5 мс»"," є абсолютно прозорим та інтуїтивним для замовників і розробників.",[10946,11472,11474,11483],{"icon":11339,"label":11473},"❓ Чи працює правило трьох сигм (68–95–99.7) для будь-яких даних?",[5278,11475,11476,11479,11480,5542],{},[5224,11477,11478],{},"Ні!"," Правило трьох сигм строго справедливе ",[5224,11481,11482],{},"лише для симетричного дзвоноподібного (нормального) розподілу",[5278,11484,11485,11486,11488,11489,5542],{},"Якщо дані мають сильний скіс (наприклад, експоненційний розподіл часу між кліками користувача чи ціни на житло), в межах ",[5613,11487],{"tex":8147,":inline":5616}," може лежати як 85%, так і 50% даних. Для довільних розподілів діє значно ширша математична нерівність Чебишова, але в реальних задачах з ненормальними даними інженери замість сигм орієнтуються на квантилі та ",[5224,11490,11491],{},"міжквартильний розмах (IQR)",[5270,11493],{},[5273,11495,11497],{"id":11496},"резюме-ключові-takeaways","Резюме: ключові takeaways",[5190,11499,11500,11528,11552,11577,11603,11631],{},[5193,11501,11504,11510,11516,11522],{"icon":11502,"title":11503},"i-lucide-maximize-2","Розмах (Range)",[5278,11505,11506,11509],{},[5224,11507,11508],{},"Формула:"," max − min",[5278,11511,11512,11515],{},[5224,11513,11514],{},"Переваги:"," Найпростіша міра, швидко обчислюється",[5278,11517,11518,11521],{},[5224,11519,11520],{},"Недоліки:"," Дуже чутлива до аутлайерів, використовує лише 2 значення",[5278,11523,11524,11527],{},[5224,11525,11526],{},"Коли використовувати:"," Швидка оцінка діапазону, побудова шкал графіків",[5193,11529,11532,11537,11542,11547],{"icon":11530,"title":11531},"i-lucide-sigma-square","Дисперсія (Variance, σ²)",[5278,11533,11534,11536],{},[5224,11535,11508],{}," середній квадрат відхилення від середнього",[5278,11538,11539,11541],{},[5224,11540,11514],{}," Математично зручна, використовує всі дані",[5278,11543,11544,11546],{},[5224,11545,11520],{}," Квадратні одиниці (важко інтерпретувати), чутлива до аутлайерів",[5278,11548,11549,11551],{},[5224,11550,11526],{}," Теоретичні обчислення, основа для стандартного відхилення",[5193,11553,11555,11560,11565,11570],{"icon":1348,"title":11554},"Стандартне відхилення (Std, σ)",[5278,11556,11557,11559],{},[5224,11558,11508],{}," √дисперсія",[5278,11561,11562,11564],{},[5224,11563,11514],{}," Ті ж одиниці, що й дані, інтуїтивна інтерпретація («типове відхилення»)",[5278,11566,11567,11569],{},[5224,11568,11520],{}," Чутлива до аутлайерів",[5278,11571,11572,5286,11574,11576],{},[5224,11573,11526],{},[5224,11575,10895],{},", симетричні розподіли без аутлайерів",[5193,11578,11580,11585,11593,11598],{"icon":62,"title":11579},"Міжквартильний розмах (IQR)",[5278,11581,11582,11584],{},[5224,11583,11508],{}," Q3 − Q1",[5278,11586,11587,5286,11589,11592],{},[5224,11588,11514],{},[5224,11590,11591],{},"Стійка до аутлайерів",", показує розкид середніх 50% даних",[5278,11594,11595,11597],{},[5224,11596,11520],{}," Ігнорує крайні значення, менш математично зручна",[5278,11599,11600,11602],{},[5224,11601,11526],{}," Дані з аутлайерами, асиметричні розподіли, виявлення аномалій",[5193,11604,11605,11610,11615,11620,11625],{"icon":11059,"title":11093},[5278,11606,11607,11609],{},[5224,11608,11508],{}," (σ \u002F μ) × 100%",[5278,11611,11612,11614],{},[5224,11613,11514],{}," Безрозмірний, дозволяє порівнювати різні змінні",[5278,11616,11617,11619],{},[5224,11618,11520],{}," Не працює для даних близьких до нуля, чутливий до аутлайерів",[5278,11621,11622,11624],{},[5224,11623,11526],{}," Порівняння варіації змінних у різних масштабах",[5278,11626,11627,11630],{},[5224,11628,11629],{},"Інтерпретація:"," CV \u003C 10% — низька варіація, > 25% — висока варіація",[5193,11632,11635,11638],{"icon":11633,"title":11634},"i-lucide-brain-circuit","Зв'язок із ML",[5278,11636,11637],{},"Міри варіації критичні в ML:",[5198,11639,11640,11646,11652,11658,11664],{},[5201,11641,11642,11645],{},[5224,11643,11644],{},"Нормалізація даних"," — використовує mean та std",[5201,11647,11648,11651],{},[5224,11649,11650],{},"Відбір ознак"," — видаляємо ознаки з низькою варіацією (константні)",[5201,11653,11654,11657],{},[5224,11655,11656],{},"Виявлення аномалій"," — значення далеко від центру (> 3σ)",[5201,11659,11660,11663],{},[5224,11661,11662],{},"Оцінка якості моделі"," — variance vs bias trade-off",[5201,11665,11666,11669],{},[5224,11667,11668],{},"Інтерпретація ризиків"," — std як міра невизначеності",[5270,11671],{},[5273,11673,11675],{"id":11674},"що-далі","Що далі?",[5278,11677,11678],{},"Ви опанували міри центральної тенденції (mean, median, mode) та міри варіації (range, variance, std, IQR). Тепер ви вмієте:",[5198,11680,11681,11684,11687,11690],{},[5201,11682,11683],{},"Знаходити «типове» значення в даних",[5201,11685,11686],{},"Вимірювати «розкиданість» даних навколо центру",[5201,11688,11689],{},"Виявляти аутлайери",[5201,11691,11692],{},"Порівнювати стабільність різних датасетів",[5278,11694,11695,11696,11699,11700,11703],{},"Але ці міри описують ",[5224,11697,11698],{},"одну змінну",". У реальних задачах ML ми часто маємо ",[5224,11701,11702],{},"багато змінних",". Як з'ясувати, чи пов'язані вони між собою?",[5278,11705,8767],{},[5198,11707,11708,11711,11714],{},[5201,11709,11710],{},"Чи впливає площа квартири на ціну?",[5201,11712,11713],{},"Чи залежить зарплата від освіти?",[5201,11715,11716],{},"Чи корелюють продажі морозива з температурою?",[5278,11718,11719,11720,11723,11724,11727],{},"Для відповіді на ці запитання потрібні ",[5224,11721,11722],{},"розподіли випадкових величин"," (наступна стаття) та ",[5224,11725,11726],{},"міри зв'язку"," (кореляція).",[8130,11729,11730,11737,11753],{},[5278,11731,11732,11733,11736],{},"💡 ",[5224,11734,11735],{},"Порада для закріплення:"," Відкрийте будь-який числовий датасет і для кожного стовпця:",[6312,11738,11739,11742,11745,11748,11751],{},[5201,11740,11741],{},"Обчисліть mean та median",[5201,11743,11744],{},"Обчисліть std та IQR",[5201,11746,11747],{},"Порівняйте std з IQR — якщо сильно відрізняються, є аутлайери",[5201,11749,11750],{},"Обчисліть CV — визначте, які змінні найбільш мінливі",[5201,11752,11252],{},[5278,11754,11755],{},"Це найкращий спосіб перетворити теорію на практичну навичку аналізу даних.",[11757,11758,11759],"style",{},"html pre.shiki code .s8xlr, html code.shiki .s8xlr{--shiki-light:#AF00DB;--shiki-default:#C586C0;--shiki-dark:#C586C0}html pre.shiki code .sHH4Y, html code.shiki .sHH4Y{--shiki-light:#000000;--shiki-default:#D4D4D4;--shiki-dark:#D4D4D4}html pre.shiki code .sJj4R, html code.shiki .sJj4R{--shiki-light:#098658;--shiki-default:#B5CEA8;--shiki-dark:#B5CEA8}html pre.shiki code .s8Opu, html code.shiki .s8Opu{--shiki-light:#795E26;--shiki-default:#DCDCAA;--shiki-dark:#DCDCAA}html pre.shiki code .su1O8, html code.shiki .su1O8{--shiki-light:#0000FF;--shiki-default:#569CD6;--shiki-dark:#569CD6}html pre.shiki code .sbdoH, html code.shiki .sbdoH{--shiki-light:#A31515;--shiki-default:#CE9178;--shiki-dark:#CE9178}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: 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.siwwj{--shiki-light:#001080;--shiki-default:#9CDCFE;--shiki-dark:#9CDCFE}",{"title":5322,"searchDepth":5346,"depth":5346,"links":11761},[11762,11763,11768,11774,11779,11780,11783,11786,11787,11788,11793,11794,11795],{"id":5275,"depth":5346,"text":5276},{"id":5643,"depth":5346,"text":5644,"children":11764},[11765,11766,11767],{"id":5655,"depth":5353,"text":5656},{"id":5662,"depth":5353,"text":5663},{"id":5990,"depth":5353,"text":5991},{"id":6283,"depth":5346,"text":6284,"children":11769},[11770,11771,11772,11773],{"id":6302,"depth":5353,"text":6303},{"id":6331,"depth":5353,"text":6332},{"id":6508,"depth":5353,"text":6509},{"id":6990,"depth":5353,"text":6991},{"id":7306,"depth":5346,"text":7307,"children":11775},[11776,11777,11778],{"id":7321,"depth":5353,"text":5656},{"id":7327,"depth":5353,"text":7328},{"id":7709,"depth":5353,"text":7710},{"id":8179,"depth":5346,"text":8180},{"id":8754,"depth":5346,"text":8755,"children":11781},[11782],{"id":8979,"depth":5353,"text":8980},{"id":9455,"depth":5346,"text":9456,"children":11784},[11785],{"id":9480,"depth":5353,"text":9481},{"id":10011,"depth":5346,"text":10012},{"id":10809,"depth":5346,"text":10810},{"id":10936,"depth":5346,"text":10937,"children":11789},[11790,11791,11792],{"id":10940,"depth":5353,"text":10941},{"id":11053,"depth":5353,"text":11054},{"id":11228,"depth":5353,"text":11229},{"id":11333,"depth":5346,"text":11334},{"id":11496,"depth":5346,"text":11497},{"id":11674,"depth":5346,"text":11675},"Дисперсія, стандартне відхилення, розмах, міжквартильний розмах та коефіцієнт варіації — як виміряти «розкиданість» даних та зрозуміти їхню стабільність","md",null,{},{"title":3735,"description":11796},"B0UyMyFHlV14l65lQmSMqmhfr3EbUdyVbDhVONpaayk",[11803,11805],{"title":3731,"path":3732,"stem":3733,"description":11804,"children":-1},"Середнє арифметичне, медіана та мода — три способи знайти «типове» значення в даних, їхні переваги, недоліки та застосування в аналізі даних",{"title":3739,"path":3740,"stem":3741,"description":11806,"children":-1},"Рівномірний, нормальний (Гауса) та розподіл Пуассона — три фундаментальні розподіли, їхні властивості, застосування та генерація даних у NumPy",1792054959868]