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vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">жасыру</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Кіріспе</div> </a> </li> <li id="toc-Мысал_ретінде_есеп" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Мысал_ретінде_есеп"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Мысал ретінде есеп</span> </div> </a> <ul id="toc-Мысал_ретінде_есеп-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дереккөздер" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Дереккөздер"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Дереккөздер</span> </div> </a> <ul id="toc-Дереккөздер-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Сілтемелер" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Сілтемелер"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Сілтемелер</span> </div> </a> <ul id="toc-Сілтемелер-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Мазмұны" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Мазмұнды көрсету/жасыру" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Мазмұнды көрсету/жасыру</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Математикалық оптимизация</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Басқа тілдегі мақалаға өту. 55 тілде қолжетімді" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-55" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">55 тіл</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%A7%D8%B3%D8%AA%D9%85%D8%AB%D8%A7%D9%84_(%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA)" title="استمثال (رياضيات) – араб тілі" lang="ar" hreflang="ar" data-title="استمثال (رياضيات)" data-language-autonym="العربية" data-language-local-name="араб тілі" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Optimalla%C5%9Fd%C4%B1rma" title="Optimallaşdırma – әзірбайжан тілі" lang="az" hreflang="az" data-title="Optimallaşdırma" data-language-autonym="Azərbaycanca" data-language-local-name="әзірбайжан тілі" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BC%D0%B0%D0%BB%D0%BB%D3%99%D1%88%D1%82%D0%B5%D1%80%D0%B5%D2%AF_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Оптималләштереү (математика) – башқұрт тілі" lang="ba" hreflang="ba" data-title="Оптималләштереү (математика)" data-language-autonym="Башҡортса" data-language-local-name="башқұрт тілі" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%B5%D1%81%D0%BA%D0%B0_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F" title="Математическа оптимизация – болгар тілі" lang="bg" hreflang="bg" data-title="Математическа оптимизация" data-language-autonym="Български" data-language-local-name="болгар тілі" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%BE%E0%A6%A3%E0%A6%BF%E0%A6%A4%E0%A6%BF%E0%A6%95_%E0%A6%95%E0%A6%BE%E0%A6%AE%E0%A7%8D%E0%A6%AF%E0%A6%A4%E0%A6%AE%E0%A6%95%E0%A6%B0%E0%A6%A3" title="গাণিতিক কাম্যতমকরণ – бенгал тілі" lang="bn" hreflang="bn" data-title="গাণিতিক কাম্যতমকরণ" data-language-autonym="বাংলা" data-language-local-name="бенгал тілі" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Optimitzaci%C3%B3_matem%C3%A0tica" title="Optimització matemàtica – каталан тілі" lang="ca" hreflang="ca" data-title="Optimització matemàtica" data-language-autonym="Català" data-language-local-name="каталан тілі" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Optimalizace_(matematika)" title="Optimalizace (matematika) – чех тілі" lang="cs" hreflang="cs" data-title="Optimalizace (matematika)" data-language-autonym="Čeština" data-language-local-name="чех тілі" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Optimering_(matematik)" title="Optimering (matematik) – дат тілі" lang="da" hreflang="da" data-title="Optimering (matematik)" data-language-autonym="Dansk" data-language-local-name="дат тілі" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Mathematische_Optimierung" title="Mathematische Optimierung – неміс тілі" lang="de" hreflang="de" data-title="Mathematische Optimierung" data-language-autonym="Deutsch" data-language-local-name="неміс тілі" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%92%CE%B5%CE%BB%CF%84%CE%B9%CF%83%CF%84%CE%BF%CF%80%CE%BF%CE%AF%CE%B7%CF%83%CE%B7" title="Βελτιστοποίηση – грек тілі" lang="el" hreflang="el" data-title="Βελτιστοποίηση" data-language-autonym="Ελληνικά" data-language-local-name="грек тілі" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematical_optimization" title="Mathematical optimization – ағылшын тілі" lang="en" hreflang="en" data-title="Mathematical optimization" data-language-autonym="English" data-language-local-name="ағылшын тілі" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Optimumigo_(matematiko)" title="Optimumigo (matematiko) – эсперанто тілі" lang="eo" hreflang="eo" data-title="Optimumigo (matematiko)" data-language-autonym="Esperanto" data-language-local-name="эсперанто тілі" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Optimizaci%C3%B3n_(matem%C3%A1tica)" title="Optimización (matemática) – испан тілі" lang="es" hreflang="es" data-title="Optimización (matemática)" data-language-autonym="Español" data-language-local-name="испан тілі" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Optimizazio_(matematika)" title="Optimizazio (matematika) – баск тілі" lang="eu" hreflang="eu" data-title="Optimizazio (matematika)" data-language-autonym="Euskara" data-language-local-name="баск тілі" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%A8%D9%87%DB%8C%D9%86%D9%87%E2%80%8C%D8%B3%D8%A7%D8%B2%DB%8C" title="بهینه‌سازی – парсы тілі" lang="fa" hreflang="fa" data-title="بهینه‌سازی" data-language-autonym="فارسی" data-language-local-name="парсы тілі" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Matemaattinen_optimointi" title="Matemaattinen optimointi – фин тілі" lang="fi" hreflang="fi" data-title="Matemaattinen optimointi" data-language-autonym="Suomi" data-language-local-name="фин тілі" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Optimisation_(math%C3%A9matiques)" title="Optimisation (mathématiques) – француз тілі" lang="fr" hreflang="fr" data-title="Optimisation (mathématiques)" data-language-autonym="Français" data-language-local-name="француз тілі" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Optimizasyon_(mat%C3%A9matik)" title="Optimizasyon (matématik) – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Optimizasyon (matématik)" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Optimizaci%C3%B3n_matem%C3%A1tica" title="Optimización matemática – галисия тілі" lang="gl" hreflang="gl" data-title="Optimización matemática" data-language-autonym="Galego" data-language-local-name="галисия тілі" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%90%D7%95%D7%A4%D7%98%D7%99%D7%9E%D7%99%D7%96%D7%A6%D7%99%D7%94_(%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94)" title="אופטימיזציה (מתמטיקה) – иврит тілі" lang="he" hreflang="he" data-title="אופטימיזציה (מתמטיקה)" data-language-autonym="עברית" data-language-local-name="иврит тілі" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%87%E0%A4%B7%E0%A5%8D%E0%A4%9F%E0%A4%A4%E0%A4%AE%E0%A4%95%E0%A4%B0%E0%A4%A3" title="इष्टतमकरण – хинди тілі" lang="hi" hreflang="hi" data-title="इष्टतमकरण" data-language-autonym="हिन्दी" data-language-local-name="хинди тілі" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Optimizacija_(matematika)" title="Optimizacija (matematika) – хорват тілі" lang="hr" hreflang="hr" data-title="Optimizacija (matematika)" data-language-autonym="Hrvatski" data-language-local-name="хорват тілі" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Matematikai_optimaliz%C3%A1l%C3%A1s" title="Matematikai optimalizálás – венгр тілі" lang="hu" hreflang="hu" data-title="Matematikai optimalizálás" data-language-autonym="Magyar" data-language-local-name="венгр тілі" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%84%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1%D5%AF%D5%A1%D5%B6_%D6%85%D5%BA%D5%BF%D5%AB%D5%B4%D5%AB%D5%A6%D5%A1%D6%81%D5%AB%D5%A1" title="Մաթեմատիկական օպտիմիզացիա – армян тілі" lang="hy" hreflang="hy" data-title="Մաթեմատիկական օպտիմիզացիա" data-language-autonym="Հայերեն" data-language-local-name="армян тілі" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hyw mw-list-item"><a href="https://hyw.wikipedia.org/wiki/%D5%88%D6%82%D5%BD%D5%B8%D5%B2%D5%A1%D5%AF%D5%A1%D5%B6_%D4%BE%D6%80%D5%A1%D5%A3%D6%80%D5%A1%D6%82%D5%B8%D6%80%D5%B8%D6%82%D5%B4" title="Ուսողական Ծրագրաւորում – Western Armenian" lang="hyw" hreflang="hyw" data-title="Ուսողական Ծրագրաւորում" data-language-autonym="Արեւմտահայերէն" data-language-local-name="Western Armenian" class="interlanguage-link-target"><span>Արեւմտահայերէն</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Optimisasi" title="Optimisasi – индонезия тілі" lang="id" hreflang="id" data-title="Optimisasi" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонезия тілі" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Ottimizzazione_(matematica)" title="Ottimizzazione (matematica) – итальян тілі" lang="it" hreflang="it" data-title="Ottimizzazione (matematica)" data-language-autonym="Italiano" data-language-local-name="итальян тілі" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B0%E7%90%86%E6%9C%80%E9%81%A9%E5%8C%96" title="数理最適化 – жапон тілі" lang="ja" hreflang="ja" data-title="数理最適化" data-language-autonym="日本語" data-language-local-name="жапон тілі" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98%ED%95%99%EC%A0%81_%EC%B5%9C%EC%A0%81%ED%99%94" title="수학적 최적화 – корей тілі" lang="ko" hreflang="ko" data-title="수학적 최적화" data-language-autonym="한국어" data-language-local-name="корей тілі" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%E0%BA%81%E0%BA%B2%E0%BA%99%E0%BA%8A%E0%BA%AD%E0%BA%81%E0%BA%84%E0%BB%88%E0%BA%B2%E0%BB%80%E0%BB%9D%E0%BA%B2%E0%BA%B0%E0%BA%AA%E0%BA%BB%E0%BA%A1_(%E0%BA%84%E0%BA%B0%E0%BA%99%E0%BA%B4%E0%BA%94%E0%BA%AA%E0%BA%B2%E0%BA%94)" title="ການຊອກຄ່າເໝາະສົມ (ຄະນິດສາດ) – лаос тілі" lang="lo" hreflang="lo" data-title="ການຊອກຄ່າເໝາະສົມ (ຄະນິດສາດ)" data-language-autonym="ລາວ" data-language-local-name="лаос тілі" class="interlanguage-link-target"><span>ລາວ</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Optimizavimas_(matematika)" title="Optimizavimas (matematika) – литва тілі" lang="lt" hreflang="lt" data-title="Optimizavimas (matematika)" data-language-autonym="Lietuvių" data-language-local-name="литва тілі" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D1%87%D0%BA%D0%B0_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%98%D0%B0" title="Математичка оптимизација – македон тілі" lang="mk" hreflang="mk" data-title="Математичка оптимизација" data-language-autonym="Македонски" data-language-local-name="македон тілі" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Pengoptimuman" title="Pengoptimuman – малай тілі" lang="ms" hreflang="ms" data-title="Pengoptimuman" data-language-autonym="Bahasa Melayu" data-language-local-name="малай тілі" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wiskundige_optimalisatie" title="Wiskundige optimalisatie – нидерланд тілі" lang="nl" hreflang="nl" data-title="Wiskundige optimalisatie" data-language-autonym="Nederlands" data-language-local-name="нидерланд тілі" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Matematisk_programmering" title="Matematisk programmering – норвегиялық нюнорск тілі" lang="nn" hreflang="nn" data-title="Matematisk programmering" data-language-autonym="Norsk nynorsk" data-language-local-name="норвегиялық нюнорск тілі" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Optimering" title="Optimering – норвегиялық букмол тілі" lang="nb" hreflang="nb" data-title="Optimering" data-language-autonym="Norsk bokmål" data-language-local-name="норвегиялық букмол тілі" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Optymalizacja_(matematyka)" title="Optymalizacja (matematyka) – поляк тілі" lang="pl" hreflang="pl" data-title="Optymalizacja (matematyka)" data-language-autonym="Polski" data-language-local-name="поляк тілі" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Otimiza%C3%A7%C3%A3o" title="Otimização – португал тілі" lang="pt" hreflang="pt" data-title="Otimização" data-language-autonym="Português" data-language-local-name="португал тілі" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Optimizare" title="Optimizare – румын тілі" lang="ro" hreflang="ro" data-title="Optimizare" data-language-autonym="Română" data-language-local-name="румын тілі" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Оптимизация (математика) – орыс тілі" lang="ru" hreflang="ru" data-title="Оптимизация (математика)" data-language-autonym="Русский" data-language-local-name="орыс тілі" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Mathematical_optimization" title="Mathematical optimization – Simple English" lang="en-simple" hreflang="en-simple" data-title="Mathematical optimization" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Optimaliz%C3%A1cia_(matematika)" title="Optimalizácia (matematika) – словак тілі" lang="sk" hreflang="sk" data-title="Optimalizácia (matematika)" data-language-autonym="Slovenčina" data-language-local-name="словак тілі" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Optimizacija_(matematika)" title="Optimizacija (matematika) – словен тілі" lang="sl" hreflang="sl" data-title="Optimizacija (matematika)" data-language-autonym="Slovenščina" data-language-local-name="словен тілі" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Optimizimi_matematikor" title="Optimizimi matematikor – албан тілі" lang="sq" hreflang="sq" data-title="Optimizimi matematikor" data-language-autonym="Shqip" data-language-local-name="албан тілі" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%98%D0%B0_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Оптимизација (математика) – серб тілі" lang="sr" hreflang="sr" data-title="Оптимизација (математика)" data-language-autonym="Српски / srpski" data-language-local-name="серб тілі" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Optimisasi_(matematik)" title="Optimisasi (matematik) – сундан тілі" lang="su" hreflang="su" data-title="Optimisasi (matematik)" data-language-autonym="Sunda" data-language-local-name="сундан тілі" class="interlanguage-link-target"><span>Sunda</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Optimeringsl%C3%A4ra" title="Optimeringslära – швед тілі" lang="sv" hreflang="sv" data-title="Optimeringslära" data-language-autonym="Svenska" data-language-local-name="швед тілі" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%81%E0%B8%B2%E0%B8%A3%E0%B8%AB%E0%B8%B2%E0%B8%84%E0%B9%88%E0%B8%B2%E0%B9%80%E0%B8%AB%E0%B8%A1%E0%B8%B2%E0%B8%B0%E0%B8%97%E0%B8%B5%E0%B9%88%E0%B8%AA%E0%B8%B8%E0%B8%94" title="การหาค่าเหมาะที่สุด – тай тілі" lang="th" hreflang="th" data-title="การหาค่าเหมาะที่สุด" data-language-autonym="ไทย" data-language-local-name="тай тілі" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Optimisasyong_matematikal" title="Optimisasyong matematikal – Tagalog" lang="tl" hreflang="tl" data-title="Optimisasyong matematikal" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Optimizasyon" title="Optimizasyon – түрік тілі" lang="tr" hreflang="tr" data-title="Optimizasyon" data-language-autonym="Türkçe" data-language-local-name="түрік тілі" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9E%D0%BF%D1%82%D0%B8%D0%BC%D1%96%D0%B7%D0%B0%D1%86%D1%96%D1%8F_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Оптимізація (математика) – украин тілі" lang="uk" hreflang="uk" data-title="Оптимізація (математика)" data-language-autonym="Українська" data-language-local-name="украин тілі" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%DA%A9%D8%A7%D9%85%D9%84%DB%8C%D8%AA_(%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA)" title="کاملیت (ریاضیات) – урду тілі" lang="ur" hreflang="ur" data-title="کاملیت (ریاضیات)" data-language-autonym="اردو" data-language-local-name="урду тілі" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/T%E1%BB%91i_%C6%B0u_h%C3%B3a_(to%C3%A1n_h%E1%BB%8Dc)" title="Tối ưu hóa (toán học) – вьетнам 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class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Көрініс</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">бүйірлік тақтаға жылжыту</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">жасыру</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Уикипедия — ашық энциклопедиясынан алынған мәлімет</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="kk" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A1%D1%83%D1%80%D0%B5%D1%82:MaximumParaboloid.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/MaximumParaboloid.png/220px-MaximumParaboloid.png" decoding="async" width="220" height="165" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/62/MaximumParaboloid.png/330px-MaximumParaboloid.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/62/MaximumParaboloid.png/440px-MaximumParaboloid.png 2x" data-file-width="756" data-file-height="567" /></a><figcaption>Парабалойд графы f(<i>x</i>,<i>y</i>) = -(<i>x</i>²+<i>y</i>²)+4. (0,0,4) нүксесіндегі глобалды максимум қызыл нүктемен белгілеулі.</figcaption></figure> <p><b>Математикалық оптимизация</b> (өзге атаулары <b>оптимизация</b> немесе <b>математикалық бағдарламалау</b>) — <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика">математикалық</a> пән. <a href="/w/index.php?title=%D0%A1%D1%8B%D0%B7%D1%8B%D2%9B%D1%82%D1%8B%D2%9B_%D1%88%D0%B5%D0%BA%D1%82%D0%B5%D1%83&action=edit&redlink=1" class="new" title="Сызықтық шектеу (мұндай бет жоқ)">Сызықтық</a> және <a href="/w/index.php?title=%D0%A1%D1%8B%D0%B7%D1%8B%D2%9B%D1%82%D1%8B%D2%9B_%D0%B5%D0%BC%D0%B5%D1%81_%D1%88%D0%B5%D0%BA%D1%82%D0%B5%D1%83&action=edit&redlink=1" class="new" title="Сызықтық емес шектеу (мұндай бет жоқ)">сызықтық емес шектеулер</a> бойынша (<a href="/wiki/%D0%A2%D0%B5%D2%A3%D0%B4%D0%B5%D1%83" title="Теңдеу">теңдеулермен</a> және <a href="/wiki/%D0%A2%D0%B5%D2%A3%D1%81%D1%96%D0%B7%D0%B4%D1%96%D0%BA" title="Теңсіздік">теңсіздіктермен</a>) анықталған жиындардағы көп <a href="/wiki/%D0%90%D0%B9%D0%BD%D1%8B%D0%BC%D0%B0%D0%BB%D1%8B" title="Айнымалы">айнымалыдан</a> <a href="/w/index.php?title=%D0%A2%D3%99%D1%83%D0%B5%D0%BB%D0%B4%D1%96_%D1%84%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D1%8F&action=edit&redlink=1" class="new" title="Тәуелді функция (мұндай бет жоқ)">тәуелді функциялардың</a> <a href="/wiki/%D0%AD%D0%BA%D1%81%D1%82%D1%80%D0%B5%D0%BC%D1%83%D0%BC" title="Экстремум">экстремумдарын</a> табу жолының <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F" title="Теория">теориясы</a> мен әдістерін оқытады.<b> М. б. ғылым ретінде 20 ғ-дың 50 — 70-ж. қалыптасты.</b> </p> <div class="mw-heading mw-heading2"><h2 id="Мысал_ретінде_есеп"><span id=".D0.9C.D1.8B.D1.81.D0.B0.D0.BB_.D1.80.D0.B5.D1.82.D1.96.D0.BD.D0.B4.D0.B5_.D0.B5.D1.81.D0.B5.D0.BF"></span>Мысал ретінде есеп</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&veaction=edit&section=1" title="Бөлімді өңдеу: Мысал ретінде есеп" class="mw-editsection-visualeditor"><span>өңдеу</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&action=edit&section=1" title="Edit section's source code: Мысал ретінде есеп"><span>қайнарын өңдеу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Математикалық оптимизация есебін жалпы түрде:<br /><br /> <big><b>gі(x1, ..., xn)0, і=1, ..., m, (x1, ..., xn)</b></big>, (мұндағы Х — Rn-нің кез келген ішкі жиыны) <br /> жүйесімен берілген мүмкін болатын G жиынында f(x1, ..., xn) мақсат функциясын максимумға келтіру түрінде жазуға болады. М. б-дың әр түрлі есептер кластары f мақсат функциясына қойылатын шартқа және мүмкін болатын G облысына қойылған шектеулерге байланысты алынады.<br /> Егер <big><b>X=Rn</b></big>, f — сызықты, gі —<a href="/w/index.php?title=%D0%90%D1%84%D1%84%D0%B8%D0%BD%D0%B4%D1%96&action=edit&redlink=1" class="new" title="Аффинді (мұндай бет жоқ)">аффинді</a> болса,<br />онда <i>сызықтық бағдарламалау есебі</i> алынады; ал осы функциялардың барлығы немесе біреуі сызықтық емес болатын есептермен <i>сызықтық емес бағдарламалау</i> айналысады; f пен мүмкін болатын жиын G дөңес болса <i>дөңес бағдарламалау</i> шығады; егер G облысы саны шектелген нүктелерден тұрса, онда <i>дискретті бағдарламалау есептері</i> шығады; f және (немесе) gі параметрлерінен тәуелді болғандағы есептерде <i>параметрлік бағдарламалауға</i> айналады; f және (немесе) gі кездейсоқ факторлардан тәуелділігі ескерілсе, <i>стохастикалық бағдарламалау</i> шығады; <i>динамикалық бағдарламалауда</i> тиімді шешім алу (f пен gі-дің нақты түрлерінен тәуелсіз) көп дымды процесс түрінде келтіріледі. Мақсаттық функция векторлы болатын есептерде М. б-ға жақындатылады. Ондай жағдайда оның экстремумын табу емес, тиімділігі жағын қарастыру керек. М. б-да экономиканы басқару, өндірістік процестерді автоматтандыру, жобалау, перспективалық жоспарлау, т.б. қарастырылады. М. б. есептерінде ЭЕМ кеңінен пайдаланылады. <i>Ә. Қазанғапов</i> </p><p><sup id="cite_ref-test_1-0" class="reference"><a href="#cite_note-test-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Дереккөздер"><span id=".D0.94.D0.B5.D1.80.D0.B5.D0.BA.D0.BA.D3.A9.D0.B7.D0.B4.D0.B5.D1.80"></span>Дереккөздер</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&veaction=edit&section=2" title="Бөлімді өңдеу: Дереккөздер" class="mw-editsection-visualeditor"><span>өңдеу</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&action=edit&section=2" title="Edit section's source code: Дереккөздер"><span>қайнарын өңдеу</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D2%9A%D0%B0%D0%B7%D0%B0%D2%9B_%D0%AD%D0%BD%D1%86%D0%B8%D0%BA%D0%BB%D0%BE%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F%D1%81%D1%8B" class="mw-redirect" title="Қазақ Энциклопедиясы">"Қазақ Энциклопедиясы"</a>, 6 том </p> <div class="mw-heading mw-heading2"><h2 id="Сілтемелер"><span id=".D0.A1.D1.96.D0.BB.D1.82.D0.B5.D0.BC.D0.B5.D0.BB.D0.B5.D1.80"></span>Сілтемелер</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&veaction=edit&section=3" title="Бөлімді өңдеу: Сілтемелер" class="mw-editsection-visualeditor"><span>өңдеу</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BE%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8%D1%8F&action=edit&section=3" title="Edit section's source code: Сілтемелер"><span>қайнарын өңдеу</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-test-1"><span class="mw-cite-backlink"><a href="#cite_ref-test_1-0">↑</a></span> <span class="reference-text">Қазақ Энциклопедиясы</span> </li> </ol> <table class="metadata plainlinks ambox ambox-style" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px;"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Ambox_wikify.svg/40px-Ambox_wikify.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e1/Ambox_wikify.svg/60px-Ambox_wikify.svg.png 1.5x, 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href="/wiki/%D0%A1%D0%B0%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Сандар теориясы">Сандар теориясы</a> (<a href="/wiki/%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA%D0%B0" title="Арифметика">Арифметика</a>)<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BB%D0%BE%D0%B3%D0%B8%D0%BA%D0%B0" title="Математикалық логика">Математикалық логика</a> (<a href="/wiki/%D0%91%D1%83%D0%BB%D1%8C_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D1%81%D1%8B" title="Буль алгебрасы">Буль алгебрасы</a>)<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%90%D2%9B%D0%BF%D0%B0%D1%80%D0%B0%D1%82_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Ақпарат теориясы">Ақпарат теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%96%D0%B8%D1%8B%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Жиындар теориясы">Жиындар теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%A2%D0%B8%D0%BF%D1%82%D0%B5%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Типтер теориясы">Типтер теориясы</a></div></td></tr><tr style="height:2px"><td colspan="2"></td></tr><tr><th scope="row" class="navbox-group"><a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0" title="Алгебра">Алгебра</a> және <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D1%82%D0%B0%D0%BB%D0%B4%D0%B0%D1%83" title="Математикалық талдау">талдау</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <a 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href="/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%82%D0%B5%D2%A3%D0%B4%D0%B5%D1%83%D0%BB%D0%B5%D1%80" title="Интегралдық теңдеулер">Интегралдық теңдеулер</a>)<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D0%B5%D1%81%D0%B5%D0%BF%D1%82%D0%B5%D1%83" title="Дифференциалдық есептеу">Дифференциалдық есептеу</a> (<a href="/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%82%D0%B5%D2%A3%D0%B4%D0%B5%D1%83" title="Дифференциалдық теңдеу">Дифференциалдық теңдеулер</a>)<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%82%D0%B0%D0%BB%D0%B4%D0%B0%D1%83" title="Функционалдық талдау">Функционалдық талдау</a> (<a href="/wiki/%D0%92%D0%B0%D1%80%D0%B8%D0%B0%D1%86%D0%B8%D1%8F%D0%BB%D1%8B%D2%9B_%D0%B5%D1%81%D0%B5%D0%BF%D1%82%D0%B5%D1%83" title="Вариациялық есептеу">Вариациялық есептеу</a>)</div></td></tr><tr style="height:2px"><td colspan="2"></td></tr><tr><th scope="row" class="navbox-group"><a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Геометрия">Геометрия</a> және топология</th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <a href="/wiki/%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%B0%D0%BB%D1%8B%D2%9B_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Алгебралық геометрия">Алгебралық</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Аналитикалық геометрия">Аналитикалық</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Дифференциалдық геометрия">Дифференциалдық</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D1%82%D1%96%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F&action=edit&redlink=1" class="new" title="Дискреттік геометрия (мұндай бет жоқ)">Дискреттік</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D1%82%D1%96%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Евклидтік геометрия">Евклидтік геометрия</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9F%D0%BB%D0%B0%D0%BD%D0%B8%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Планиметрия">Планиметрия</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%A1%D1%82%D0%B5%D1%80%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80%D0%B8%D1%8F" title="Стереометрия">Стереометрия</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8%D1%8F" title="Топология">Топология</a></div></td></tr><tr style="height:2px"><td colspan="2"></td></tr><tr><th scope="row" class="navbox-group"><a href="/wiki/%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82%D1%82%D1%96%D0%BA_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Дискреттік математика">Дискреттік математика</a></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <a href="/wiki/%D0%9A%D0%BE%D0%BC%D0%B1%D0%B8%D0%BD%D0%B0%D1%82%D0%BE%D1%80%D0%B8%D0%BA%D0%B0" title="Комбинаторика">Комбинаторика</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%93%D1%80%D0%B0%D1%84%D1%82%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Графтар теориясы">Графтар теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%D0%A0%D0%B5%D1%82%D1%82%D0%B5%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B&action=edit&redlink=1" class="new" title="Реттер теориясы (мұндай бет жоқ)">Реттер теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9E%D0%B9%D1%8B%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Ойындар теориясы">Ойындар теориясы</a></div></td></tr><tr style="height:2px"><td colspan="2"></td></tr><tr><th scope="row" class="navbox-group"><a href="/wiki/%D2%9A%D0%BE%D0%BB%D0%B4%D0%B0%D0%BD%D0%B1%D0%B0%D0%BB%D1%8B_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Қолданбалы математика">Қолданбалы математика</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA%D0%B0" title="Математикалық физика">Математикалық физика</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D0%BC%D0%BE%D0%B4%D0%B5%D0%BB%D1%8C%D0%B4%D0%B5%D1%83" title="Математикалық модельдеу">Математикалық модельдеу</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D1%8D%D0%BA%D0%BE%D0%BD%D0%BE%D0%BC%D0%B8%D0%BA%D0%B0" title="Математикалық экономика">Математикалық экономика</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D0%BB%D1%8B%D2%9B_%D1%81%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA%D0%B0" title="Математикалық статистика">Математикалық статистика</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%A1%D0%B0%D0%BD%D0%B4%D1%8B%D2%9B_%D1%82%D0%B0%D0%BB%D0%B4%D0%B0%D1%83" title="Сандық талдау">Сандық талдау</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%AB%D2%9B%D1%82%D0%B8%D0%BC%D0%B0%D0%BB%D0%B4%D1%8B%D2%9B_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Ықтималдық теориясы">Ықтималдық теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%D0%91%D0%B0%D1%81%D2%9B%D0%B0%D1%80%D1%83_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B&action=edit&redlink=1" class="new" title="Басқару теориясы (мұндай бет жоқ)">Басқару теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%BE%D1%80%D0%B8%D1%82%D0%BC%D0%B4%D0%B5%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B&action=edit&redlink=1" class="new" title="Алгоритмдер теориясы (мұндай бет жоқ)">Алгоритмдер теориясы</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%D0%95%D1%81%D0%B5%D0%BF%D1%82%D0%B5%D1%83_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0%D1%81%D1%8B" title="Есептеу математикасы">Есептеу математикасы</a></div></td></tr><tr style="height:2px"><td colspan="2"></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><span typeof="mw:File"><a href="/wiki/%D0%A1%D1%83%D1%80%D0%B5%D1%82:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/20px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="20" height="20" class="mw-file-element" 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