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class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Сайт"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Гарчиг" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Гарчиг</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">хажуугийн цэсэнд шилжүүлэх</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">хумих</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">Эхлэл</div> </a> </li> <li id="toc-Математик_хэмээх_нэрний_учир_нь" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Математик_хэмээх_нэрний_учир_нь"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Математик хэмээх нэрний учир нь</span> </div> </a> <ul id="toc-Математик_хэмээх_нэрний_учир_нь-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Түүх" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Түүх"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Түүх</span> </div> </a> <ul id="toc-Түүх-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Гадны_нөлөөлөл,_цэвэр_ба_хэрэглээний_математик,_гоо_сайхан" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Гадны_нөлөөлөл,_цэвэр_ба_хэрэглээний_математик,_гоо_сайхан"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Гадны нөлөөлөл, цэвэр ба хэрэглээний математик, гоо сайхан</span> </div> </a> <ul id="toc-Гадны_нөлөөлөл,_цэвэр_ба_хэрэглээний_математик,_гоо_сайхан-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Математикийн_салбарууд" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Математикийн_салбарууд"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Математикийн салбарууд</span> </div> </a> <button aria-controls="toc-Математикийн_салбарууд-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Математикийн салбарууд хэсгийг нээж хаах</span> </button> <ul id="toc-Математикийн_салбарууд-sublist" class="vector-toc-list"> <li id="toc-Тоо_хэмжээ" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Тоо_хэмжээ"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.1</span> <span>Тоо хэмжээ</span> </div> </a> <ul id="toc-Тоо_хэмжээ-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Бүтэц" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Бүтэц"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.2</span> <span>Бүтэц</span> </div> </a> <ul id="toc-Бүтэц-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Огторгуй" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Огторгуй"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.3</span> <span>Огторгуй</span> </div> </a> <ul id="toc-Огторгуй-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Өөрчлөлт" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Өөрчлөлт"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.4</span> <span>Өөрчлөлт</span> </div> </a> <ul id="toc-Өөрчлөлт-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Тулгуур_салбарууд_ба_философи" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Тулгуур_салбарууд_ба_философи"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.5</span> <span>Тулгуур салбарууд ба философи</span> </div> </a> <ul id="toc-Тулгуур_салбарууд_ба_философи-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Дискрет_математик" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Дискрет_математик"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.6</span> <span>Дискрет математик</span> </div> </a> <ul id="toc-Дискрет_математик-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Хэрэглээний_математик" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Хэрэглээний_математик"> <div class="vector-toc-text"> <span class="vector-toc-numb">4.7</span> <span>Хэрэглээний математик</span> </div> </a> <ul id="toc-Хэрэглээний_математик-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Мөн_үзэх" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Мөн_үзэх"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Мөн үзэх</span> </div> </a> <ul id="toc-Мөн_үзэх-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Тэмдэглэлүүд" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Тэмдэглэлүүд"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Тэмдэглэлүүд</span> </div> </a> <ul id="toc-Тэмдэглэлүүд-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ном_хэвлэл" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Ном_хэвлэл"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Ном хэвлэл</span> </div> </a> <ul id="toc-Ном_хэвлэл-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="Гарчиг" 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="Гарчигийг нээж хаах" > <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">Гарчигийг нээж хаах</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">Математик</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="Go to an article in another language. Available in 254 languages" > <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-254" 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">254 хэлээр</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Wiskunde" title="Wiskunde – африкаанс" lang="af" hreflang="af" data-title="Wiskunde" data-language-autonym="Afrikaans" data-language-local-name="африкаанс" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Mathematik" title="Mathematik – швейцари-герман" lang="gsw" hreflang="gsw" data-title="Mathematik" data-language-autonym="Alemannisch" data-language-local-name="швейцари-герман" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%89%B5%E1%88%9D%E1%88%85%E1%88%AD%E1%89%B0_%E1%88%82%E1%88%B3%E1%89%A5" title="ትምህርተ ሂሳብ – амхар" lang="am" hreflang="am" data-title="ትምህርተ ሂሳብ" data-language-autonym="አማርኛ" data-language-local-name="амхар" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Matematicas" title="Matematicas – арагон" lang="an" hreflang="an" data-title="Matematicas" data-language-autonym="Aragonés" data-language-local-name="арагон" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ang mw-list-item"><a href="https://ang.wikipedia.org/wiki/R%C4%ABmcr%C3%A6ft" title="Rīmcræft – Old English" lang="ang" hreflang="ang" data-title="Rīmcræft" data-language-autonym="Ænglisc" data-language-local-name="Old English" class="interlanguage-link-target"><span>Ænglisc</span></a></li><li class="interlanguage-link interwiki-anp mw-list-item"><a href="https://anp.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – ангик" lang="anp" hreflang="anp" data-title="गणित" data-language-autonym="अंगिका" data-language-local-name="ангик" class="interlanguage-link-target"><span>अंगिका</span></a></li><li class="interlanguage-link interwiki-ar badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA" title="رياضيات – араб" lang="ar" hreflang="ar" data-title="رياضيات" data-language-autonym="العربية" data-language-local-name="араб" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%84%D9%85%D8%A7%D8%B7" title="لماط – Moroccan Arabic" lang="ary" hreflang="ary" data-title="لماط" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA" title="رياضيات – Egyptian Arabic" lang="arz" hreflang="arz" data-title="رياضيات" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত – ассам" lang="as" hreflang="as" data-title="গণিত" data-language-autonym="অসমীয়া" data-language-local-name="ассам" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Matem%C3%A1tiques" title="Matemátiques – астури" lang="ast" hreflang="ast" data-title="Matemátiques" data-language-autonym="Asturianu" data-language-local-name="астури" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-avk mw-list-item"><a href="https://avk.wikipedia.org/wiki/Solokseropa" title="Solokseropa – Kotava" lang="avk" hreflang="avk" data-title="Solokseropa" data-language-autonym="Kotava" data-language-local-name="Kotava" class="interlanguage-link-target"><span>Kotava</span></a></li><li class="interlanguage-link interwiki-awa mw-list-item"><a href="https://awa.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – авадхи" lang="awa" hreflang="awa" data-title="गणित" data-language-autonym="अवधी" data-language-local-name="авадхи" class="interlanguage-link-target"><span>अवधी</span></a></li><li class="interlanguage-link interwiki-ay mw-list-item"><a href="https://ay.wikipedia.org/wiki/Jakhu" title="Jakhu – аймара" lang="ay" hreflang="ay" data-title="Jakhu" data-language-autonym="Aymar aru" data-language-local-name="аймара" class="interlanguage-link-target"><span>Aymar aru</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Riyaziyyat" title="Riyaziyyat – азербайжан" lang="az" hreflang="az" data-title="Riyaziyyat" data-language-autonym="Azərbaycanca" data-language-local-name="азербайжан" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-azb mw-list-item"><a href="https://azb.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="ریاضیات – South Azerbaijani" lang="azb" hreflang="azb" data-title="ریاضیات" data-language-autonym="تۆرکجه" data-language-local-name="South Azerbaijani" class="interlanguage-link-target"><span>تۆرکجه</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – башкир" lang="ba" hreflang="ba" data-title="Математика" data-language-autonym="Башҡортса" data-language-local-name="башкир" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bar mw-list-item"><a href="https://bar.wikipedia.org/wiki/Mathematik" title="Mathematik – Bavarian" lang="bar" hreflang="bar" data-title="Mathematik" data-language-autonym="Boarisch" data-language-local-name="Bavarian" class="interlanguage-link-target"><span>Boarisch</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Matemat%C4%97ka" title="Matematėka – Samogitian" lang="sgs" hreflang="sgs" data-title="Matematėka" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Matematika" title="Matematika – Central Bikol" lang="bcl" hreflang="bcl" data-title="Matematika" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка – беларусь" lang="be" hreflang="be" data-title="Матэматыка" data-language-autonym="Беларуская" data-language-local-name="беларусь" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Матэматыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Матэматыка" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</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%D0%BA%D0%B0" title="Математика – болгар" lang="bg" hreflang="bg" data-title="Математика" data-language-autonym="Български" data-language-local-name="болгар" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bh mw-list-item"><a href="https://bh.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – Bhojpuri" lang="bh" hreflang="bh" data-title="गणित" data-language-autonym="भोजपुरी" data-language-local-name="Bhojpuri" class="interlanguage-link-target"><span>भोजपुरी</span></a></li><li class="interlanguage-link interwiki-bi mw-list-item"><a href="https://bi.wikipedia.org/wiki/Matematikis" title="Matematikis – бислам" lang="bi" hreflang="bi" data-title="Matematikis" data-language-autonym="Bislama" data-language-local-name="бислам" class="interlanguage-link-target"><span>Bislama</span></a></li><li class="interlanguage-link interwiki-bjn mw-list-item"><a href="https://bjn.wikipedia.org/wiki/Matamatika" title="Matamatika – Banjar" lang="bjn" hreflang="bjn" data-title="Matamatika" data-language-autonym="Banjar" data-language-local-name="Banjar" class="interlanguage-link-target"><span>Banjar</span></a></li><li class="interlanguage-link interwiki-blk mw-list-item"><a href="https://blk.wikipedia.org/wiki/%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သင်္ချာ – Pa'O" lang="blk" hreflang="blk" data-title="သင်္ချာ" data-language-autonym="ပအိုဝ်ႏဘာႏသာႏ" data-language-local-name="Pa'O" class="interlanguage-link-target"><span>ပအိုဝ်ႏဘာႏသာႏ</span></a></li><li class="interlanguage-link interwiki-bm mw-list-item"><a href="https://bm.wikipedia.org/wiki/Matematiki" title="Matematiki – бамбара" lang="bm" hreflang="bm" data-title="Matematiki" data-language-autonym="Bamanankan" data-language-local-name="бамбара" class="interlanguage-link-target"><span>Bamanankan</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত – бенгал" lang="bn" hreflang="bn" data-title="গণিত" data-language-autonym="বাংলা" data-language-local-name="бенгал" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bo mw-list-item"><a href="https://bo.wikipedia.org/wiki/%E0%BD%A2%E0%BE%A9%E0%BD%B2%E0%BD%A6%E0%BC%8B%E0%BD%A2%E0%BD%B2%E0%BD%82" title="རྩིས་རིག – төвд" lang="bo" hreflang="bo" data-title="རྩིས་རིག" data-language-autonym="བོད་ཡིག" data-language-local-name="төвд" class="interlanguage-link-target"><span>བོད་ཡིག</span></a></li><li class="interlanguage-link interwiki-bpy mw-list-item"><a href="https://bpy.wikipedia.org/wiki/%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="গণিত – Bishnupriya" lang="bpy" hreflang="bpy" data-title="গণিত" data-language-autonym="বিষ্ণুপ্রিয়া মণিপুরী" data-language-local-name="Bishnupriya" class="interlanguage-link-target"><span>বিষ্ণুপ্রিয়া মণিপুরী</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Matematik" title="Matematik – бретон" lang="br" hreflang="br" data-title="Matematik" data-language-autonym="Brezhoneg" data-language-local-name="бретон" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Matematika" title="Matematika – босни" lang="bs" hreflang="bs" data-title="Matematika" data-language-autonym="Bosanski" data-language-local-name="босни" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-bug mw-list-item"><a href="https://bug.wikipedia.org/wiki/%E1%A8%86%E1%A8%88%E1%A8%9B%E1%A8%86%E1%A8%88%E1%A8%97%E1%A8%80" title="ᨆᨈᨛᨆᨈᨗᨀ – буги" lang="bug" hreflang="bug" data-title="ᨆᨈᨛᨆᨈᨗᨀ" data-language-autonym="Basa Ugi" data-language-local-name="буги" class="interlanguage-link-target"><span>Basa Ugi</span></a></li><li class="interlanguage-link interwiki-bxr mw-list-item"><a href="https://bxr.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D0%B3%D0%BE%D0%B9_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Тоогой ухаан – Russia Buriat" lang="bxr" hreflang="bxr" data-title="Тоогой ухаан" data-language-autonym="Буряад" data-language-local-name="Russia Buriat" class="interlanguage-link-target"><span>Буряад</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques" title="Matemàtiques – каталан" lang="ca" hreflang="ca" data-title="Matemàtiques" data-language-autonym="Català" data-language-local-name="каталан" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cbk-zam mw-list-item"><a href="https://cbk-zam.wikipedia.org/wiki/Matematica" title="Matematica – Chavacano" lang="cbk" hreflang="cbk" data-title="Matematica" data-language-autonym="Chavacano de Zamboanga" data-language-local-name="Chavacano" class="interlanguage-link-target"><span>Chavacano de Zamboanga</span></a></li><li class="interlanguage-link interwiki-cdo mw-list-item"><a href="https://cdo.wikipedia.org/wiki/S%C3%B3-h%C5%8Fk" title="Só-hŏk – Mindong" lang="cdo" hreflang="cdo" data-title="Só-hŏk" data-language-autonym="閩東語 / Mìng-dĕ̤ng-ngṳ̄" data-language-local-name="Mindong" class="interlanguage-link-target"><span>閩東語 / Mìng-dĕ̤ng-ngṳ̄</span></a></li><li class="interlanguage-link interwiki-ce mw-list-item"><a href="https://ce.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – чечень" lang="ce" hreflang="ce" data-title="Математика" data-language-autonym="Нохчийн" data-language-local-name="чечень" class="interlanguage-link-target"><span>Нохчийн</span></a></li><li class="interlanguage-link interwiki-ceb mw-list-item"><a href="https://ceb.wikipedia.org/wiki/Isip" title="Isip – себуано" lang="ceb" hreflang="ceb" data-title="Isip" data-language-autonym="Cebuano" data-language-local-name="себуано" class="interlanguage-link-target"><span>Cebuano</span></a></li><li class="interlanguage-link interwiki-ch mw-list-item"><a href="https://ch.wikipedia.org/wiki/Matematika" title="Matematika – чаморро" lang="ch" hreflang="ch" data-title="Matematika" data-language-autonym="Chamoru" data-language-local-name="чаморро" class="interlanguage-link-target"><span>Chamoru</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%85%D8%A7%D8%AA%D9%85%D8%A7%D8%AA%DB%8C%DA%A9" title="ماتماتیک – төв курд" lang="ckb" hreflang="ckb" data-title="ماتماتیک" data-language-autonym="کوردی" data-language-local-name="төв курд" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-co mw-list-item"><a href="https://co.wikipedia.org/wiki/Matematica" title="Matematica – корсик" lang="co" hreflang="co" data-title="Matematica" data-language-autonym="Corsu" data-language-local-name="корсик" class="interlanguage-link-target"><span>Corsu</span></a></li><li class="interlanguage-link interwiki-crh mw-list-item"><a href="https://crh.wikipedia.org/wiki/Riyaziyat" title="Riyaziyat – Crimean Tatar" lang="crh" hreflang="crh" data-title="Riyaziyat" data-language-autonym="Qırımtatarca" data-language-local-name="Crimean Tatar" class="interlanguage-link-target"><span>Qırımtatarca</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Matematika" title="Matematika – чех" lang="cs" hreflang="cs" data-title="Matematika" data-language-autonym="Čeština" data-language-local-name="чех" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-csb mw-list-item"><a href="https://csb.wikipedia.org/wiki/Matematika" title="Matematika – Kashubian" lang="csb" hreflang="csb" data-title="Matematika" data-language-autonym="Kaszëbsczi" data-language-local-name="Kashubian" class="interlanguage-link-target"><span>Kaszëbsczi</span></a></li><li class="interlanguage-link interwiki-cu mw-list-item"><a href="https://cu.wikipedia.org/wiki/%D0%9C%D0%B0%D1%B3%D0%B8%D0%BC%D0%B0%D1%82%D1%97%D0%BA%D0%B0" title="Маѳиматїка – сүмийн славян" lang="cu" hreflang="cu" data-title="Маѳиматїка" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="сүмийн славян" class="interlanguage-link-target"><span>Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – чуваш" lang="cv" hreflang="cv" data-title="Математика" data-language-autonym="Чӑвашла" data-language-local-name="чуваш" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Mathemateg" title="Mathemateg – уэльс" lang="cy" hreflang="cy" data-title="Mathemateg" data-language-autonym="Cymraeg" data-language-local-name="уэльс" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da badge-Q17559452 badge-recommendedarticle mw-list-item" title="recommended article"><a href="https://da.wikipedia.org/wiki/Matematik" title="Matematik – дани" lang="da" hreflang="da" data-title="Matematik" data-language-autonym="Dansk" data-language-local-name="дани" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-dag mw-list-item"><a href="https://dag.wikipedia.org/wiki/Laasabu_malibu" title="Laasabu malibu – Dagbani" lang="dag" hreflang="dag" data-title="Laasabu malibu" data-language-autonym="Dagbanli" data-language-local-name="Dagbani" class="interlanguage-link-target"><span>Dagbanli</span></a></li><li class="interlanguage-link interwiki-de badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://de.wikipedia.org/wiki/Mathematik" title="Mathematik – герман" lang="de" hreflang="de" data-title="Mathematik" data-language-autonym="Deutsch" data-language-local-name="герман" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-din mw-list-item"><a href="https://din.wikipedia.org/wiki/Aku%C3%ABnk%C3%A4%C5%8B" title="Akuënkäŋ – Dinka" lang="din" hreflang="din" data-title="Akuënkäŋ" data-language-autonym="Thuɔŋjäŋ" data-language-local-name="Dinka" class="interlanguage-link-target"><span>Thuɔŋjäŋ</span></a></li><li class="interlanguage-link interwiki-diq mw-list-item"><a href="https://diq.wikipedia.org/wiki/Matematik" title="Matematik – Zazaki" lang="diq" hreflang="diq" data-title="Matematik" data-language-autonym="Zazaki" data-language-local-name="Zazaki" class="interlanguage-link-target"><span>Zazaki</span></a></li><li class="interlanguage-link interwiki-dsb mw-list-item"><a href="https://dsb.wikipedia.org/wiki/Matematika" title="Matematika – доод сорби" lang="dsb" hreflang="dsb" data-title="Matematika" data-language-autonym="Dolnoserbski" data-language-local-name="доод сорби" class="interlanguage-link-target"><span>Dolnoserbski</span></a></li><li class="interlanguage-link interwiki-dtp mw-list-item"><a href="https://dtp.wikipedia.org/wiki/Matematik" title="Matematik – Central Dusun" lang="dtp" hreflang="dtp" data-title="Matematik" data-language-autonym="Kadazandusun" data-language-local-name="Central Dusun" class="interlanguage-link-target"><span>Kadazandusun</span></a></li><li class="interlanguage-link interwiki-dv mw-list-item"><a href="https://dv.wikipedia.org/wiki/%DE%83%DE%A8%DE%94%DE%A7%DE%9F%DE%A8%DE%87%DE%B0%DE%94%DE%A7%DE%8C%DE%AA" title="ރިޔާޟިއްޔާތު – дивехи" lang="dv" hreflang="dv" data-title="ރިޔާޟިއްޔާތު" data-language-autonym="ދިވެހިބަސް" data-language-local-name="дивехи" class="interlanguage-link-target"><span>ދިވެހިބަސް</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9C%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Μαθηματικά – грек" lang="el" hreflang="el" data-title="Μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="грек" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-eml mw-list-item"><a href="https://eml.wikipedia.org/wiki/Matem%C3%A2tica" title="Matemâtica – Emiliano-Romagnolo" lang="egl" hreflang="egl" data-title="Matemâtica" data-language-autonym="Emiliàn e rumagnòl" data-language-local-name="Emiliano-Romagnolo" class="interlanguage-link-target"><span>Emiliàn e rumagnòl</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Mathematics" title="Mathematics – англи" lang="en" hreflang="en" data-title="Mathematics" data-language-autonym="English" data-language-local-name="англи" 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/Matematiko" title="Matematiko – эсперанто" lang="eo" hreflang="eo" data-title="Matematiko" data-language-autonym="Esperanto" data-language-local-name="эсперанто" 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/Matem%C3%A1ticas" title="Matemáticas – испани" lang="es" hreflang="es" data-title="Matemáticas" data-language-autonym="Español" data-language-local-name="испани" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Matemaatika" title="Matemaatika – эстони" lang="et" hreflang="et" data-title="Matemaatika" data-language-autonym="Eesti" data-language-local-name="эстони" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Matematika" title="Matematika – баск" lang="eu" hreflang="eu" data-title="Matematika" data-language-autonym="Euskara" data-language-local-name="баск" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-ext mw-list-item"><a href="https://ext.wikipedia.org/wiki/Matem%C3%A1ticas" title="Matemáticas – Extremaduran" lang="ext" hreflang="ext" data-title="Matemáticas" data-language-autonym="Estremeñu" data-language-local-name="Extremaduran" class="interlanguage-link-target"><span>Estremeñu</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="ریاضیات – перс" lang="fa" hreflang="fa" data-title="ریاضیات" data-language-autonym="فارسی" data-language-local-name="перс" 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/Matematiikka" title="Matematiikka – фин" lang="fi" hreflang="fi" data-title="Matematiikka" data-language-autonym="Suomi" data-language-local-name="фин" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Mat%C3%B5maatiga" title="Matõmaatiga – Võro" lang="vro" hreflang="vro" data-title="Matõmaatiga" data-language-autonym="Võro" data-language-local-name="Võro" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Fika" title="Fika – фижи" lang="fj" hreflang="fj" data-title="Fika" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="фижи" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fo mw-list-item"><a href="https://fo.wikipedia.org/wiki/St%C3%B8ddfr%C3%B8%C3%B0i" title="Støddfrøði – фарер" lang="fo" hreflang="fo" data-title="Støddfrøði" data-language-autonym="Føroyskt" data-language-local-name="фарер" class="interlanguage-link-target"><span>Føroyskt</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Math%C3%A9matiques" title="Mathématiques – франц" lang="fr" hreflang="fr" data-title="Mathématiques" data-language-autonym="Français" data-language-local-name="франц" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frp mw-list-item"><a href="https://frp.wikipedia.org/wiki/Mat%C3%A8matiques" title="Matèmatiques – Arpitan" lang="frp" hreflang="frp" data-title="Matèmatiques" data-language-autonym="Arpetan" data-language-local-name="Arpitan" class="interlanguage-link-target"><span>Arpetan</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Matematiik" title="Matematiik – хойд фриз" lang="frr" hreflang="frr" data-title="Matematiik" data-language-autonym="Nordfriisk" data-language-local-name="хойд фриз" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-fur mw-list-item"><a href="https://fur.wikipedia.org/wiki/Matematiche" title="Matematiche – фриулан" lang="fur" hreflang="fur" data-title="Matematiche" data-language-autonym="Furlan" data-language-local-name="фриулан" class="interlanguage-link-target"><span>Furlan</span></a></li><li class="interlanguage-link interwiki-fy mw-list-item"><a href="https://fy.wikipedia.org/wiki/Wiskunde" title="Wiskunde – баруун фриз" lang="fy" hreflang="fy" data-title="Wiskunde" data-language-autonym="Frysk" data-language-local-name="баруун фриз" class="interlanguage-link-target"><span>Frysk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Matamaitic" title="Matamaitic – ирланд" lang="ga" hreflang="ga" data-title="Matamaitic" data-language-autonym="Gaeilge" data-language-local-name="ирланд" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 – Gan" lang="gan" hreflang="gan" data-title="數學" data-language-autonym="贛語" data-language-local-name="Gan" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/Mat%C3%A9matik" title="Matématik – Guianan Creole" lang="gcr" hreflang="gcr" data-title="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-gd mw-list-item"><a href="https://gd.wikipedia.org/wiki/Matamataig" title="Matamataig – шотландын гел" lang="gd" hreflang="gd" data-title="Matamataig" data-language-autonym="Gàidhlig" data-language-local-name="шотландын гел" class="interlanguage-link-target"><span>Gàidhlig</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Matem%C3%A1ticas" title="Matemáticas – галего" lang="gl" hreflang="gl" data-title="Matemáticas" data-language-autonym="Galego" data-language-local-name="галего" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gn mw-list-item"><a href="https://gn.wikipedia.org/wiki/Papapykuaa" title="Papapykuaa – гуарани" lang="gn" hreflang="gn" data-title="Papapykuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="гуарани" class="interlanguage-link-target"><span>Avañe'ẽ</span></a></li><li class="interlanguage-link interwiki-gom mw-list-item"><a href="https://gom.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%E0%B3%8D" title="ಗಣಿತ್ – Goan Konkani" lang="gom" hreflang="gom" data-title="ಗಣಿತ್" data-language-autonym="गोंयची कोंकणी / Gõychi Konknni" data-language-local-name="Goan Konkani" class="interlanguage-link-target"><span>गोंयची कोंकणी / Gõychi Konknni</span></a></li><li class="interlanguage-link interwiki-gor mw-list-item"><a href="https://gor.wikipedia.org/wiki/Matematika" title="Matematika – горонтало" lang="gor" hreflang="gor" data-title="Matematika" data-language-autonym="Bahasa Hulontalo" data-language-local-name="горонтало" class="interlanguage-link-target"><span>Bahasa Hulontalo</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%97%E0%AA%A3%E0%AA%BF%E0%AA%A4" title="ગણિત – гужарати" lang="gu" hreflang="gu" data-title="ગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="гужарати" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-gv mw-list-item"><a href="https://gv.wikipedia.org/wiki/Maddaght" title="Maddaght – манкс" lang="gv" hreflang="gv" data-title="Maddaght" data-language-autonym="Gaelg" data-language-local-name="манкс" class="interlanguage-link-target"><span>Gaelg</span></a></li><li class="interlanguage-link interwiki-ha mw-list-item"><a href="https://ha.wikipedia.org/wiki/Lissafi" title="Lissafi – хауса" lang="ha" hreflang="ha" data-title="Lissafi" data-language-autonym="Hausa" data-language-local-name="хауса" class="interlanguage-link-target"><span>Hausa</span></a></li><li class="interlanguage-link interwiki-hak mw-list-item"><a href="https://hak.wikipedia.org/wiki/Su-ho%CC%8Dk" title="Su-ho̍k – Hakka Chinese" lang="hak" hreflang="hak" data-title="Su-ho̍k" data-language-autonym="客家語 / Hak-kâ-ngî" data-language-local-name="Hakka Chinese" class="interlanguage-link-target"><span>客家語 / Hak-kâ-ngî</span></a></li><li class="interlanguage-link interwiki-haw mw-list-item"><a href="https://haw.wikipedia.org/wiki/Makemakika" title="Makemakika – хавай" lang="haw" hreflang="haw" data-title="Makemakika" data-language-autonym="Hawaiʻi" data-language-local-name="хавай" class="interlanguage-link-target"><span>Hawaiʻi</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94" title="מתמטיקה – еврей" lang="he" hreflang="he" data-title="מתמטיקה" data-language-autonym="עברית" data-language-local-name="еврей" 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%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – хинди" lang="hi" hreflang="hi" data-title="गणित" data-language-autonym="हिन्दी" data-language-local-name="хинди" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Mathematics" title="Mathematics – Fiji Hindi" lang="hif" hreflang="hif" data-title="Mathematics" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Matematika" title="Matematika – хорват" lang="hr" hreflang="hr" data-title="Matematika" data-language-autonym="Hrvatski" data-language-local-name="хорват" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-ht mw-list-item"><a href="https://ht.wikipedia.org/wiki/Matematik" title="Matematik – Гаитийн креол" lang="ht" hreflang="ht" data-title="Matematik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Гаитийн креол" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Matematika" title="Matematika – мажар" lang="hu" hreflang="hu" data-title="Matematika" data-language-autonym="Magyar" data-language-local-name="мажар" 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" title="Մաթեմատիկա – армен" lang="hy" hreflang="hy" data-title="Մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="армен" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://ia.wikipedia.org/wiki/Mathematica" title="Mathematica – интерлингво" lang="ia" hreflang="ia" data-title="Mathematica" data-language-autonym="Interlingua" data-language-local-name="интерлингво" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-iba mw-list-item"><a href="https://iba.wikipedia.org/wiki/Matematik" title="Matematik – ибан" lang="iba" hreflang="iba" data-title="Matematik" data-language-autonym="Jaku Iban" data-language-local-name="ибан" class="interlanguage-link-target"><span>Jaku Iban</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika" title="Matematika – индонези" lang="id" hreflang="id" data-title="Matematika" data-language-autonym="Bahasa Indonesia" data-language-local-name="индонези" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-ie mw-list-item"><a href="https://ie.wikipedia.org/wiki/Matematica" title="Matematica – нэгдмэл хэл" lang="ie" hreflang="ie" data-title="Matematica" data-language-autonym="Interlingue" data-language-local-name="нэгдмэл хэл" class="interlanguage-link-target"><span>Interlingue</span></a></li><li class="interlanguage-link interwiki-ig mw-list-item"><a href="https://ig.wikipedia.org/wiki/%E1%BB%8Cm%C3%BAm%C3%BA-%C3%B3n%C3%BA%E1%BB%8Dg%E1%BB%A5g%E1%BB%A5" title="Ọmúmú-ónúọgụgụ – игбо" lang="ig" hreflang="ig" data-title="Ọmúmú-ónúọgụgụ" data-language-autonym="Igbo" data-language-local-name="игбо" class="interlanguage-link-target"><span>Igbo</span></a></li><li class="interlanguage-link interwiki-ilo mw-list-item"><a href="https://ilo.wikipedia.org/wiki/Matematika" title="Matematika – илоко" lang="ilo" hreflang="ilo" data-title="Matematika" data-language-autonym="Ilokano" data-language-local-name="илоко" class="interlanguage-link-target"><span>Ilokano</span></a></li><li class="interlanguage-link interwiki-inh mw-list-item"><a href="https://inh.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – ингуш" lang="inh" hreflang="inh" data-title="Математика" data-language-autonym="ГӀалгӀай" data-language-local-name="ингуш" class="interlanguage-link-target"><span>ГӀалгӀай</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Matematiko" title="Matematiko – идо" lang="io" hreflang="io" data-title="Matematiko" data-language-autonym="Ido" data-language-local-name="идо" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/St%C3%A6r%C3%B0fr%C3%A6%C3%B0i" title="Stærðfræði – исланд" lang="is" hreflang="is" data-title="Stærðfræði" data-language-autonym="Íslenska" data-language-local-name="исланд" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Matematica" title="Matematica – итали" lang="it" hreflang="it" data-title="Matematica" data-language-autonym="Italiano" data-language-local-name="итали" 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%E5%AD%A6" title="数学 – япон" lang="ja" hreflang="ja" data-title="数学" data-language-autonym="日本語" data-language-local-name="япон" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Matimatix" title="Matimatix – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Matimatix" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/cmaci" title="cmaci – ложбан" lang="jbo" hreflang="jbo" data-title="cmaci" data-language-autonym="La .lojban." data-language-local-name="ложбан" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://jv.wikipedia.org/wiki/Mat%C3%A9matika" title="Matématika – ява" lang="jv" hreflang="jv" data-title="Matématika" data-language-autonym="Jawa" data-language-local-name="ява" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://ka.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="მათემატიკა – гүрж" lang="ka" hreflang="ka" data-title="მათემატიკა" data-language-autonym="ქართული" data-language-local-name="гүрж" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kaa mw-list-item"><a href="https://kaa.wikipedia.org/wiki/Matematika" title="Matematika – Kara-Kalpak" lang="kaa" hreflang="kaa" data-title="Matematika" data-language-autonym="Qaraqalpaqsha" data-language-local-name="Kara-Kalpak" class="interlanguage-link-target"><span>Qaraqalpaqsha</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Tusnakt" title="Tusnakt – кабиле" lang="kab" hreflang="kab" data-title="Tusnakt" data-language-autonym="Taqbaylit" data-language-local-name="кабиле" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-kge mw-list-item"><a href="https://kge.wikipedia.org/wiki/Matematika" title="Matematika – Komering" lang="kge" hreflang="kge" data-title="Matematika" data-language-autonym="Kumoring" data-language-local-name="Komering" class="interlanguage-link-target"><span>Kumoring</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – казах" lang="kk" hreflang="kk" data-title="Математика" data-language-autonym="Қазақша" data-language-local-name="казах" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kl mw-list-item"><a href="https://kl.wikipedia.org/wiki/Matematikki" title="Matematikki – калалисут" lang="kl" hreflang="kl" data-title="Matematikki" data-language-autonym="Kalaallisut" data-language-local-name="калалисут" class="interlanguage-link-target"><span>Kalaallisut</span></a></li><li class="interlanguage-link interwiki-km mw-list-item"><a href="https://km.wikipedia.org/wiki/%E1%9E%82%E1%9E%8E%E1%9E%B7%E1%9E%8F%E1%9E%9C%E1%9E%B7%E1%9E%91%E1%9F%92%E1%9E%99%E1%9E%B6" title="គណិតវិទ្យា – кхмер" lang="km" hreflang="km" data-title="គណិតវិទ្យា" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="кхмер" class="interlanguage-link-target"><span>ភាសាខ្មែរ</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಗಣಿತ – каннада" lang="kn" hreflang="kn" data-title="ಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="каннада" class="interlanguage-link-target"><span>ಕನ್ನಡ</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" title="수학 – солонгос" lang="ko" hreflang="ko" data-title="수학" data-language-autonym="한국어" data-language-local-name="солонгос" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-krc mw-list-item"><a href="https://krc.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – карачай-балкар" lang="krc" hreflang="krc" data-title="Математика" data-language-autonym="Къарачай-малкъар" data-language-local-name="карачай-балкар" class="interlanguage-link-target"><span>Къарачай-малкъар</span></a></li><li class="interlanguage-link interwiki-ks mw-list-item"><a href="https://ks.wikipedia.org/wiki/%DA%AF%D8%B1%D9%9B%D8%A0%D9%86%D8%AF%D9%8F%D8%AA" title="گرٛؠندُت – кашмир" lang="ks" hreflang="ks" data-title="گرٛؠندُت" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="кашмир" class="interlanguage-link-target"><span>कॉशुर / کٲشُر</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/Matemat%C3%AEk" title="Matematîk – курд" lang="ku" hreflang="ku" data-title="Matematîk" data-language-autonym="Kurdî" data-language-local-name="курд" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-kw mw-list-item"><a href="https://kw.wikipedia.org/wiki/Awgrym" title="Awgrym – корн" lang="kw" hreflang="kw" data-title="Awgrym" data-language-autonym="Kernowek" data-language-local-name="корн" class="interlanguage-link-target"><span>Kernowek</span></a></li><li class="interlanguage-link interwiki-ky mw-list-item"><a href="https://ky.wikipedia.org/wiki/%D0%92%D0%B8%D0%BA%D0%B8%D0%BF%D0%B5%D0%B4%D0%B8%D1%8F:%D0%A1%D0%BE%D0%BC%D0%BE/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Википедия:Сомо/Математика – киргиз" lang="ky" hreflang="ky" data-title="Википедия:Сомо/Математика" data-language-autonym="Кыргызча" data-language-local-name="киргиз" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://la.wikipedia.org/wiki/Mathematica" title="Mathematica – латин" lang="la" hreflang="la" data-title="Mathematica" data-language-autonym="Latina" data-language-local-name="латин" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lad mw-list-item"><a href="https://lad.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika – ладин" lang="lad" hreflang="lad" data-title="Matemátika" data-language-autonym="Ladino" data-language-local-name="ладин" class="interlanguage-link-target"><span>Ladino</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Mathematik" title="Mathematik – люксембург" lang="lb" hreflang="lb" data-title="Mathematik" data-language-autonym="Lëtzebuergesch" data-language-local-name="люксембург" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lez mw-list-item"><a href="https://lez.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – лезги" lang="lez" hreflang="lez" data-title="Математика" data-language-autonym="Лезги" data-language-local-name="лезги" class="interlanguage-link-target"><span>Лезги</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Matematica" title="Matematica – Lingua Franca Nova" lang="lfn" hreflang="lfn" data-title="Matematica" data-language-autonym="Lingua Franca Nova" data-language-local-name="Lingua Franca Nova" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lg mw-list-item"><a href="https://lg.wikipedia.org/wiki/Ekibalangulo" title="Ekibalangulo – ганда" lang="lg" hreflang="lg" data-title="Ekibalangulo" data-language-autonym="Luganda" data-language-local-name="ганда" class="interlanguage-link-target"><span>Luganda</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Mathematiek" title="Mathematiek – лимбург" lang="li" hreflang="li" data-title="Mathematiek" data-language-autonym="Limburgs" data-language-local-name="лимбург" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-lij mw-list-item"><a href="https://lij.wikipedia.org/wiki/Matematica" title="Matematica – Лигури" lang="lij" hreflang="lij" data-title="Matematica" data-language-autonym="Ligure" data-language-local-name="Лигури" class="interlanguage-link-target"><span>Ligure</span></a></li><li class="interlanguage-link interwiki-lld mw-list-item"><a href="https://lld.wikipedia.org/wiki/Matematica" title="Matematica – Ladin" lang="lld" hreflang="lld" data-title="Matematica" data-language-autonym="Ladin" data-language-local-name="Ladin" class="interlanguage-link-target"><span>Ladin</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Matematega" title="Matematega – Lombard" lang="lmo" hreflang="lmo" data-title="Matematega" data-language-autonym="Lombard" data-language-local-name="Lombard" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lo mw-list-item"><a href="https://lo.wikipedia.org/wiki/%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="ຄະນິດສາດ – лаос" lang="lo" hreflang="lo" data-title="ຄະນິດສາດ" data-language-autonym="ລາວ" data-language-local-name="лаос" 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/Matematika" title="Matematika – литва" lang="lt" hreflang="lt" data-title="Matematika" data-language-autonym="Lietuvių" data-language-local-name="литва" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Matem%C4%81tika" title="Matemātika – латви" lang="lv" hreflang="lv" data-title="Matemātika" data-language-autonym="Latviešu" data-language-local-name="латви" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mad mw-list-item"><a href="https://mad.wikipedia.org/wiki/Matematika" title="Matematika – мадури хэл" lang="mad" hreflang="mad" data-title="Matematika" data-language-autonym="Madhurâ" data-language-local-name="мадури хэл" class="interlanguage-link-target"><span>Madhurâ</span></a></li><li class="interlanguage-link interwiki-mai mw-list-item"><a href="https://mai.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – май" lang="mai" hreflang="mai" data-title="गणित" data-language-autonym="मैथिली" data-language-local-name="май" class="interlanguage-link-target"><span>मैथिली</span></a></li><li class="interlanguage-link interwiki-map-bms mw-list-item"><a href="https://map-bms.wikipedia.org/wiki/Matematika" title="Matematika – Banyumasan" lang="jv-x-bms" hreflang="jv-x-bms" data-title="Matematika" data-language-autonym="Basa Banyumasan" data-language-local-name="Banyumasan" class="interlanguage-link-target"><span>Basa Banyumasan</span></a></li><li class="interlanguage-link interwiki-mg mw-list-item"><a href="https://mg.wikipedia.org/wiki/Matematika" title="Matematika – малагаси" lang="mg" hreflang="mg" data-title="Matematika" data-language-autonym="Malagasy" data-language-local-name="малагаси" class="interlanguage-link-target"><span>Malagasy</span></a></li><li class="interlanguage-link interwiki-mhr mw-list-item"><a href="https://mhr.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B5" title="Математике – Eastern Mari" lang="mhr" hreflang="mhr" data-title="Математике" data-language-autonym="Олык марий" data-language-local-name="Eastern Mari" class="interlanguage-link-target"><span>Олык марий</span></a></li><li class="interlanguage-link interwiki-min mw-list-item"><a href="https://min.wikipedia.org/wiki/Matematika" title="Matematika – минангкабау" lang="min" hreflang="min" data-title="Matematika" data-language-autonym="Minangkabau" data-language-local-name="минангкабау" class="interlanguage-link-target"><span>Minangkabau</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%D0%BA%D0%B0" title="Математика – македон" lang="mk" hreflang="mk" data-title="Математика" data-language-autonym="Македонски" data-language-local-name="македон" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="ഗണിതം – малаялам" lang="ml" hreflang="ml" data-title="ഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="малаялам" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mni mw-list-item"><a href="https://mni.wikipedia.org/wiki/%EA%AF%86%EA%AF%A9%EA%AF%81%EA%AF%A4%EA%AF%A1%EA%AF%82%EA%AF%A3%EA%AF%9F" title="ꯆꯩꯁꯤꯡꯂꯣꯟ – манипури" lang="mni" hreflang="mni" data-title="ꯆꯩꯁꯤꯡꯂꯣꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="манипури" class="interlanguage-link-target"><span>ꯃꯤꯇꯩ ꯂꯣꯟ</span></a></li><li class="interlanguage-link interwiki-mnw mw-list-item"><a href="https://mnw.wikipedia.org/wiki/%E1%80%9E%E1%81%9A%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သၚ်္ချာ – Mon" lang="mnw" hreflang="mnw" data-title="သၚ်္ချာ" data-language-autonym="ဘာသာမန်" data-language-local-name="Mon" class="interlanguage-link-target"><span>ဘာသာမန်</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – марати" lang="mr" hreflang="mr" data-title="गणित" data-language-autonym="मराठी" data-language-local-name="марати" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Matematik" title="Matematik – малай" lang="ms" hreflang="ms" data-title="Matematik" data-language-autonym="Bahasa Melayu" data-language-local-name="малай" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Matematika" title="Matematika – малта" lang="mt" hreflang="mt" data-title="Matematika" data-language-autonym="Malti" data-language-local-name="малта" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Matem%C3%A1tica" title="Matemática – меранди" lang="mwl" hreflang="mwl" data-title="Matemática" data-language-autonym="Mirandés" data-language-local-name="меранди" class="interlanguage-link-target"><span>Mirandés</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="သင်္ချာ – бирм" lang="my" hreflang="my" data-title="သင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="бирм" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-myv mw-list-item"><a href="https://myv.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – эрзя" lang="myv" hreflang="myv" data-title="Математика" data-language-autonym="Эрзянь" data-language-local-name="эрзя" class="interlanguage-link-target"><span>Эрзянь</span></a></li><li class="interlanguage-link interwiki-mzn mw-list-item"><a href="https://mzn.wikipedia.org/wiki/%D8%B1%D9%82%D9%85" title="رقم – мазандерани" lang="mzn" hreflang="mzn" data-title="رقم" data-language-autonym="مازِرونی" data-language-local-name="мазандерани" class="interlanguage-link-target"><span>مازِرونی</span></a></li><li class="interlanguage-link interwiki-nah mw-list-item"><a href="https://nah.wikipedia.org/wiki/Tlap%C5%8Dhualmatiliztli" title="Tlapōhualmatiliztli – Nahuatl" lang="nah" hreflang="nah" data-title="Tlapōhualmatiliztli" data-language-autonym="Nāhuatl" data-language-local-name="Nahuatl" class="interlanguage-link-target"><span>Nāhuatl</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Mathematik" title="Mathematik – доод герман" lang="nds" hreflang="nds" data-title="Mathematik" data-language-autonym="Plattdüütsch" data-language-local-name="доод герман" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nds-nl mw-list-item"><a href="https://nds-nl.wikipedia.org/wiki/Wiskunde" title="Wiskunde – Low Saxon" lang="nds-NL" hreflang="nds-NL" data-title="Wiskunde" data-language-autonym="Nedersaksies" data-language-local-name="Low Saxon" class="interlanguage-link-target"><span>Nedersaksies</span></a></li><li class="interlanguage-link interwiki-ne mw-list-item"><a href="https://ne.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="गणित – балба" lang="ne" hreflang="ne" data-title="गणित" data-language-autonym="नेपाली" data-language-local-name="балба" class="interlanguage-link-target"><span>नेपाली</span></a></li><li class="interlanguage-link interwiki-new mw-list-item"><a href="https://new.wikipedia.org/wiki/%E0%A4%B2%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%83%E0%A4%9C%E0%A5%8D%E0%A4%AF%E0%A4%BE" title="ल्याःज्या – невари" lang="new" hreflang="new" data-title="ल्याःज्या" data-language-autonym="नेपाल भाषा" data-language-local-name="невари" class="interlanguage-link-target"><span>नेपाल भाषा</span></a></li><li class="interlanguage-link interwiki-nia mw-list-item"><a href="https://nia.wikipedia.org/wiki/Matematika" title="Matematika – ниас хэл" lang="nia" hreflang="nia" data-title="Matematika" data-language-autonym="Li Niha" data-language-local-name="ниас хэл" class="interlanguage-link-target"><span>Li Niha</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Wiskunde" title="Wiskunde – нидерланд" lang="nl" hreflang="nl" data-title="Wiskunde" data-language-autonym="Nederlands" data-language-local-name="нидерланд" 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/Matematikk" title="Matematikk – норвегийн нинорск" lang="nn" hreflang="nn" data-title="Matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="норвегийн нинорск" 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/Matematikk" title="Matematikk – норвегийн букмол" lang="nb" hreflang="nb" data-title="Matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="норвегийн букмол" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-nov mw-list-item"><a href="https://nov.wikipedia.org/wiki/Matematike" title="Matematike – Novial" lang="nov" hreflang="nov" data-title="Matematike" data-language-autonym="Novial" data-language-local-name="Novial" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-nrm mw-list-item"><a href="https://nrm.wikipedia.org/wiki/Caltchul" title="Caltchul – Norman" lang="nrf" hreflang="nrf" data-title="Caltchul" data-language-autonym="Nouormand" data-language-local-name="Norman" class="interlanguage-link-target"><span>Nouormand</span></a></li><li class="interlanguage-link interwiki-nv mw-list-item"><a href="https://nv.wikipedia.org/wiki/A%C5%82hii%CA%BCn%C3%ADn%C3%A1%CA%BCiidz%C3%B3%C3%B3h" title="Ałhiiʼnínáʼiidzóóh – навахо" lang="nv" hreflang="nv" data-title="Ałhiiʼnínáʼiidzóóh" data-language-autonym="Diné bizaad" data-language-local-name="навахо" class="interlanguage-link-target"><span>Diné bizaad</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Matematicas" title="Matematicas – окситан" lang="oc" hreflang="oc" data-title="Matematicas" data-language-autonym="Occitan" data-language-local-name="окситан" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-olo mw-list-item"><a href="https://olo.wikipedia.org/wiki/Matematiekku" title="Matematiekku – Livvi-Karelian" lang="olo" hreflang="olo" data-title="Matematiekku" data-language-autonym="Livvinkarjala" data-language-local-name="Livvi-Karelian" class="interlanguage-link-target"><span>Livvinkarjala</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Herrega" title="Herrega – оромо" lang="om" hreflang="om" data-title="Herrega" data-language-autonym="Oromoo" data-language-local-name="оромо" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-or mw-list-item"><a href="https://or.wikipedia.org/wiki/%E0%AC%97%E0%AC%A3%E0%AC%BF%E0%AC%A4" title="ଗଣିତ – ория" lang="or" hreflang="or" data-title="ଗଣିତ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="ория" class="interlanguage-link-target"><span>ଓଡ଼ିଆ</span></a></li><li class="interlanguage-link interwiki-os mw-list-item"><a href="https://os.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%C3%A6" title="Математикæ – оссетин" lang="os" hreflang="os" data-title="Математикæ" data-language-autonym="Ирон" data-language-local-name="оссетин" class="interlanguage-link-target"><span>Ирон</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%97%E0%A8%A3%E0%A8%BF%E0%A8%A4" title="ਗਣਿਤ – панжаби" lang="pa" hreflang="pa" data-title="ਗਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="панжаби" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pag mw-list-item"><a href="https://pag.wikipedia.org/wiki/Matematiks" title="Matematiks – пангасин" lang="pag" hreflang="pag" data-title="Matematiks" data-language-autonym="Pangasinan" data-language-local-name="пангасин" class="interlanguage-link-target"><span>Pangasinan</span></a></li><li class="interlanguage-link interwiki-pam mw-list-item"><a href="https://pam.wikipedia.org/wiki/Matematica" title="Matematica – пампанга" lang="pam" hreflang="pam" data-title="Matematica" data-language-autonym="Kapampangan" data-language-local-name="пампанга" class="interlanguage-link-target"><span>Kapampangan</span></a></li><li class="interlanguage-link interwiki-pap mw-list-item"><a href="https://pap.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika – папьяменто" lang="pap" hreflang="pap" data-title="Matemátika" data-language-autonym="Papiamentu" data-language-local-name="папьяменто" class="interlanguage-link-target"><span>Papiamentu</span></a></li><li class="interlanguage-link interwiki-pcd mw-list-item"><a href="https://pcd.wikipedia.org/wiki/Mat%C3%A9matikes" title="Matématikes – Picard" lang="pcd" hreflang="pcd" data-title="Matématikes" data-language-autonym="Picard" data-language-local-name="Picard" class="interlanguage-link-target"><span>Picard</span></a></li><li class="interlanguage-link interwiki-pi mw-list-item"><a href="https://pi.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%82" title="गणितं – Pali" lang="pi" hreflang="pi" data-title="गणितं" data-language-autonym="पालि" data-language-local-name="Pali" class="interlanguage-link-target"><span>पालि</span></a></li><li class="interlanguage-link interwiki-pih mw-list-item"><a href="https://pih.wikipedia.org/wiki/Maethamatiks" title="Maethamatiks – Norfuk / Pitkern" lang="pih" hreflang="pih" data-title="Maethamatiks" data-language-autonym="Norfuk / Pitkern" data-language-local-name="Norfuk / Pitkern" class="interlanguage-link-target"><span>Norfuk / Pitkern</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyka" title="Matematyka – польш" lang="pl" hreflang="pl" data-title="Matematyka" data-language-autonym="Polski" data-language-local-name="польш" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Matem%C3%A0tica" title="Matemàtica – Piedmontese" lang="pms" hreflang="pms" data-title="Matemàtica" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی – Western Punjabi" lang="pnb" hreflang="pnb" data-title="ریاضی" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-ps mw-list-item"><a href="https://ps.wikipedia.org/wiki/%D8%B4%D9%85%DB%90%D8%B1%D9%BE%D9%88%D9%87%D9%86%D9%87" title="شمېرپوهنه – пушту" lang="ps" hreflang="ps" data-title="شمېرپوهنه" data-language-autonym="پښتو" data-language-local-name="пушту" class="interlanguage-link-target"><span>پښتو</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica" title="Matemática – португал" lang="pt" hreflang="pt" data-title="Matemática" data-language-autonym="Português" data-language-local-name="португал" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-qu mw-list-item"><a href="https://qu.wikipedia.org/wiki/Yupay_yachay" title="Yupay yachay – кечуа" lang="qu" hreflang="qu" data-title="Yupay yachay" data-language-autonym="Runa Simi" data-language-local-name="кечуа" class="interlanguage-link-target"><span>Runa Simi</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Matematic%C4%83" title="Matematică – румын" lang="ro" hreflang="ro" data-title="Matematică" data-language-autonym="Română" data-language-local-name="румын" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-roa-rup mw-list-item"><a href="https://roa-rup.wikipedia.org/wiki/Mathematic%C3%A2" title="Mathematicâ – ароманы" lang="rup" hreflang="rup" data-title="Mathematicâ" data-language-autonym="Armãneashti" data-language-local-name="ароманы" class="interlanguage-link-target"><span>Armãneashti</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – орос" lang="ru" hreflang="ru" data-title="Математика" data-language-autonym="Русский" data-language-local-name="орос" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-rue mw-list-item"><a href="https://rue.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D1%96%D0%BA%D0%B0" title="Математіка – Rusyn" lang="rue" hreflang="rue" data-title="Математіка" data-language-autonym="Русиньскый" data-language-local-name="Rusyn" class="interlanguage-link-target"><span>Русиньскый</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4%E0%A4%AE%E0%A5%8D" title="गणितम् – санскрит" lang="sa" hreflang="sa" data-title="गणितम्" data-language-autonym="संस्कृतम्" data-language-local-name="санскрит" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – саха" lang="sah" hreflang="sah" data-title="Математика" data-language-autonym="Саха тыла" data-language-local-name="саха" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-sat mw-list-item"><a href="https://sat.wikipedia.org/wiki/%E1%B1%AE%E1%B1%9E%E1%B1%A0%E1%B1%B7%E1%B1%9F" title="ᱮᱞᱠᱷᱟ – сантали" lang="sat" hreflang="sat" data-title="ᱮᱞᱠᱷᱟ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="сантали" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-sc badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://sc.wikipedia.org/wiki/Matem%C3%A0tica" title="Matemàtica – сардин" lang="sc" hreflang="sc" data-title="Matemàtica" data-language-autonym="Sardu" data-language-local-name="сардин" class="interlanguage-link-target"><span>Sardu</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Matim%C3%A0tica" title="Matimàtica – сицил" lang="scn" hreflang="scn" data-title="Matimàtica" data-language-autonym="Sicilianu" data-language-local-name="сицил" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Mathematics" title="Mathematics – шотланд" lang="sco" hreflang="sco" data-title="Mathematics" data-language-autonym="Scots" data-language-local-name="шотланд" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sd mw-list-item"><a href="https://sd.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="رياضي – синдхи" lang="sd" hreflang="sd" data-title="رياضي" data-language-autonym="سنڌي" data-language-local-name="синдхи" class="interlanguage-link-target"><span>سنڌي</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Matematika" title="Matematika – хорватын серб" lang="sh" hreflang="sh" data-title="Matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="хорватын серб" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-shi mw-list-item"><a href="https://shi.wikipedia.org/wiki/Tusnakt" title="Tusnakt – тачелхит" lang="shi" hreflang="shi" data-title="Tusnakt" data-language-autonym="Taclḥit" data-language-local-name="тачелхит" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-si mw-list-item"><a href="https://si.wikipedia.org/wiki/%E0%B6%9C%E0%B6%AB%E0%B7%92%E0%B6%AD%E0%B6%BA" title="ගණිතය – синхала" lang="si" hreflang="si" data-title="ගණිතය" data-language-autonym="සිංහල" data-language-local-name="синхала" class="interlanguage-link-target"><span>සිංහල</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Mathematics" title="Mathematics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Mathematics" 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/Matematika" title="Matematika – словак" lang="sk" hreflang="sk" data-title="Matematika" data-language-autonym="Slovenčina" data-language-local-name="словак" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-skr mw-list-item"><a href="https://skr.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی – Saraiki" lang="skr" hreflang="skr" data-title="ریاضی" data-language-autonym="سرائیکی" data-language-local-name="Saraiki" class="interlanguage-link-target"><span>سرائیکی</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Matematika" title="Matematika – словени" lang="sl" hreflang="sl" data-title="Matematika" data-language-autonym="Slovenščina" data-language-local-name="словени" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sm mw-list-item"><a href="https://sm.wikipedia.org/wiki/Matematika" title="Matematika – самоа" lang="sm" hreflang="sm" data-title="Matematika" data-language-autonym="Gagana Samoa" data-language-local-name="самоа" class="interlanguage-link-target"><span>Gagana Samoa</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Masvomhu" title="Masvomhu – шона" lang="sn" hreflang="sn" data-title="Masvomhu" data-language-autonym="ChiShona" data-language-local-name="шона" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-so mw-list-item"><a href="https://so.wikipedia.org/wiki/Tiromaal" title="Tiromaal – сомали" lang="so" hreflang="so" data-title="Tiromaal" data-language-autonym="Soomaaliga" data-language-local-name="сомали" class="interlanguage-link-target"><span>Soomaaliga</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Matematika" title="Matematika – албани" lang="sq" hreflang="sq" data-title="Matematika" data-language-autonym="Shqip" data-language-local-name="албани" 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%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – серб" lang="sr" hreflang="sr" data-title="Математика" data-language-autonym="Српски / srpski" data-language-local-name="серб" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-srn mw-list-item"><a href="https://srn.wikipedia.org/wiki/Sabi_fu_Teri" title="Sabi fu Teri – сранан тонго" lang="srn" hreflang="srn" data-title="Sabi fu Teri" data-language-autonym="Sranantongo" data-language-local-name="сранан тонго" class="interlanguage-link-target"><span>Sranantongo</span></a></li><li class="interlanguage-link interwiki-ss mw-list-item"><a href="https://ss.wikipedia.org/wiki/Tekubala" title="Tekubala – свати" lang="ss" hreflang="ss" data-title="Tekubala" data-language-autonym="SiSwati" data-language-local-name="свати" class="interlanguage-link-target"><span>SiSwati</span></a></li><li class="interlanguage-link interwiki-stq mw-list-item"><a href="https://stq.wikipedia.org/wiki/Mathematik" title="Mathematik – Saterland Frisian" lang="stq" hreflang="stq" data-title="Mathematik" data-language-autonym="Seeltersk" data-language-local-name="Saterland Frisian" class="interlanguage-link-target"><span>Seeltersk</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Matematika" title="Matematika – сундан" lang="su" hreflang="su" data-title="Matematika" data-language-autonym="Sunda" data-language-local-name="сундан" 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/Matematik" title="Matematik – швед" lang="sv" hreflang="sv" data-title="Matematik" data-language-autonym="Svenska" data-language-local-name="швед" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Hisabati" title="Hisabati – свахили" lang="sw" hreflang="sw" data-title="Hisabati" data-language-autonym="Kiswahili" data-language-local-name="свахили" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-szl mw-list-item"><a href="https://szl.wikipedia.org/wiki/Matymatyka" title="Matymatyka – Silesian" lang="szl" hreflang="szl" data-title="Matymatyka" data-language-autonym="Ślůnski" data-language-local-name="Silesian" class="interlanguage-link-target"><span>Ślůnski</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="கணிதம் – тамил" lang="ta" hreflang="ta" data-title="கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="тамил" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-tcy mw-list-item"><a href="https://tcy.wikipedia.org/wiki/%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4" title="ಗಣಿತ – Tulu" lang="tcy" hreflang="tcy" data-title="ಗಣಿತ" data-language-autonym="ತುಳು" data-language-local-name="Tulu" class="interlanguage-link-target"><span>ತುಳು</span></a></li><li class="interlanguage-link interwiki-tdd mw-list-item"><a href="https://tdd.wikipedia.org/wiki/%E1%A5%99%E1%A5%A3%E1%A5%AD%E1%A5%B0_%E1%A5%98%E1%A5%99%E1%A5%B3" title="ᥙᥣᥭᥰ ᥘᥙᥳ – Tai Nuea" lang="tdd" hreflang="tdd" data-title="ᥙᥣᥭᥰ ᥘᥙᥳ" data-language-autonym="ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ" data-language-local-name="Tai Nuea" class="interlanguage-link-target"><span>ᥖᥭᥰ ᥖᥬᥲ ᥑᥨᥒᥰ</span></a></li><li class="interlanguage-link interwiki-te mw-list-item"><a href="https://te.wikipedia.org/wiki/%E0%B0%97%E0%B0%A3%E0%B0%BF%E0%B0%A4%E0%B0%82" title="గణితం – тэлүгү" lang="te" hreflang="te" data-title="గణితం" data-language-autonym="తెలుగు" data-language-local-name="тэлүгү" class="interlanguage-link-target"><span>తెలుగు</span></a></li><li class="interlanguage-link interwiki-tet mw-list-item"><a href="https://tet.wikipedia.org/wiki/Matem%C3%A1tika" title="Matemátika – тетум" lang="tet" hreflang="tet" data-title="Matemátika" data-language-autonym="Tetun" data-language-local-name="тетум" class="interlanguage-link-target"><span>Tetun</span></a></li><li class="interlanguage-link interwiki-tg mw-list-item"><a href="https://tg.wikipedia.org/wiki/%D0%A0%D0%B8%D1%91%D0%B7%D0%B8%D1%91%D1%82" title="Риёзиёт – тажик" lang="tg" hreflang="tg" data-title="Риёзиёт" data-language-autonym="Тоҷикӣ" data-language-local-name="тажик" class="interlanguage-link-target"><span>Тоҷикӣ</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%93%E0%B8%B4%E0%B8%95%E0%B8%A8%E0%B8%B2%E0%B8%AA%E0%B8%95%E0%B8%A3%E0%B9%8C" title="คณิตศาสตร์ – тай" lang="th" hreflang="th" data-title="คณิตศาสตร์" data-language-autonym="ไทย" data-language-local-name="тай" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Matematika" title="Matematika – туркмен" lang="tk" hreflang="tk" data-title="Matematika" data-language-autonym="Türkmençe" data-language-local-name="туркмен" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Matematika" title="Matematika – Tagalog" lang="tl" hreflang="tl" data-title="Matematika" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tly mw-list-item"><a href="https://tly.wikipedia.org/wiki/Rijozijot" title="Rijozijot – Talysh" lang="tly" hreflang="tly" data-title="Rijozijot" data-language-autonym="Tolışi" data-language-local-name="Talysh" class="interlanguage-link-target"><span>Tolışi</span></a></li><li class="interlanguage-link interwiki-tn mw-list-item"><a href="https://tn.wikipedia.org/wiki/Dipalo" title="Dipalo – цвана" lang="tn" hreflang="tn" data-title="Dipalo" data-language-autonym="Setswana" data-language-local-name="цвана" class="interlanguage-link-target"><span>Setswana</span></a></li><li class="interlanguage-link interwiki-tpi mw-list-item"><a href="https://tpi.wikipedia.org/wiki/Ol_matematik" title="Ol matematik – ток писин" lang="tpi" hreflang="tpi" data-title="Ol matematik" data-language-autonym="Tok Pisin" data-language-local-name="ток писин" class="interlanguage-link-target"><span>Tok Pisin</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Matematik" title="Matematik – турк" lang="tr" hreflang="tr" data-title="Matematik" data-language-autonym="Türkçe" data-language-local-name="турк" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ts mw-list-item"><a href="https://ts.wikipedia.org/wiki/Dyondzo-Tinhlayo" title="Dyondzo-Tinhlayo – цонга" lang="ts" hreflang="ts" data-title="Dyondzo-Tinhlayo" data-language-autonym="Xitsonga" data-language-local-name="цонга" class="interlanguage-link-target"><span>Xitsonga</span></a></li><li class="interlanguage-link interwiki-tt mw-list-item"><a href="https://tt.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – татар" lang="tt" hreflang="tt" data-title="Математика" data-language-autonym="Татарча / tatarça" data-language-local-name="татар" class="interlanguage-link-target"><span>Татарча / tatarça</span></a></li><li class="interlanguage-link interwiki-udm mw-list-item"><a href="https://udm.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – удмурт" lang="udm" hreflang="udm" data-title="Математика" data-language-autonym="Удмурт" data-language-local-name="удмурт" class="interlanguage-link-target"><span>Удмурт</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – украин" lang="uk" hreflang="uk" data-title="Математика" data-language-autonym="Українська" data-language-local-name="украин" 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/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="ریاضی – урду" lang="ur" hreflang="ur" data-title="ریاضی" data-language-autonym="اردو" data-language-local-name="урду" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Matematika" title="Matematika – узбек" lang="uz" hreflang="uz" data-title="Matematika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="узбек" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vec mw-list-item"><a href="https://vec.wikipedia.org/wiki/Matem%C3%A0tega" title="Matemàtega – венец" lang="vec" hreflang="vec" data-title="Matemàtega" data-language-autonym="Vèneto" data-language-local-name="венец" class="interlanguage-link-target"><span>Vèneto</span></a></li><li class="interlanguage-link interwiki-vep mw-list-item"><a href="https://vep.wikipedia.org/wiki/Matematik" title="Matematik – Veps" lang="vep" hreflang="vep" data-title="Matematik" data-language-autonym="Vepsän kel’" data-language-local-name="Veps" class="interlanguage-link-target"><span>Vepsän kel’</span></a></li><li class="interlanguage-link interwiki-vi badge-Q17437798 badge-goodarticle mw-list-item" title="good article badge"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc" title="Toán học – вьетнам" lang="vi" hreflang="vi" data-title="Toán học" data-language-autonym="Tiếng Việt" data-language-local-name="вьетнам" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vls mw-list-item"><a href="https://vls.wikipedia.org/wiki/Wiskunde" title="Wiskunde – West Flemish" lang="vls" hreflang="vls" data-title="Wiskunde" data-language-autonym="West-Vlams" data-language-local-name="West Flemish" class="interlanguage-link-target"><span>West-Vlams</span></a></li><li class="interlanguage-link interwiki-vo badge-Q17437796 badge-featuredarticle mw-list-item" title="онцлох өгүүлэл"><a href="https://vo.wikipedia.org/wiki/Matemat" title="Matemat – волапюк" lang="vo" hreflang="vo" data-title="Matemat" data-language-autonym="Volapük" data-language-local-name="волапюк" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-wa mw-list-item"><a href="https://wa.wikipedia.org/wiki/Matematike" title="Matematike – уоллун" lang="wa" hreflang="wa" data-title="Matematike" data-language-autonym="Walon" data-language-local-name="уоллун" class="interlanguage-link-target"><span>Walon</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Matematika" title="Matematika – варай" lang="war" hreflang="war" data-title="Matematika" data-language-autonym="Winaray" data-language-local-name="варай" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wo mw-list-item"><a href="https://wo.wikipedia.org/wiki/Xayma" title="Xayma – волоф" lang="wo" hreflang="wo" data-title="Xayma" data-language-autonym="Wolof" data-language-local-name="волоф" class="interlanguage-link-target"><span>Wolof</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6" title="数学 – хятад, ву хэл" lang="wuu" hreflang="wuu" data-title="数学" data-language-autonym="吴语" data-language-local-name="хятад, ву хэл" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xal mw-list-item"><a href="https://xal.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Математика – халимаг" lang="xal" hreflang="xal" data-title="Математика" data-language-autonym="Хальмг" data-language-local-name="халимаг" class="interlanguage-link-target"><span>Хальмг</span></a></li><li class="interlanguage-link interwiki-xh mw-list-item"><a href="https://xh.wikipedia.org/wiki/I-Mathematics" title="I-Mathematics – хоса" lang="xh" hreflang="xh" data-title="I-Mathematics" data-language-autonym="IsiXhosa" data-language-local-name="хоса" class="interlanguage-link-target"><span>IsiXhosa</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90" title="მათემატიკა – Mingrelian" lang="xmf" hreflang="xmf" data-title="მათემატიკა" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%9E%D7%90%D7%98%D7%A2%D7%9E%D7%90%D7%98%D7%99%D7%A7" title="מאטעמאטיק – иддиш" lang="yi" hreflang="yi" data-title="מאטעמאטיק" data-language-autonym="ייִדיש" data-language-local-name="иддиш" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-yo mw-list-item"><a href="https://yo.wikipedia.org/wiki/Mathim%C3%A1t%C3%ADk%C3%AC" title="Mathimátíkì – ёруба" lang="yo" hreflang="yo" data-title="Mathimátíkì" data-language-autonym="Yorùbá" data-language-local-name="ёруба" class="interlanguage-link-target"><span>Yorùbá</span></a></li><li class="interlanguage-link interwiki-za mw-list-item"><a href="https://za.wikipedia.org/wiki/Soqyoz" title="Soqyoz – Zhuang" lang="za" hreflang="za" data-title="Soqyoz" data-language-autonym="Vahcuengh" data-language-local-name="Zhuang" class="interlanguage-link-target"><span>Vahcuengh</span></a></li><li class="interlanguage-link interwiki-zea mw-list-item"><a href="https://zea.wikipedia.org/wiki/Wiskunde" title="Wiskunde – Zeelandic" lang="zea" hreflang="zea" data-title="Wiskunde" data-language-autonym="Zeêuws" data-language-local-name="Zeelandic" class="interlanguage-link-target"><span>Zeêuws</span></a></li><li class="interlanguage-link interwiki-zgh mw-list-item"><a href="https://zgh.wikipedia.org/wiki/%E2%B5%9C%E2%B5%93%E2%B5%99%E2%B5%8F%E2%B4%B0%E2%B4%BD%E2%B5%9C" title="ⵜⵓⵙⵏⴰⴽⵜ – стандарт тамазайт (Морокко)" lang="zgh" hreflang="zgh" data-title="ⵜⵓⵙⵏⴰⴽⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" 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typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Euclid.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/220px-Euclid.jpg" decoding="async" width="220" height="184" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/330px-Euclid.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/21/Euclid.jpg/440px-Euclid.jpg 2x" data-file-width="806" data-file-height="675" /></a><figcaption>МЭӨ III зууны Грекийн математикч, геометрын эцэг хэмээн нэрлэгддэг <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид">Евклид</a>, <a href="/w/index.php?title=%D0%A0%D0%B0%D1%84%D0%B0%D0%B5%D0%BB&action=edit&redlink=1" class="new" title="Рафаел (ийм хуудас байхгүй)">Рафаелийн</a> <i><a href="/w/index.php?title=%D0%90%D1%84%D0%B8%D0%BD%D1%8B_%D1%81%D1%83%D1%80%D0%B3%D1%83%D1%83%D0%BB%D1%8C&action=edit&redlink=1" class="new" title="Афины сургууль (ийм хуудас байхгүй)">Афины сургууль</a></i> зургийн нэгэн хэсэг дээр дүрслэгдсэн байгаа нь.</figcaption></figure> <p><b>Математик</b> (<a href="/wiki/%D0%93%D1%80%D0%B5%D0%BA_%D1%85%D1%8D%D0%BB" title="Грек хэл">Грек</a>: μάθημα, <a href="/wiki/%D0%90%D0%BD%D0%B3%D0%BB%D0%B8_%D1%85%D1%8D%D0%BB" title="Англи хэл">Англи</a>: mathematics, <a href="/wiki/%D0%9E%D1%80%D0%BE%D1%81_%D1%85%D1%8D%D0%BB" title="Орос хэл">Орос</a>: математика) буюу <b>Тоон ухаан</b> нь <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE_%D1%85%D1%8D%D0%BC%D0%B6%D1%8D%D1%8D&action=edit&redlink=1" class="new" title="Тоо хэмжээ (ийм хуудас байхгүй)">тоо хэмжээ</a>, <a href="/w/index.php?title=%D0%91%D2%AF%D1%82%D1%8D%D1%86&action=edit&redlink=1" class="new" title="Бүтэц (ийм хуудас байхгүй)">бүтэц</a>, <a href="/wiki/%D0%9E%D0%B3%D1%82%D0%BE%D1%80%D0%B3%D1%83%D0%B9" title="Огторгуй">огторгуй</a>, <a href="/w/index.php?title=%D3%A8%D3%A9%D1%80%D1%87%D0%BB%D3%A9%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Өөрчлөлт (ийм хуудас байхгүй)">өөрчлөлт</a> зэрэг ойлголтууд дээр төвлөрсөн мэдлэгийн цогц, мөн тэдгээрийн тухай судалдаг шинжлэх ухаан юм. Бенжамин Пиерс математикийг "зайлшгүй дүгнэлтүүдийг гаргадаг шинжлэх ухаан" хэмээсэн.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Линн Стийн<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> ба Кейт Девлин<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> нар математик нь зүй тогтлын шинжлэх ухаан бөгөөд тоонууд, огторгуй, шинжлэх ухаан, компьютер, эсвэл хийсвэр зүйлүүдэд зүй тогтлуудыг эрдэг гэж үзсэн. </p><p>Математик нь <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D0%BB%D0%BE%D1%85&action=edit&redlink=1" class="new" title="Тоолох (ийм хуудас байхгүй)">тоолох</a>, <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BE%D1%85&action=edit&redlink=1" class="new" title="Тооцоолох (ийм хуудас байхгүй)">тооцоолох</a> ба <a href="/w/index.php?title=%D0%A5%D1%8D%D0%BC%D0%B6%D0%B8%D1%85&action=edit&redlink=1" class="new" title="Хэмжих (ийм хуудас байхгүй)">хэмжих</a> үйлдлүүд, мөн физик объектуудын <a href="/w/index.php?title=%D0%A5%D1%8D%D0%BB%D0%B1%D1%8D%D1%80_%D0%B4%D2%AF%D1%80%D1%81&action=edit&redlink=1" class="new" title="Хэлбэр дүрс (ийм хуудас байхгүй)">хэлбэр дүрс</a> ба <a href="/wiki/%D0%A5%D3%A9%D0%B4%D3%A9%D0%BB%D0%B3%D3%A9%D3%A9%D0%BD" class="mw-redirect" title="Хөдөлгөөн">хөдөлгөөний</a> системтэй судалгаан дээр <a href="/wiki/%D0%A5%D0%B8%D0%B9%D1%81%D0%B2%D1%8D%D1%80%D0%BB%D1%8D%D0%BB" title="Хийсвэрлэл">хийсвэрлэл</a>, <a href="/wiki/%D0%9B%D0%BE%D0%B3%D0%B8%D0%BA" title="Логик">логик</a> сэтгэлгээг хэрэглэсний үр дүнд үүссэн. Математикчид эдгээр ойлголтуудын талаар шинэ <a href="/wiki/%D0%A2%D0%B0%D0%B0%D0%BC%D0%B0%D0%B3%D0%BB%D0%B0%D0%BB" title="Таамаглал">таамаглал</a> дэвшүүлж, тэдгээрийн үнэн болохыг зохих <a href="/wiki/%D0%90%D0%BA%D1%81%D0%B8%D0%BE%D0%BC" title="Аксиом">аксиомууд</a> ба <a href="/w/index.php?title=%D0%A2%D0%BE%D0%B4%D0%BE%D1%80%D1%85%D0%BE%D0%B9%D0%BB%D0%BE%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Тодорхойлолт (ийм хуудас байхгүй)">тодорхойлолтуудаас</a> логик дүрмүүдийг чанд баримтлан батлах зорилготой судалгаа хийдэг.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Математикийн наад захын хэмжээний мэдлэг ба хэрэглээ нь хувь хүн болон нийгмийн зайлшгүй чухал хэсэг болсоор ирсэн. Энэ үндсэн санаануудын сайжруулсан хэлбэр <a href="/wiki/%D0%AD%D1%80%D1%82%D0%BD%D0%B8%D0%B9_%D0%95%D0%B3%D0%B8%D0%BF%D0%B5%D1%82" title="Эртний Египет">эртний Египет</a>, <a href="/wiki/%D0%92%D0%B0%D0%B2%D0%B8%D0%BB%D0%BE%D0%BD%D0%B8" title="Вавилони">Вавилони</a>, <a href="/w/index.php?title=%D0%AD%D1%80%D1%82%D0%BD%D0%B8%D0%B9_%D0%AD%D0%BD%D1%8D%D1%82%D1%85%D1%8D%D0%B3&action=edit&redlink=1" class="new" title="Эртний Энэтхэг (ийм хуудас байхгүй)">Энэтхэг</a>, <a href="/wiki/%D0%AD%D1%80%D1%82%D0%BD%D0%B8%D0%B9_%D0%A5%D1%8F%D1%82%D0%B0%D0%B4" class="mw-redirect" title="Эртний Хятад">Хятад</a> ба <a href="/wiki/%D0%AD%D1%80%D1%82%D0%BD%D0%B8%D0%B9_%D0%93%D1%80%D0%B5%D0%BA" title="Эртний Грек">Грекийн</a> ном судруудад хадгалагдан үлдсэн байдаг. Хамгийн анх Евклид <a href="/wiki/%D0%AD%D1%85%D0%BB%D1%8D%D0%BB" title="Эхлэл">"Эхлэл"</a> бүтээлдээ логикийн хатуу чанд хэрэглээ ямар байх ёстойг харуулсан. Үүнээс хойш математикт том дэвшил гарах нь их цөөн байж байгаад <a href="/w/index.php?title=XVI_%D0%B7%D1%83%D1%83%D0%BD&action=edit&redlink=1" class="new" title="XVI зуун (ийм хуудас байхгүй)">XVI зууны</a> <a href="/w/index.php?title=%D0%A1%D1%8D%D1%80%D0%B3%D1%8D%D0%BD_%D0%9C%D0%B0%D0%BD%D0%B4%D0%BB%D1%8B%D0%BD_%D2%AE%D0%B5&action=edit&redlink=1" class="new" title="Сэргэн Мандлын Үе (ийм хуудас байхгүй)">Сэргэн Мандлын Үед</a> математикийн шинэчлэл дараа дараагаараа гарч байсан <a href="/w/index.php?title=%D0%A8%D0%B8%D0%BD%D0%B6%D0%BB%D1%8D%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD%D1%8B_%D0%BD%D1%8D%D1%8D%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Шинжлэх ухааны нээлт (ийм хуудас байхгүй)">шинжлэх ухааны нээлтүүдтэй</a> харилцан үйлчилсний дүнд өнөөг хүртэл үргэлжилсэн их хурдацтай судалгааг эхлүүлсэн юм.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p><a href="/w/index.php?title=%D3%A8%D0%BD%D3%A9%D3%A9%D0%B4%D3%A9%D1%80_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Өнөөдөр математик (ийм хуудас байхгүй)">Өнөөдөр математик</a> нь <a href="/wiki/%D0%91%D0%B0%D0%B9%D0%B3%D0%B0%D0%BB%D0%B8%D0%B9%D0%BD_%D1%88%D0%B8%D0%BD%D0%B6%D0%BB%D1%8D%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Байгалийн шинжлэх ухаан">байгалийн шинжлэх ухаан</a>, <a href="/wiki/%D0%98%D0%BD%D0%B6%D0%B5%D0%BD%D0%B5%D1%80%D1%87%D0%BB%D1%8D%D0%BB" class="mw-redirect" title="Инженерчлэл">инженерчлэл</a>, <a href="/wiki/%D0%90%D0%BD%D0%B0%D0%B3%D0%B0%D0%B0%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Анагаах ухаан">анагаах ухаан</a>, <a href="/wiki/%D0%AD%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B7%D0%B0%D1%81%D0%B0%D0%B3" title="Эдийн засаг">эдийн засаг</a> гэх мэт олон салбаруудад дэлхий даяар хэрэглэгдэж байна. Математикийг эдгээр салбарт хэрэглэснийг ихэвчлэн <a href="/w/index.php?title=%D0%A5%D1%8D%D1%80%D1%8D%D0%B3%D0%BB%D1%8D%D1%8D%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Хэрэглээний математик (ийм хуудас байхгүй)">хэрэглээний математик</a> гэдэг ба энэ нь математикийн нээлтүүдийг хэрэглэдэг, уг нээлтүүдэд хүргэдэг, заримдаа цоо шинэ шинжлэх ухааныг ч төрүүлдэг математикийн нэг салбар юм. Математикчид мөн <a href="/w/index.php?title=%D0%A6%D1%8D%D0%B2%D1%8D%D1%80_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Цэвэр математик (ийм хуудас байхгүй)">цэвэр математикийн</a>, өөрөөр хэлбэл юунд хэрэглэхийг нь харгалзахгүйгээр зөвхөн математикийг өөрийг нь судлах судалгаа хийдэг. Сонирхолтой нь цэвэр математикийн ихэнх судалгаанууд эрт орой хэзээ нэгэн цагт амьдрал практикт хэрэглэгддэг байна.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <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%B8%D0%B9%D0%BD_%D0%B3%D0%BE%D0%BE_%D1%81%D0%B0%D0%B9%D1%85%D0%B0%D0%BD&action=edit&redlink=1" class="new" title="Математикийн гоо сайхан (ийм хуудас байхгүй)">Математикийн гоо сайхан</a> чанар нь математикчдын мэргэжилдээ дурлах гол шалтгаан болдог. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Математик_хэмээх_нэрний_учир_нь"><span id=".D0.9C.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D0.BA_.D1.85.D1.8D.D0.BC.D1.8D.D1.8D.D1.85_.D0.BD.D1.8D.D1.80.D0.BD.D0.B8.D0.B9_.D1.83.D1.87.D0.B8.D1.80_.D0.BD.D1.8C"></span>Математик хэмээх нэрний учир нь</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&veaction=edit&section=1" title="Хэсгийг засварлах: Математик хэмээх нэрний учир нь" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=1" title="Edit section's source code: Математик хэмээх нэрний учир нь"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Манай орон төдийгүй дэлхийн ихэнх оронд хэрэглэгддэг «математик» гэдэг үг нь <a href="/wiki/%D0%AD%D1%80%D1%82%D0%BD%D0%B8%D0%B9_%D0%B3%D1%80%D0%B5%D0%BA_%D1%85%D1%8D%D0%BB" class="mw-redirect" title="Эртний грек хэл">эртний грек хэлний</a> μάθημα (<i>máthema</i>, монголоор: сурах, судлах, шинжлэх) ба холбогдох тэмдэг нэр болох μαθηματικός (<i>mathēmatikós</i>, монголоор: сурах, судлахтай холбоотой) гэдгээс гаралтай. </p> <div class="mw-heading mw-heading2"><h2 id="Түүх"><span id=".D0.A2.D2.AF.D2.AF.D1.85"></span>Түүх</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&veaction=edit&section=2" title="Хэсгийг засварлах: Түүх" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=2" title="Edit section's source code: Түүх"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Quipu.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/cc/Quipu.png/220px-Quipu.png" decoding="async" width="220" height="330" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/c/cc/Quipu.png 1.5x" data-file-width="299" data-file-height="449" /></a><figcaption>Дундад эртний үед Өмнөд Америкт оршин тогтнож байсан <a href="/w/index.php?title=%D0%98%D0%BD%D0%BA%D0%B0%D0%B3%D0%B8%D0%B9%D0%BD_%D0%AD%D0%B7%D1%8D%D0%BD%D1%82_%D0%93%D2%AF%D1%80%D1%8D%D0%BD&action=edit&redlink=1" class="new" title="Инкагийн Эзэнт Гүрэн (ийм хуудас байхгүй)">Инкагийн Эзэнт Гүрэнд</a> тоолохдоо олсон зангилаанаас бүтсэн "куипу" гэгдэх энэхүү багажийг хэрэглэдэг байв</figcaption></figure> <p>Бүх математикийн түүхийг төвшин нь улам улам өндөрсөх <a href="/wiki/%D0%A5%D0%B8%D0%B9%D1%81%D0%B2%D1%8D%D1%80%D0%BB%D1%8D%D0%BB" title="Хийсвэрлэл">хийсвэрлэлүүдийн</a> дараалал, эсвэл судлах зүйлүүдийнх нь хүрээ яаж өргөссөн тухай түүх гэж үзэж болно. Хамгийн анхны хийсвэрлэл нь <a href="/wiki/%D0%A2%D0%BE%D0%BE" title="Тоо">тоо</a> байсан байж мэднэ. Гурван үхэр ба гурван чулууны хооронд ямар нэг ерөнхий зүйл байгааг ойлгосон явдал хүний сэтгэхүйд гарсан том үсрэлтүүдийн нэг байсан юм. Бодит <i>физик</i> объектуудыг <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D0%BB%D0%BE%D1%85&action=edit&redlink=1" class="new" title="Тоолох (ийм хуудас байхгүй)">тоолж</a> сураад зогсохгүй эртний хүмүүс <i>хийсвэр</i> хэмжигдэхүүнүүдийг тоолж эхэлсэн. Жишээлбэл <a href="/wiki/%D0%A6%D0%B0%D0%B3_%D1%85%D1%83%D0%B3%D0%B0%D1%86%D0%B0%D0%B0" title="Цаг хугацаа">цаг хугацааг</a> тоолохын тулд <a href="/wiki/%D3%A8%D0%B4%D3%A9%D1%80" title="Өдөр">өдөр</a>, <a href="/wiki/%D0%A1%D0%B0%D1%80" title="Сар">сар</a>, <a href="/wiki/%D0%96%D0%B8%D0%BB" title="Жил">жил</a> хэмээх ойлголтуудыг хэрэглэж ирсэн. Үүний дараа <a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Арифметик (ийм хуудас байхгүй)">арифметик</a> (<a href="/w/index.php?title=%D0%9D%D1%8D%D0%BC%D1%8D%D1%85&action=edit&redlink=1" class="new" title="Нэмэх (ийм хуудас байхгүй)">нэмэх</a>, <a href="/w/index.php?title=%D0%A5%D0%B0%D1%81%D0%B0%D1%85&action=edit&redlink=1" class="new" title="Хасах (ийм хуудас байхгүй)">хасах</a>, <a href="/w/index.php?title=%D2%AE%D1%80%D0%B6%D0%B8%D1%85&action=edit&redlink=1" class="new" title="Үржих (ийм хуудас байхгүй)">үржих</a>, <a href="/w/index.php?title=%D0%A5%D1%83%D0%B2%D0%B0%D0%B0%D1%85&action=edit&redlink=1" class="new" title="Хуваах (ийм хуудас байхгүй)">хуваах</a>) хөгжсөн ба эртний балгасын ул мөрүүд тэр үеийн хүмүүс <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Геометр">геометрийн</a> мэдлэгтэй байсныг гэрчилдэг. </p><p>Цаашилбал тоонуудыг бүртгэж авах ямар нэг арга, жишээлбэл бичих, жижиг чулуунууд ашиглах, эсвэл <a href="/w/index.php?title=%D0%98%D0%BD%D0%BA%D0%B0%D0%B3%D0%B8%D0%B9%D0%BD_%D0%AD%D0%B7%D1%8D%D0%BD%D1%82_%D0%93%D2%AF%D1%80%D1%8D%D0%BD&action=edit&redlink=1" class="new" title="Инкагийн Эзэнт Гүрэн (ийм хуудас байхгүй)">Инкагийн Эзэнт Гүрэнд</a> хэрэглэдэг байсан шиг <a href="/w/index.php?title=%D0%9A%D1%83%D0%B9%D0%BF%D1%83&action=edit&redlink=1" class="new" title="Куйпу (ийм хуудас байхгүй)">куйпу</a> гэгдэх олсон зангилаа хэрэг болж эхэлсэн байна. Энэ явцдаа хүн төрөлхтөн төрөл бүрийн <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Тооллын систем (ийм хуудас байхгүй)">тооллын системүүдийг</a> зохиожээ. </p><p>Түүхэнд тэмдэглэгдэж үлдсэнээр математикт хамрагдах гол салбарууд <a href="/wiki/%D0%A2%D0%B0%D1%82%D0%B2%D0%B0%D1%80" title="Татвар">татвар</a> ба <a href="/wiki/%D0%A5%D1%83%D0%B4%D0%B0%D0%BB%D0%B4%D0%B0%D0%B0" title="Худалдаа">худалдаатай</a> холбоотой тооцоо хийх, тоонуудын хоорондох харьцаа хамаарлуудыг ойлгох, <a href="/w/index.php?title=%D0%93%D0%B0%D0%B7%D0%B0%D1%80_%D1%85%D1%8D%D0%BC%D0%B6%D0%B8%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Газар хэмжилт (ийм хуудас байхгүй)">газрыг хэмжих</a>, <a href="/wiki/%D0%9E%D0%B4%D0%BE%D0%BD_%D0%BE%D1%80%D0%BE%D0%BD" title="Одон орон">одон орны үзэгдлүүдийг</a> урьдчилан хэлэх шаардлагуудаас үүдэн бий болсон аж. Эдгээр шаардлагуудыг барагцаагаар <i>тоо хэмжээ</i>, <i>бүтэц</i>, <i>огторгуй</i>, ба <i>өөрчлөлт</i>ийн судалгаануудад харгалзуулж болж байгааг анзаараарай. </p><p>Энэ үеэс хойш математик асар ихээр өргөжсөн бөгөөд математик ба шинжлэх ухаанууд хоорондоо нягт холбоотойгоор хөгжсөн. Математикийн нээлтүүд түүхийн туршид хийгдэж ирсэн ба одоо ч хийгдсээр байгаа. <a href="/w/index.php?title=%D0%90%D0%BC%D0%B5%D1%80%D0%B8%D0%BA%D0%B8%D0%B9%D0%BD_%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B8%D0%B9%D0%BD_%D0%9D%D0%B8%D0%B9%D0%B3%D1%8D%D0%BC%D0%BB%D1%8D%D0%B3%D0%B8%D0%B9%D0%BD_%D0%9C%D1%8D%D0%B4%D1%8D%D1%8D&action=edit&redlink=1" class="new" title="Америкийн Математикийн Нийгэмлэгийн Мэдээ (ийм хуудас байхгүй)">Америкийн Математикийн Нийгэмлэгийн Мэдээ</a> сэтгүүлийн 2006 оны 1-р сарын дугаарт Михайл Б. Севрюкийн бичсэнээр "<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%B8%D0%B9%D0%BD_%D0%A1%D1%83%D0%B4%D0%B0%D0%BB%D0%B3%D0%B0%D0%B0&action=edit&redlink=1" class="new" title="Математикийн Судалгаа (ийм хуудас байхгүй)">Математикийн Судалгаа</a> санд 1940 （энэ сангийн ажиллаж эхэлсэн жил）оноос хойш хамрагдсан ном хэвлэлүүдийн тоо нь одоо 1.9 саяыг даваад байгаа ба жил бүр 75 мянган ном хэвлэл нэмэгдэж байна. Энэ их далай дахь ажлууд бараг бүгдээрээ математикийн <a href="/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B5%D0%BC" title="Теорем">теоремууд</a> ба тэдгээрийн <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%B1%D0%B0%D1%82%D0%B0%D0%BB%D0%B3%D0%B0%D0%B0&action=edit&redlink=1" class="new" title="Математик баталгаа (ийм хуудас байхгүй)">баталгаануудыг</a> агуулдаг".<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Гадны_нөлөөлөл,_цэвэр_ба_хэрэглээний_математик,_гоо_сайхан"><span id=".D0.93.D0.B0.D0.B4.D0.BD.D1.8B_.D0.BD.D3.A9.D0.BB.D3.A9.D3.A9.D0.BB.D3.A9.D0.BB.2C_.D1.86.D1.8D.D0.B2.D1.8D.D1.80_.D0.B1.D0.B0_.D1.85.D1.8D.D1.80.D1.8D.D0.B3.D0.BB.D1.8D.D1.8D.D0.BD.D0.B8.D0.B9_.D0.BC.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D0.BA.2C_.D0.B3.D0.BE.D0.BE_.D1.81.D0.B0.D0.B9.D1.85.D0.B0.D0.BD"></span>Гадны нөлөөлөл, цэвэр ба хэрэглээний математик, гоо сайхан</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&veaction=edit&section=3" title="Хэсгийг засварлах: Гадны нөлөөлөл, цэвэр ба хэрэглээний математик, гоо сайхан" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=3" title="Edit section's source code: Гадны нөлөөлөл, цэвэр ба хэрэглээний математик, гоо сайхан"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:GodfreyKneller-IsaacNewton-1689.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/220px-GodfreyKneller-IsaacNewton-1689.jpg" decoding="async" width="220" height="309" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/330px-GodfreyKneller-IsaacNewton-1689.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/39/GodfreyKneller-IsaacNewton-1689.jpg/440px-GodfreyKneller-IsaacNewton-1689.jpg 2x" data-file-width="1364" data-file-height="1916" /></a><figcaption><a href="/wiki/%D0%98%D1%81%D0%B0%D0%B0%D0%BA_%D0%9D%D1%8C%D1%8E%D1%82%D0%BE%D0%BD" title="Исаак Ньютон">Исаак Ньютон</a> (1643-1727), бүх үеийн хамгийн агуу физикч, <a href="/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол">интеграл ба дифференциал тооллыг</a> үндэслэгчдийн нэг.</figcaption></figure> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Hopf-torus.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/mn/7/70/Hopf-torus.jpg" decoding="async" width="213" height="170" class="mw-file-element" data-file-width="213" data-file-height="170" /></a><figcaption><a href="/w/index.php?title=%D0%A5%D0%BE%D0%BF%D1%84%D1%8B%D0%BD_%D1%82%D0%BE%D1%80&action=edit&redlink=1" class="new" title="Хопфын тор (ийм хуудас байхгүй)">Хопфын тор</a>.</figcaption></figure> <p>Хаана л тоо хэмжээ, бүтэц, огторгуй, эсвэл өөрчлөлт оролцсон хэцүү бодлогууд байна тэнд математик илэрдэг. Ийм бодлогууд эхлээд <a href="/wiki/%D0%A5%D1%83%D0%B4%D0%B0%D0%BB%D0%B4%D0%B0%D0%B0" title="Худалдаа">худалдаа</a>, <a href="/w/index.php?title=%D0%93%D0%B0%D0%B7%D0%B0%D1%80_%D1%85%D1%8D%D0%BC%D0%B6%D0%B8%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Газар хэмжилт (ийм хуудас байхгүй)">газар хэмжилт</a>, сүүлд <a href="/wiki/%D0%9E%D0%B4%D0%BE%D0%BD_%D0%BE%D1%80%D0%BE%D0%BD" title="Одон орон">одон оронд</a> олддог байсан бөгөөд одоо үед бүх шинжлэх ухаан, түүнчлэн математик өөрөө төрөл бүрийн математикийн бодлогуудын эх үүсвэр болдог. Тухайлбал <a href="/wiki/%D0%98%D1%81%D0%B0%D0%B0%D0%BA_%D0%9D%D1%8C%D1%8E%D1%82%D0%BE%D0%BD" title="Исаак Ньютон">Исаак Ньютон</a> <a href="/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол">интеграл ба дифференциал тооллыг</a> үндэслэгчдийн нэг байсан, <a href="/w/index.php?title=%D0%A4%D0%B5%D0%B9%D0%BD%D0%BC%D0%B0%D0%BD%D1%8B_%D0%B7%D0%B0%D0%BC%D1%8B%D0%BD_%D0%B8%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Фейнманы замын интеграл (ийм хуудас байхгүй)">Фейнманы замын интегралыг</a> физик сэтгэлгээний үндсэн дээр <a href="/w/index.php?title=%D0%A4%D0%B5%D0%B9%D0%BD%D0%BC%D0%B0%D0%BD&action=edit&redlink=1" class="new" title="Фейнман (ийм хуудас байхгүй)">Фейнман</a> оруулсан, мөн өнөөгийн <a href="/w/index.php?title=%D0%A3%D1%82%D0%B0%D1%81%D0%BD%D1%8B_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Утасны онол (ийм хуудас байхгүй)">утасны онол</a> шинэ математикийг бий болгоход нөлөөлж байна. Математикийн зарим онолууд зөвхөн түүнийг бий болгоход нөлөөлсөн талбарт л ашиглагддаг бол ихэнх онолууд бусад олон талбарт мөн ашиглагддаг. "Хамгийн цэвэр" математикт ч хэзээ нэгэн цагт ашиглагдах газар олддог явдлыг <a href="/w/index.php?title=%D0%95%D0%B2%D0%B3%D0%B5%D0%BD_%D0%92%D0%B8%D0%B3%D0%BD%D0%B5%D1%80&action=edit&redlink=1" class="new" title="Евген Вигнер (ийм хуудас байхгүй)">Евген Вигнер</a> <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%B8%D0%B9%D0%BD_%D0%B5%D1%80_%D0%B1%D1%83%D1%81%D1%8B%D0%BD_%D1%85%D1%8D%D0%BC%D0%BD%D1%8D%D0%BB%D1%82%D1%82%D1%8D%D0%B9_%D0%B1%D0%B0%D0%B9%D0%B4%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Математикийн ер бусын хэмнэлттэй байдал (ийм хуудас байхгүй)">математикийн ер бусын хэмнэлттэй байдал</a> гэж нэрлэсэн. </p><p>Математикийг дотор нь барагцаагаар <a href="/w/index.php?title=%D0%A6%D1%8D%D0%B2%D1%8D%D1%80_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Цэвэр математик (ийм хуудас байхгүй)">цэвэр математик</a> ба <a href="/w/index.php?title=%D0%A5%D1%8D%D1%80%D1%8D%D0%B3%D0%BB%D1%8D%D1%8D%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Хэрэглээний математик (ийм хуудас байхгүй)">хэрэглээний математик</a> гэж хоёр том хэсэгт хуваадаг. Хэрэглээний математикийн олон салбар математикийн гаднах харгалзах шинжлэх ухаануудтай нийлж <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA" title="Статистик">статистик</a>, <a href="/w/index.php?title=%D2%AE%D0%B9%D0%BB%D0%B4%D0%BB%D0%B8%D0%B9%D0%BD_%D1%81%D1%83%D0%B4%D0%B0%D0%BB%D0%B3%D0%B0%D0%B0&action=edit&redlink=1" class="new" title="Үйлдлийн судалгаа (ийм хуудас байхгүй)">үйлдлийн судалгаа</a>, <a href="/w/index.php?title=%D0%9A%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80_%D1%81%D1%83%D0%B4%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Компьютер судлал (ийм хуудас байхгүй)">компьютер судлал</a> гэх мэт биеэ даасан шинэ шинжлэх ухаанууд болж хөгжсөн. </p><p>Математикт <a href="/w/index.php?title=%D0%AD%D0%BD%D0%B3%D0%B8%D0%B9%D0%BD_%D0%B1%D0%B0%D0%B9%D0%B4%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Энгийн байдал (ийм хуудас байхгүй)">энгийн байдал</a> ба <a href="/w/index.php?title=%D0%95%D1%80%D3%A9%D0%BD%D1%85%D0%B8%D0%B9_%D0%B1%D0%B0%D0%B9%D0%B4%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Ерөнхий байдал (ийм хуудас байхгүй)">ерөнхий байдал</a> чухал. Мөн <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4" title="Евклид">Евклидийн</a> <a href="/wiki/%D0%AD%D0%BD%D0%B3%D0%B8%D0%B9%D0%BD_%D1%82%D0%BE%D0%BE" class="mw-redirect" title="Энгийн тоо">энгийн тооны</a> тоог хязгааргүй гэж баталсан баталгаа шиг ур ухаан шаардсан баталгаа, <a href="/w/index.php?title=%D0%A4%D1%83%D1%80%D1%8C%D0%B5%D0%B3%D0%B8%D0%B9%D0%BD_%D1%85%D1%83%D1%80%D0%B4%D0%B0%D0%BD_%D1%85%D1%83%D0%B2%D0%B8%D1%80%D0%B3%D0%B0%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Фурьегийн хурдан хувиргалт (ийм хуудас байхгүй)">Фурьегийн хурдан хувиргалт</a> шиг тооцооллыг хурдасгах аргуудад гоо сайхан чанар бий. Ихэнх математикчид өөрийн ажлаас болон математикаас гоо сайхны таашаал авдаг. Зарим <a href="/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D1%87%D0%B8%D0%B4" class="mw-redirect" title="Математикчид">математикчид</a> математикийг <a href="/wiki/%D0%A3%D1%80%D0%BB%D0%B0%D0%B3" title="Урлаг">урлагийн</a> төрөл, ядаж л бүтээлч үйл ажиллагаа гэж үздэг бөгөөд математикийг <a href="/wiki/%D0%A5%D3%A9%D0%B3%D0%B6%D0%B8%D0%BC" title="Хөгжим">хөгжим</a> ба <a href="/w/index.php?title=%D0%AF%D1%80%D1%83%D1%83_%D0%BD%D0%B0%D0%B9%D1%80%D0%B0%D0%B3&action=edit&redlink=1" class="new" title="Яруу найраг (ийм хуудас байхгүй)">яруу найрагтай</a> жишдэг. </p><p><a href="/wiki/%D0%91%D0%B5%D1%80%D1%82%D1%80%D0%B0%D0%BD%D0%B4_%D0%A0%D0%B0%D1%81%D1%81%D0%B5%D0%BB" class="mw-redirect" title="Бертранд Рассел">Бертранд Рассел</a> математикийн гоо сайхныг ингэж илэрхийлжээ: </p> <blockquote> <p>Математикийг зөвөөр харвал энэ нь зөвхөн үнэнийг агуулаад зогсохгүй дээд гоо сайхан - баримал мэт хүйтэн бөгөөд хатуу чанд, бидний сул байдлын аль ч талтай холбоогүй, зураг эсвэл хөгжим шиг элдэв гоёл чимэглэл байхгүй боловч гайхамшигтай цэвэр бөгөөд зөвхөн хамгийн сайн урлагтай зүйрлэж болохоор гуйвшгүй төгс төгөлдөр байдалтай холбоотой тийм гоо сайхныг агуулдаг. Хамгийн дээд давамгайллын жишиг болсон жинхэнэ баяр бахдал, сэтгэлийн хөөрөл, мах цуснаас бүтсэн хүнээс илүү болохоо мэдрэх мэдрэмжийг математикаас яруу найрагтай адилаар олж болно. </p> </blockquote> <p><a href="/w/index.php?title=%D0%9F%D0%BE%D0%BB%D1%8C_%D0%AD%D1%80%D0%B4%D0%BE%D1%81&action=edit&redlink=1" class="new" title="Поль Эрдос (ийм хуудас байхгүй)">Поль Эрдос</a> ингэж хэлсэн байна: "<i>Тоонууд яагаад сайхан гэж? Энэ нь яагаад Бетховений 9-р симфони сайхан бэ гэж асуусантай адил. Хэрэв чи яагаад гэдгийг нь харахгүй байгаа бол хэн ч чамд ойлгуулж чадахгүй. Би тоонууд сайхан гэдгийг мэдэж байна. Хэрэв тоо сайхан биш бол юу ч тийм биш."</i> </p> <div class="mw-heading mw-heading2"><h2 id="Математикийн_салбарууд"><span id=".D0.9C.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D0.BA.D0.B8.D0.B9.D0.BD_.D1.81.D0.B0.D0.BB.D0.B1.D0.B0.D1.80.D1.83.D1.83.D0.B4"></span>Математикийн салбарууд</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&veaction=edit&section=4" title="Хэсгийг засварлах: Математикийн салбарууд" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=4" title="Edit section's source code: Математикийн салбарууд"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Abacus_6.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/af/Abacus_6.png/220px-Abacus_6.png" decoding="async" width="220" height="129" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/af/Abacus_6.png 1.5x" data-file-width="247" data-file-height="145" /></a><figcaption>Хятад <a href="/wiki/%D0%A1%D0%B0%D0%BC%D0%BF%D0%B8%D0%BD" title="Сампин">сампин</a>. Эхний үеийн математик нь бүхлээрээ практик тооцоо хийхтэй холбоотой байсан.</figcaption></figure> <p>Дээр дурдсанаар математикийн гол салбарууд татвар ба худалдаатай холбоотой тооцоо хийх, тоонуудын хоорондох харьцаа хамаарлуудыг ойлгох, газрыг хэмжих, одон орны үзэгдлүүдийг урьдчилан хэлэх шаардлагуудаас үүдэн бий болсон. Эдгээр шаардлагуудыг барагцаагаар <i>тоо хэмжээ</i>, <i>бүтэц</i>, <i>огторгуй</i>, ба <i>өөрчлөлт</i>ийн судалгаануудад (ө.х. <a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Арифметик (ийм хуудас байхгүй)">арифметик</a>, <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80&action=edit&redlink=1" class="new" title="Алгебр (ийм хуудас байхгүй)">алгебр</a>, <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Геометр">геометр</a>, ба <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%BD%D0%B0%D0%BB%D0%B8%D0%B7&action=edit&redlink=1" class="new" title="Математик анализ (ийм хуудас байхгүй)">анализ</a>) харгалзуулж болно. Эдгээр гол хэсгүүдээс гадна математикийн цөмөөс бусад салбарууд руу холбогдсон холбоог судлах зорилготой дэд хэсгүүд бий: <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%BB%D0%BE%D0%B3%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Математик логик (ийм хуудас байхгүй)">логик</a>, <a href="/w/index.php?title=%D0%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Олонлогийн онол (ийм хуудас байхгүй)">олонлогийн онолтой</a> холбоотой <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%B8%D0%B9%D0%BD_%D1%82%D1%83%D0%BB%D0%B3%D1%83%D1%83%D1%80_%D1%81%D0%B0%D0%BB%D0%B1%D0%B0%D1%80%D1%83%D1%83%D0%B4&action=edit&redlink=1" class="new" title="Математикийн тулгуур салбарууд (ийм хуудас байхгүй)">тулгуур салбарууд</a>, төрөл бүрийн шинжлэх ухааны туршлагын математиктай холбоотой <a href="/w/index.php?title=%D0%A5%D1%8D%D1%80%D1%8D%D0%B3%D0%BB%D1%8D%D1%8D%D0%BD%D0%B8%D0%B9_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Хэрэглээний математик (ийм хуудас байхгүй)">хэрэглээний математик</a> гэх мэт. </p> <div class="mw-heading mw-heading3"><h3 id="Тоо_хэмжээ"><span id=".D0.A2.D0.BE.D0.BE_.D1.85.D1.8D.D0.BC.D0.B6.D1.8D.D1.8D"></span>Тоо хэмжээ</h3><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&veaction=edit&section=5" title="Хэсгийг засварлах: Тоо хэмжээ" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=5" title="Edit section's source code: Тоо хэмжээ"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Тоо хэмжээний судлал нь бидний мэдэх <a href="/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE" title="Натурал тоо">натурал тоонууд</a>, <a href="/wiki/%D0%91%D2%AF%D1%85%D1%8D%D0%BB_%D1%82%D0%BE%D0%BE" title="Бүхэл тоо">бүхэл тоонууд</a> ба тэдгээр дээр хийгдэх арифметик үйлдлүүдээр эхлэх бөгөөд энэ нь <a href="/w/index.php?title=%D0%90%D1%80%D0%B8%D1%84%D0%BC%D0%B5%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Арифметик (ийм хуудас байхгүй)">арифметикийг</a> төрүүлнэ. Бүхэл тоонуудын илүү гүнзгий шинж чанаруудыг <a href="/wiki/%D0%A2%D0%BE%D0%BE%D0%BD%D1%8B_%D0%BE%D0%BD%D0%BE%D0%BB" title="Тооны онол">тооны онол</a> судлах ба <a href="/w/index.php?title=%D0%A4%D0%B5%D1%80%D0%BC%D0%B0%D0%B3%D0%B8%D0%B9%D0%BD_%D1%81%D2%AF%D2%AF%D0%BB%D1%87%D0%B8%D0%B9%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Фермагийн сүүлчийн теорем (ийм хуудас байхгүй)">Фермагийн сүүлчийн теорем</a> гэх мэт үр дүнгүүдийг гаргадаг. Тооны онолын алдартай бодогдоогүй бодлогуудад <a href="/w/index.php?title=%D0%A5%D0%BE%D1%81_%D1%8D%D0%BD%D0%B3%D0%B8%D0%B9%D0%BD_%D1%82%D0%BE%D0%BE%D0%BD%D1%8B_%D1%82%D0%B0%D0%B0%D0%BC%D0%B0%D0%B3%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Хос энгийн тооны таамаглал (ийм хуудас байхгүй)">хос энгийн тооны</a> болон <a href="/w/index.php?title=%D0%93%D0%BE%D0%BB%D1%8C%D0%B4%D0%B1%D0%B0%D1%85%D1%8B%D0%BD_%D1%82%D0%B0%D0%B0%D0%BC%D0%B0%D0%B3%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Гольдбахын таамаглал (ийм хуудас байхгүй)">Гольдбахын</a> таамаглалууд орно. </p><p>Тоон системийн цаашдын хөгжил бүхэл тоонуудыг <a href="/w/index.php?title=%D0%A0%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Рациональ тоо (ийм хуудас байхгүй)">рациональ тоонууд</a> буюу "бутархай" тоонуудын <a href="/wiki/%D0%94%D1%8D%D0%B4_%D0%BE%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3" title="Дэд олонлог">дэд олонлог</a> болгоход хүргэсэн. Рациональ тоонууд нь мөн өөрийн ээлжинд тасралтгүй тоо хэмжээг илэрхийлдэг <a href="/w/index.php?title=%D0%91%D0%BE%D0%B4%D0%B8%D1%82_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Бодит тоо (ийм хуудас байхгүй)">бодит тоонуудад</a> агуулагдана. Бодит тоонууд нь комплекс тоонууд руу өргөтгөгддөг. Энэ шаталсан дараалал цаашаа <a href="/wiki/%D0%9A%D0%B2%D0%B0%D1%82%D0%B5%D1%80%D0%BD%D0%B8%D0%BE%D0%BD" title="Кватернион">кватернион</a> ба <a href="/w/index.php?title=%D0%9E%D0%BA%D1%82%D0%BE%D0%BD%D0%B8%D0%BE%D0%BD&action=edit&redlink=1" class="new" title="Октонион (ийм хуудас байхгүй)">октонион</a> хүртэл явна. Нөгөө талаас натурал тоонуудын судлал төгсгөлгүй хүртэл тоолохыг формальжуулдаг <a href="/w/index.php?title=%D0%A2%D1%80%D0%B0%D0%BD%D1%81%D1%84%D0%B8%D0%BD%D0%B8%D1%82_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Трансфинит тоо (ийм хуудас байхгүй)">трансфинит тоонуудад</a> хүргэдэг. Хэмжээний судлал <a href="/w/index.php?title=%D0%9A%D0%B0%D1%80%D0%B4%D0%B8%D0%BD%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Кардинал тоо (ийм хуудас байхгүй)">кардинал тоонуудыг</a> оруулдаг бөгөөд энэ нь төгсгөлгүй том хэмжээтэй олонлогуудыг хооронд нь харьцуулах боломж олгодог <a href="/w/index.php?title=%D0%90%D0%BB%D1%8C%D0%B5%D1%84_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Альеф тоо (ийм хуудас байхгүй)">альеф тоонуудад</a> хүргэнэ. </p> <dl><dd><table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="20"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1,2,3\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1,2,3\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/41a7f6e2ad3fcba08cbe7cdd4803bc04aefd34ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:5.942ex; height:2.509ex;" alt="{\displaystyle 1,2,3\,\!}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -2,-1,0,1,2\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mo>−</mo> <mn>1</mn> <mo>,</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -2,-1,0,1,2\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b7f4e28c92fbe1cc1f26530dc165eb19223a67f7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:13.951ex; height:2.509ex;" alt="{\displaystyle -2,-1,0,1,2\,\!}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -2,{\frac {2}{3}},1.21\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mn>2</mn> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mo>,</mo> <mn>1.21</mn> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -2,{\frac {2}{3}},1.21\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/46f69bde2e37e56443b3c6839be8c010fdaad7a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; margin-right: -0.387ex; width:11.558ex; height:5.176ex;" alt="{\displaystyle -2,{\frac {2}{3}},1.21\,\!}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {2}},{\sqrt {3}},{\sqrt {5}},\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>3</mn> </msqrt> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>5</mn> </msqrt> </mrow> <mo>,</mo> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}},{\sqrt {3}},{\sqrt {5}},\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/64fb5032aa019fc182eadaa132d6344d0134d877" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.229ex; width:11.852ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}},{\sqrt {3}},{\sqrt {5}},\!}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -e,{\sqrt {2}},3,\pi \,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mi>e</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mi>π</mi> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -e,{\sqrt {2}},3,\pi \,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4344d8d6a980cb805d7b6cc29cd8770d8d8d61c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:11.973ex; height:3.009ex;" alt="{\displaystyle -e,{\sqrt {2}},3,\pi \,\!}"></span></td> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 2,i,-2+3i,2e^{i{\frac {4\pi }{3}}}\,\!}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>,</mo> <mi>i</mi> <mo>,</mo> <mo>−</mo> <mn>2</mn> <mo>+</mo> <mn>3</mn> <mi>i</mi> <mo>,</mo> <mn>2</mn> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>4</mn> <mi>π</mi> </mrow> <mn>3</mn> </mfrac> </mrow> </mrow> </msup> <mspace width="thinmathspace" /> <mspace width="negativethinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2,i,-2+3i,2e^{i{\frac {4\pi }{3}}}\,\!}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/694cccd4f4f8bf7e7159431b59477c67387b77ee" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-right: -0.387ex; width:18.543ex; height:3.843ex;" alt="{\displaystyle 2,i,-2+3i,2e^{i{\frac {4\pi }{3}}}\,\!}"></span> </td></tr> <tr> <td><a href="/wiki/%D0%9D%D0%B0%D1%82%D1%83%D1%80%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE" title="Натурал тоо">Натурал тоонууд</a></td> <td><a href="/wiki/%D0%91%D2%AF%D1%85%D1%8D%D0%BB_%D1%82%D0%BE%D0%BE" title="Бүхэл тоо">Бүхэл тоонууд</a></td> <td><a href="/w/index.php?title=%D0%A0%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Рациональ тоо (ийм хуудас байхгүй)">Рациональ тоонууд</a></td> <td><a href="/w/index.php?title=%D0%98%D1%80%D1%80%D0%B0%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB%D1%8C_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Иррациональ тоо (ийм хуудас байхгүй)">Иррациональ тоонууд</a></td> <td><a href="/w/index.php?title=%D0%91%D0%BE%D0%B4%D0%B8%D1%82_%D1%82%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Бодит тоо (ийм хуудас байхгүй)">Бодит тоонууд</a></td> <td><a href="/wiki/%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81_%D1%82%D0%BE%D0%BE" title="Комплекс тоо">Комплекс тоонууд</a> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Бүтэц"><span id=".D0.91.D2.AF.D1.82.D1.8D.D1.86"></span>Бүтэц</h3><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&veaction=edit&section=6" title="Хэсгийг засварлах: Бүтэц" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=6" title="Edit section's source code: Бүтэц"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D0%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3" title="Олонлог">Олонлог</a>, <a href="/wiki/%D0%A4%D1%83%D0%BD%D0%BA%D1%86_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)" title="Функц (математик)">функц</a> гэх мэт олон математик объектууд өөрийн дотоод бүтэцтэй байдаг. Ийм объектуудын бүтцийн шинж чанаруудыг <a href="/w/index.php?title=%D0%91%D2%AF%D0%BB%D1%8D%D0%B3_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)&action=edit&redlink=1" class="new" title="Бүлэг (математик) (ийм хуудас байхгүй)">бүлэг</a>, <a href="/w/index.php?title=%D0%A6%D0%B0%D0%B3%D0%B8%D1%80%D0%B0%D0%B3_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)&action=edit&redlink=1" class="new" title="Цагираг (математик) (ийм хуудас байхгүй)">цагираг</a>, ба <a href="/w/index.php?title=%D0%A2%D0%B0%D0%BB%D0%B1%D0%B0%D1%80_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA)&action=edit&redlink=1" class="new" title="Талбар (математик) (ийм хуудас байхгүй)">талбар</a> болон бусад абстракт системүүдийн тусламжтай судалдаг. Эдгээр нь өөрсдөө мөн математик объектууд болох бөгөөд эдгээрийн судалгаа <a href="/w/index.php?title=%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80&action=edit&redlink=1" class="new" title="Абстракт алгебр (ийм хуудас байхгүй)">абстракт алгебрыг</a> бүрдүүлнэ. Нэг чухал ойлголт бол <a href="/wiki/%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80" class="mw-disambig" title="Вектор">векторууд</a> ба эдгээрийг <a href="/w/index.php?title=%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D0%BE%D0%B3%D1%82%D0%BE%D1%80%D0%B3%D1%83%D0%B9&action=edit&redlink=1" class="new" title="Вектор огторгуй (ийм хуудас байхгүй)">вектор огторгуй</a> болгож өргөтгөн <a href="/w/index.php?title=%D0%A8%D1%83%D0%B3%D0%B0%D0%BC%D0%B0%D0%BD_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80&action=edit&redlink=1" class="new" title="Шугаман алгебр (ийм хуудас байхгүй)">шугаман алгебрт</a> судална. Векторуудын судалгаа нь тоо хэмжээ, бүтэц, огторгуй гэсэн математикийн гурван үндсэн судлагдахууныг нэг дор авч үздэг. Цаашилбал <a href="/w/index.php?title=%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Вектор тоолол (ийм хуудас байхгүй)">вектор тоололд</a> дөрөвдэх үндсэн судлагдахуун болох өөрчлөлтийг мөн авч үздэг байна. </p> <dl><dd><table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Elliptic_curve_simple.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Elliptic_curve_simple.png/96px-Elliptic_curve_simple.png" decoding="async" width="96" height="117" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/76/Elliptic_curve_simple.png/144px-Elliptic_curve_simple.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/76/Elliptic_curve_simple.png/192px-Elliptic_curve_simple.png 2x" data-file-width="200" data-file-height="243" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Rubik_float.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/mn/thumb/1/10/Rubik_float.png/96px-Rubik_float.png" decoding="async" width="96" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/mn/thumb/1/10/Rubik_float.png/144px-Rubik_float.png 1.5x, //upload.wikimedia.org/wikipedia/mn/thumb/1/10/Rubik_float.png/192px-Rubik_float.png 2x" data-file-width="256" data-file-height="275" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Group_diagdram_D6.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Group_diagdram_D6.svg/96px-Group_diagdram_D6.svg.png" decoding="async" width="96" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Group_diagdram_D6.svg/144px-Group_diagdram_D6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/0e/Group_diagdram_D6.svg/192px-Group_diagdram_D6.svg.png 2x" data-file-width="180" data-file-height="180" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Lattice_of_the_divisibility_of_60.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/96px-Lattice_of_the_divisibility_of_60.svg.png" decoding="async" width="96" height="77" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/144px-Lattice_of_the_divisibility_of_60.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/51/Lattice_of_the_divisibility_of_60.svg/192px-Lattice_of_the_divisibility_of_60.svg.png 2x" data-file-width="313" data-file-height="250" /></a></span> </td></tr> <tr> <td><a href="/wiki/%D0%A2%D0%BE%D0%BE%D0%BD%D1%8B_%D0%BE%D0%BD%D0%BE%D0%BB" title="Тооны онол">Тооны онол</a></td> <td><a href="/w/index.php?title=%D0%90%D0%B1%D1%81%D1%82%D1%80%D0%B0%D0%BA%D1%82_%D0%B0%D0%BB%D0%B3%D0%B5%D0%B1%D1%80&action=edit&redlink=1" class="new" title="Абстракт алгебр (ийм хуудас байхгүй)">Абстракт алгебр</a></td> <td><a href="/w/index.php?title=%D0%91%D2%AF%D0%BB%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Бүлгийн онол (ийм хуудас байхгүй)">Бүлгийн онол</a></td> <td><a href="/w/index.php?title=%D0%AD%D1%80%D1%8D%D0%BC%D0%B1%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Эрэмбийн онол (ийм хуудас байхгүй)">Эрэмбийн онол</a> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Огторгуй"><span id=".D0.9E.D0.B3.D1.82.D0.BE.D1.80.D0.B3.D1.83.D0.B9"></span>Огторгуй</h3><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&veaction=edit&section=7" title="Хэсгийг засварлах: Огторгуй" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=7" title="Edit section's source code: Огторгуй"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Огторгуйн судалгаа нь <a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Геометр">геометрээс</a>, тухайлбал <a href="/wiki/%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Евклидийн геометр">Евклидийн геометрээс</a> эхлэлтэй. <a href="/w/index.php?title=%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Тригонометр (ийм хуудас байхгүй)">Тригонометр</a> нь огторгуй, тоо хоёрыг хооронд нь холбодог ба бидний сайн мэдэх <a href="/wiki/%D0%9F%D0%B8%D1%84%D0%B0%D0%B3%D0%BE%D1%80%D1%8B%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC" title="Пифагорын теорем">Пифагорын теорем</a> дээр үндсэндээ тулгуурладаг. Огторгуйн тухай орчин үеийн онолууд эдгээр санаануудыг өргөтгөн олон хэмжээст геометр, <a href="/w/index.php?title=%D0%95%D0%B2%D0%BA%D0%BB%D0%B8%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B1%D0%B8%D1%88_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Евклидийн биш геометр (ийм хуудас байхгүй)">Евклидийн биш геометрууд</a> (энэ геометрууд <a href="/w/index.php?title=%D0%A5%D0%B0%D1%80%D1%8C%D1%86%D0%B0%D0%BD%D0%B3%D1%83%D0%B9%D0%BD_%D0%B5%D1%80%D3%A9%D0%BD%D1%85%D0%B8%D0%B9_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Харьцангуйн ерөнхий онол (ийм хуудас байхгүй)">харьцангуйн ерөнхий онолд</a> гол үүрэг гүйцэтгэдэг) ба <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8&action=edit&redlink=1" class="new" title="Топологи (ийм хуудас байхгүй)">топологийг</a> судалдаг. <a href="/wiki/%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D1%82%D0%B8%D0%BA_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Аналитик геометр">Аналитик геометр</a>, <a href="/w/index.php?title=%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%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Дифференциал геометр (ийм хуудас байхгүй)">дифференциал геометр</a>, болон <a href="/w/index.php?title=%D0%90%D0%BB%D0%B3%D0%B5%D0%B1%D1%80%D0%BB%D0%B0%D0%B3_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Алгебрлаг геометр (ийм хуудас байхгүй)">алгебрлаг геометрт</a> тоо хэмжээ ба огторгуй хоёул чухал үүрэг гүйцэтгэдэг. Дифференциал геометр нь <a href="/w/index.php?title=%D0%A8%D0%B8%D1%80%D1%85%D1%8D%D0%B3_%D0%B1%D0%B0%D0%B3%D1%86&action=edit&redlink=1" class="new" title="Ширхэг багц (ийм хуудас байхгүй)">ширхэг багц</a> ба <a href="/w/index.php?title=%D0%A6%D0%BE%D0%B3%D1%86%D0%BE%D1%81&action=edit&redlink=1" class="new" title="Цогцос (ийм хуудас байхгүй)">цогцос</a> дээрх тооллыг агуулна. Алгебрлаг геометр нь геометрын объектуудыг <a href="/w/index.php?title=%D0%9E%D0%BB%D0%BE%D0%BD_%D0%B3%D0%B8%D1%88%D2%AF%D2%AF%D0%BD%D1%82&action=edit&redlink=1" class="new" title="Олон гишүүнт (ийм хуудас байхгүй)">олон гишүүнт</a> тэгшитгэлүүдийн шийдийн олонлогоор дүрсэлснээр тоо хэмжээ ба огторгуйг хооронд нь холбоод зогсохгүй <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8_%D0%B1%D2%AF%D0%BB%D1%8D%D0%B3&action=edit&redlink=1" class="new" title="Топологи бүлэг (ийм хуудас байхгүй)">топологи бүлгийн</a> тухай судалж бүтэц ба огторгуйг хооронд нь холбодог байна. <a href="/w/index.php?title=%D0%9B%D0%B8_%D0%B1%D2%AF%D0%BB%D1%8D%D0%B3&action=edit&redlink=1" class="new" title="Ли бүлэг (ийм хуудас байхгүй)">Ли бүлгүүдийг</a> огторгуй, бүтэц, өөрчлөлтийг зэрэг судлахад ашигладаг. <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8&action=edit&redlink=1" class="new" title="Топологи (ийм хуудас байхгүй)">Топологи</a> нь бүх дүрс хувирлуудынхаа хамт магадгүй XX зуунд хамгийн их хөгжсөн математикийн салбар юм. Энд жишээлбэл удаан хугацаанд шийдэгдээгүй байсан <a href="/w/index.php?title=%D0%9F%D1%83%D0%B0%D0%BD%D0%BA%D0%B0%D1%80%D1%8C%D0%B5%D0%B3%D0%B8%D0%B9%D0%BD_%D1%82%D0%B0%D0%B0%D0%BC%D0%B0%D0%B3%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Пуанкарьегийн таамаглал (ийм хуудас байхгүй)">Пуанкарьегийн таамаглал</a> ба компьютерээр баталсан боловч хүн хэзээ ч баталгааг нь шалгаагүй <a href="/w/index.php?title=%D0%94%D3%A9%D1%80%D0%B2%D3%A9%D0%BD_%D3%A9%D0%BD%D0%B3%D0%B8%D0%B9%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Дөрвөн өнгийн теорем (ийм хуудас байхгүй)">дөрвөн өнгийн теорем</a> зэрэг хамрагдана. </p> <dl><dd><table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Pythagorean.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/96px-Pythagorean.svg.png" decoding="async" width="96" height="87" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/144px-Pythagorean.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d2/Pythagorean.svg/192px-Pythagorean.svg.png 2x" data-file-width="512" data-file-height="466" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Taylorsine.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Taylorsine.svg/96px-Taylorsine.svg.png" decoding="async" width="96" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Taylorsine.svg/144px-Taylorsine.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b6/Taylorsine.svg/192px-Taylorsine.svg.png 2x" data-file-width="1600" data-file-height="1200" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Osculating_circle.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Osculating_circle.svg/96px-Osculating_circle.svg.png" decoding="async" width="96" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/84/Osculating_circle.svg/144px-Osculating_circle.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/84/Osculating_circle.svg/192px-Osculating_circle.svg.png 2x" data-file-width="480" data-file-height="360" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Torus.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/96px-Torus.png" decoding="async" width="96" height="61" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/144px-Torus.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/17/Torus.png/192px-Torus.png 2x" data-file-width="784" data-file-height="502" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Von_koch_6_etapes.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Von_koch_6_etapes.svg/96px-Von_koch_6_etapes.svg.png" decoding="async" width="96" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/36/Von_koch_6_etapes.svg/144px-Von_koch_6_etapes.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/36/Von_koch_6_etapes.svg/192px-Von_koch_6_etapes.svg.png 2x" data-file-width="600" data-file-height="174" /></a></span> </td></tr> <tr> <td><a href="/wiki/%D0%93%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80" title="Геометр">Геометр</a></td> <td><a href="/w/index.php?title=%D0%A2%D1%80%D0%B8%D0%B3%D0%BE%D0%BD%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Тригонометр (ийм хуудас байхгүй)">Тригонометр</a></td> <td><a href="/w/index.php?title=%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%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Дифференциал геометр (ийм хуудас байхгүй)">Дифференциал геометр</a></td> <td><a href="/w/index.php?title=%D0%A2%D0%BE%D0%BF%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8&action=edit&redlink=1" class="new" title="Топологи (ийм хуудас байхгүй)">Топологи</a></td> <td><a href="/w/index.php?title=%D0%A4%D1%80%D0%B0%D0%BA%D1%82%D0%B0%D0%BB_%D0%B3%D0%B5%D0%BE%D0%BC%D0%B5%D1%82%D1%80&action=edit&redlink=1" class="new" title="Фрактал геометр (ийм хуудас байхгүй)">Фрактал геометр</a> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Өөрчлөлт"><span id=".D3.A8.D3.A9.D1.80.D1.87.D0.BB.D3.A9.D0.BB.D1.82"></span>Өөрчлөлт</h3><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&veaction=edit&section=8" title="Хэсгийг засварлах: Өөрчлөлт" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=8" title="Edit section's source code: Өөрчлөлт"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Өөрчлөлт хувьслыг ойлгож тайлбарлах асуудал нь <a href="/wiki/%D0%91%D0%B0%D0%B9%D0%B3%D0%B0%D0%BB%D0%B8%D0%B9%D0%BD_%D1%88%D0%B8%D0%BD%D0%B6%D0%BB%D1%8D%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Байгалийн шинжлэх ухаан">байгалийн шинжлэх ухааны</a> нийтлэг асуудал бөгөөд <a href="/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол">интеграл ба дифференциал тоолол</a> нь яг үүнийг судлахын тулд бий болгосон хүчтэй хэрэгсэл юм. Өөрчлөгдөж байгаа хэмжигдэхүүнийг илэрхийлэх тулгуур ойлголт болгон <a href="/w/index.php?title=%D0%A4%D1%83%D0%BD%D0%BA%D1%86&action=edit&redlink=1" class="new" title="Функц (ийм хуудас байхгүй)">функцийг</a> энд оруулж ирдэг. Бодит тоонууд ба бодит утга авдаг функцүүдийн судалгааг <a href="/w/index.php?title=%D0%91%D0%BE%D0%B4%D0%B8%D1%82_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7&action=edit&redlink=1" class="new" title="Бодит анализ (ийм хуудас байхгүй)">бодит анализ</a> гэдэг бөгөөд комплекс тоотой холбоотой ийм салбарыг нь <a href="/w/index.php?title=%D0%9A%D0%BE%D0%BC%D0%BF%D0%BB%D0%B5%D0%BA%D1%81_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7&action=edit&redlink=1" class="new" title="Комплекс анализ (ийм хуудас байхгүй)">комплекс анализ</a> гэж нэрлэдэг. Математикийн хамгийн тулгуур шийдэгдээгүй асуудлуудын нэг болох <a href="/wiki/%D0%A0%D0%B8%D0%BC%D0%B0%D0%BD%D1%8B_%D1%82%D0%B0%D0%B0%D0%BC%D0%B0%D0%B3%D0%BB%D0%B0%D0%BB" title="Риманы таамаглал">Риманы таамаглал</a> комплекс анализаас урган гарсан. <a href="/w/index.php?title=%D0%A4%D1%83%D0%BD%D0%BA%D1%86%D0%B8%D0%BE%D0%BD%D0%B0%D0%BB_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7&action=edit&redlink=1" class="new" title="Функционал анализ (ийм хуудас байхгүй)">Функционал анализ</a> нь функцүүдийн (ерөнхийдөө төгсгөлгүй хэмжээстэй) <a href="/wiki/%D0%9E%D0%B3%D1%82%D0%BE%D1%80%D0%B3%D1%83%D0%B9" title="Огторгуй">огторгуй</a> дээр төвлөрдөг бөгөөд үүний нэг хэрэглээ нь <a href="/wiki/%D0%9A%D0%B2%D0%B0%D0%BD%D1%82_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA" title="Квант механик">квант механик</a> юм. Нийтлэг илэрдэг тоо хэмжээ болон түүний өөрчлөлтийн хоорондох холбоог <a href="/w/index.php?title=%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D1%8D%D0%B3%D1%88%D0%B8%D1%82%D0%B3%D1%8D%D0%BB&action=edit&redlink=1" class="new" title="Дифференциал тэгшитгэл (ийм хуудас байхгүй)">дифференциал тэгшитгэл</a> болгож судалдаг. Байгалийн олон үзэгдэл <a href="/w/index.php?title=%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Динамик систем (ийм хуудас байхгүй)">динамик системээр</a> илэрхийлэгддэг. Эдгээр системүүд ямар үед <a href="/w/index.php?title=%D0%94%D0%B5%D1%82%D0%B5%D1%80%D0%BC%D0%B8%D0%BD%D0%B8%D1%81%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Детерминистик (ийм хуудас байхгүй)">детерминистик</a> боловч урьдчилж таахын аргагүй шинж байдал үзүүлэх вэ гэдгийг <a href="/wiki/%D0%A5%D0%B0%D0%BE%D1%81%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Хаосын онол">хаосын онолд</a> судална. </p> <table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="20"> <tbody><tr> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Integral_as_region_under_curve.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/96px-Integral_as_region_under_curve.svg.png" decoding="async" width="96" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/144px-Integral_as_region_under_curve.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f2/Integral_as_region_under_curve.svg/192px-Integral_as_region_under_curve.svg.png 2x" data-file-width="750" data-file-height="700" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Vectorfield_jaredwf.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Vectorfield_jaredwf.png/96px-Vectorfield_jaredwf.png" decoding="async" width="96" height="85" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/88/Vectorfield_jaredwf.png/144px-Vectorfield_jaredwf.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/88/Vectorfield_jaredwf.png/192px-Vectorfield_jaredwf.png 2x" data-file-width="400" data-file-height="356" /></a></span></td> <td></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Limitcycle.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Limitcycle.jpg/96px-Limitcycle.jpg" decoding="async" width="96" height="72" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Limitcycle.jpg/144px-Limitcycle.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a1/Limitcycle.jpg/192px-Limitcycle.jpg 2x" data-file-width="400" data-file-height="300" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Lorenz_attractor.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Lorenz_attractor.svg/96px-Lorenz_attractor.svg.png" decoding="async" width="96" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Lorenz_attractor.svg/144px-Lorenz_attractor.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/f4/Lorenz_attractor.svg/192px-Lorenz_attractor.svg.png 2x" data-file-width="750" data-file-height="750" /></a></span> </td></tr> <tr> <td><a href="/wiki/%D0%98%D0%BD%D1%82%D0%B5%D0%B3%D1%80%D0%B0%D0%BB_%D0%B1%D0%B0_%D0%B4%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB" title="Интеграл ба дифференциал тоолол">Интеграл ба дифференциал тоолол</a></td> <td><a href="/w/index.php?title=%D0%92%D0%B5%D0%BA%D1%82%D0%BE%D1%80_%D1%82%D0%BE%D0%BE%D0%BB%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Вектор тоолол (ийм хуудас байхгүй)">Вектор тоолол</a></td> <td><a href="/w/index.php?title=%D0%94%D0%B8%D1%84%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%86%D0%B8%D0%B0%D0%BB_%D1%82%D1%8D%D0%B3%D1%88%D0%B8%D1%82%D0%B3%D1%8D%D0%BB&action=edit&redlink=1" class="new" title="Дифференциал тэгшитгэл (ийм хуудас байхгүй)">Дифференциал тэгшитгэл</a></td> <td><a href="/w/index.php?title=%D0%94%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA_%D1%81%D0%B8%D1%81%D1%82%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Динамик систем (ийм хуудас байхгүй)">Динамик систем</a></td> <td><a href="/wiki/%D0%A5%D0%B0%D0%BE%D1%81%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Хаосын онол">Хаосын онол</a> </td></tr></tbody></table> <div class="mw-heading mw-heading3"><h3 id="Тулгуур_салбарууд_ба_философи"><span id=".D0.A2.D1.83.D0.BB.D0.B3.D1.83.D1.83.D1.80_.D1.81.D0.B0.D0.BB.D0.B1.D0.B0.D1.80.D1.83.D1.83.D0.B4_.D0.B1.D0.B0_.D1.84.D0.B8.D0.BB.D0.BE.D1.81.D0.BE.D1.84.D0.B8"></span>Тулгуур салбарууд ба философи</h3><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&veaction=edit&section=9" title="Хэсгийг засварлах: Тулгуур салбарууд ба философи" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=9" title="Edit section's source code: Тулгуур салбарууд ба философи"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Бүх математикийн дээр нь тогтож байгаа <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%B8%D0%B9%D0%BD_%D1%82%D1%83%D0%BB%D0%B3%D1%83%D1%83%D1%80_%D1%81%D0%B0%D0%BB%D0%B1%D0%B0%D1%80%D1%83%D1%83%D0%B4&action=edit&redlink=1" class="new" title="Математикийн тулгуур салбарууд (ийм хуудас байхгүй)">үндэс суурийг</a> тодорхой болгохын тулд <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%BB%D0%BE%D0%B3%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Математик логик (ийм хуудас байхгүй)">математик логик</a> ба <a href="/w/index.php?title=%D0%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Олонлогийн онол (ийм хуудас байхгүй)">олонлогийн онол</a>, мөн одоогоор бүрэн төгөлдөржөөгүй байгаа <a href="/w/index.php?title=%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Категорийн онол (ийм хуудас байхгүй)">категорийн онолыг</a> үүсгэжээ. </p><p>Математик логик нь математикийг хатуу <a href="/wiki/%D0%90%D0%BA%D1%81%D0%B8%D0%BE%D0%BC" title="Аксиом">аксиомчилсан</a> системийн хүрээнд авч үзэх ба үүнээс гарах үр дагавруудыг судалдаг. Энд жишээлбэл логикийн хамгийн алдартай үр дүн байж мэдэх <a href="/w/index.php?title=%D0%93%D1%91%D0%B4%D0%B5%D0%BB%D0%B8%D0%B9%D0%BD_%D0%B3%D2%AF%D0%B9%D1%86%D1%8D%D0%B4_%D0%B1%D1%83%D1%81%D1%8B%D0%BD_%D1%85%D0%BE%D1%91%D1%80%D0%B4%D1%83%D0%B3%D0%B0%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B5%D0%BC&action=edit&redlink=1" class="new" title="Гёделийн гүйцэд бусын хоёрдугаар теорем (ийм хуудас байхгүй)">Гёделийн гүйцэд бусын хоёрдугаар теорем</a> хамаарагдана. Энэ теорем нь (барагцаагаар хэлбэл) үндсэн арифметикийг багтаасан дурын формаль систем хэрэв уг системд баталж болох бүх теорем үнэн бол <i>уг систем дотор</i> батлах боломжгүй, үнэн теоремууд оршин байна гэдэг. Гёдель тооны онолын дурын аксиомууд өгөгдсөн байхад уг аксиомуудаас гарахгүй, тооны онолын үнэн баримтыг илэрхийлэх логик өгүүлбэрийг яаж байгуулахыг зааж өгсөн. Иймд ямар ч формаль систем тооны онолын жинхэнэ аксиомчлал болж чадахгүй юм. Орчин үеийн логик нь <a href="/w/index.php?title=%D0%A0%D0%B5%D0%BA%D1%83%D1%80%D1%81%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Рекурсын онол (ийм хуудас байхгүй)">рекурсын онол</a>, <a href="/w/index.php?title=%D0%9C%D0%BE%D0%B4%D0%B5%D0%BB%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Моделийн онол (ийм хуудас байхгүй)">моделийн онол</a>, ба <a href="/w/index.php?title=%D0%91%D0%B0%D1%82%D0%B0%D0%BB%D0%B3%D0%B0%D0%B0%D0%BD%D1%8B_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Баталгааны онол (ийм хуудас байхгүй)">баталгааны онол</a> гэж хуваагддаг бөгөөд <a href="/w/index.php?title=%D0%9E%D0%BD%D0%BE%D0%BB%D1%8B%D0%BD_%D0%BA%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80_%D1%81%D1%83%D0%B4%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Онолын компьютер судлал (ийм хуудас байхгүй)">онолын</a> <a href="/w/index.php?title=%D0%9A%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80_%D1%81%D1%83%D0%B4%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Компьютер судлал (ийм хуудас байхгүй)">компьютер судлалтай</a> нягт холбоотой оршдог. </p> <dl><dd><table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P\Rightarrow Q\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">⇒</mo> <mi>Q</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P\Rightarrow Q\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c34a3223a111dfb9db58cb329bfc3ac40562588" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.585ex; height:2.509ex;" alt="{\displaystyle P\Rightarrow Q\,}"></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Venn_A_intersect_B.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/128px-Venn_A_intersect_B.svg.png" decoding="async" width="128" height="91" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/192px-Venn_A_intersect_B.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Venn_A_intersect_B.svg/256px-Venn_A_intersect_B.svg.png 2x" data-file-width="350" data-file-height="250" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Commutative_diagram_for_morphism.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Commutative_diagram_for_morphism.svg/96px-Commutative_diagram_for_morphism.svg.png" decoding="async" width="96" height="96" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Commutative_diagram_for_morphism.svg/144px-Commutative_diagram_for_morphism.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/ef/Commutative_diagram_for_morphism.svg/192px-Commutative_diagram_for_morphism.svg.png 2x" data-file-width="100" data-file-height="100" /></a></span> </td></tr> <tr> <td><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%BB%D0%BE%D0%B3%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Математик логик (ийм хуудас байхгүй)">Математик логик</a></td> <td><a href="/w/index.php?title=%D0%9E%D0%BB%D0%BE%D0%BD%D0%BB%D0%BE%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Олонлогийн онол (ийм хуудас байхгүй)">Олонлогийн онол</a></td> <td><a href="/w/index.php?title=%D0%9A%D0%B0%D1%82%D0%B5%D0%B3%D0%BE%D1%80%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Категорийн онол (ийм хуудас байхгүй)">Категорийн онол</a></td> <td> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Дискрет_математик"><span id=".D0.94.D0.B8.D1.81.D0.BA.D1.80.D0.B5.D1.82_.D0.BC.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D0.BA"></span>Дискрет математик</h3><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&veaction=edit&section=10" title="Хэсгийг засварлах: Дискрет математик" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=10" title="Edit section's source code: Дискрет математик"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=%D0%94%D0%B8%D1%81%D0%BA%D1%80%D0%B5%D1%82_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Дискрет математик (ийм хуудас байхгүй)">Дискрет математик</a> нь ерөнхийдөө <a href="/w/index.php?title=%D0%9E%D0%BD%D0%BE%D0%BB%D1%8B%D0%BD_%D0%BA%D0%BE%D0%BC%D0%BF%D1%8C%D1%8E%D1%82%D0%B5%D1%80_%D1%81%D1%83%D0%B4%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Онолын компьютер судлал (ийм хуудас байхгүй)">онолын компьютер судлалд</a> хэрэглэгддэг математикийн салбаруудыг нэрлэсэн нэр юм. Үүнд <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BE%D0%B3%D0%B4%D0%BE%D1%85_%D0%B1%D0%B0%D0%B9%D0%B4%D0%BB%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Тооцоологдох байдлын онол (ийм хуудас байхгүй)">тооцоологдох байдлын онол</a>, <a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D0%BD%D0%B8%D0%B9%D0%BB%D0%BC%D1%8D%D0%BB_%D0%B1%D0%B0%D0%B9%D0%B4%D0%BB%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Тооцооллын нийлмэл байдлын онол (ийм хуудас байхгүй)">тооцооллын нийлмэл байдлын онол</a>, ба <a href="/wiki/%D0%9C%D1%8D%D0%B4%D1%8D%D1%8D%D0%BB%D0%BB%D0%B8%D0%B9%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Мэдээллийн онол">мэдээллийн онол</a> багтана. Тооцоологдох байдлын онол нь одоогоор мэдэгдэж байгаа хамгийн хүчирхэг загвар болох <a href="/w/index.php?title=%D0%A2%D1%8E%D1%80%D0%B8%D0%BD%D0%B3%D0%B8%D0%B9%D0%BD_%D0%B7%D0%B0%D0%B3%D0%B2%D0%B0%D1%80&action=edit&redlink=1" class="new" title="Тюрингийн загвар (ийм хуудас байхгүй)">Тюрингийн загварыг</a> оролцуулан компьютерийн төрөл бүрийн онолын загваруудын боломжийн хязгаарыг судалдаг. Нийлмэл байдлын онол нь компьютер ашиглан бодлогуудыг бодох үед зарцуулах өртгийг судална. Зарим бодлогыг зарчмын хув </p> <pre>компьютерээр бодож болох боловч практик дээр компьютер хичнээн ч хөгжлөө гэсэн бүтээх аргагүй их санах ой болон цаг хугацаа шаардахаар байж болдог. Өгөгдсөн орчинд хэр их хэмжээний мэдээлэл хадгалж болох вэ гэдгийг мэдээллийн онол судлах ба <a href="/w/index.php?title=%D3%A8%D0%B3%D3%A9%D0%B3%D0%B4%D0%BB%D0%B8%D0%B9%D0%B3_%D1%88%D0%B0%D1%85%D0%B0%D1%85&action=edit&redlink=1" class="new" title="Өгөгдлийг шахах (ийм хуудас байхгүй)">өгөгдлийг шахах</a>, <a href="/wiki/%D0%AD%D0%BD%D1%82%D1%80%D0%BE%D0%BF%D0%B8" title="Энтропи">энтропи</a> гэх мэт ойлголтуудыг оруулж ирдэг. </pre> <p>Харьцангуй шинэ салбар тул дискрет математикт шийдэгдээгүй тулгуур асуудлууд нилээд бий. Эдгээрээс хамгийн алдартай нь <a href="/w/index.php?title=%D0%9C%D1%8F%D0%BD%D0%B3%D0%B0%D0%BD%D1%8B_%D0%A8%D0%B0%D0%B3%D0%BD%D0%B0%D0%BB%D1%82_%D0%91%D0%BE%D0%B4%D0%BB%D0%BE%D0%B3%D1%83%D1%83%D0%B4&action=edit&redlink=1" class="new" title="Мянганы Шагналт Бодлогууд (ийм хуудас байхгүй)">Мянганы Шагналт Бодлогуудын</a> нэг болох "<a href="/w/index.php?title=%D0%9D%D0%B8%D0%B9%D0%BB%D0%BC%D1%8D%D0%BB_%D0%B1%D0%B0%D0%B9%D0%B4%D0%BB%D1%8B%D0%BD_%D0%B0%D0%BD%D0%B3%D0%B8%D1%83%D0%B4_P_%D0%B1%D0%B0_NP&action=edit&redlink=1" class="new" title="Нийлмэл байдлын ангиуд P ба NP (ийм хуудас байхгүй)">P=NP?</a>" бодлого юм. </p> <dl><dd><table style="border:1px solid #ddd; text-align:center; margin: auto;" cellspacing="15"> <tbody><tr> <td><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{matrix}(1,2,3)&(1,3,2)\\(2,1,3)&(2,3,1)\\(3,1,2)&(3,2,1)\end{matrix}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable rowspacing="4pt" columnspacing="1em"> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mo stretchy="false">(</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mtd> <mtd> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}(1,2,3)&(1,3,2)\\(2,1,3)&(2,3,1)\\(3,1,2)&(3,2,1)\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/329c4717bdfa2ba585b14793665ae413ee5107c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:17.803ex; height:9.843ex;" alt="{\displaystyle {\begin{matrix}(1,2,3)&(1,3,2)\\(2,1,3)&(2,3,1)\\(3,1,2)&(3,2,1)\end{matrix}}}"></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:DFAexample.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/DFAexample.svg/96px-DFAexample.svg.png" decoding="async" width="96" height="57" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/9d/DFAexample.svg/144px-DFAexample.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/9d/DFAexample.svg/192px-DFAexample.svg.png 2x" data-file-width="500" data-file-height="299" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:Caesar3.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Caesar3.svg/96px-Caesar3.svg.png" decoding="async" width="96" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Caesar3.svg/144px-Caesar3.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2b/Caesar3.svg/192px-Caesar3.svg.png 2x" data-file-width="856" data-file-height="361" /></a></span></td> <td><span typeof="mw:File"><a href="/wiki/%D0%A4%D0%B0%D0%B9%D0%BB:6n-graf.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n-graf.svg/96px-6n-graf.svg.png" decoding="async" width="96" height="63" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n-graf.svg/144px-6n-graf.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5b/6n-graf.svg/192px-6n-graf.svg.png 2x" data-file-width="333" data-file-height="220" /></a></span> </td></tr> <tr> <td><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" title="Комбинаторик">Комбинаторик</a></td> <td><a href="/w/index.php?title=%D0%A2%D0%BE%D0%BE%D1%86%D0%BE%D0%BE%D0%BB%D0%BB%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB&action=edit&redlink=1" class="new" title="Тооцооллын онол (ийм хуудас байхгүй)">Тооцооллын онол</a></td> <td><a href="/wiki/%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D0%B3%D1%80%D0%B0%D1%84" title="Криптограф">Криптограф</a></td> <td><a href="/wiki/%D0%93%D1%80%D0%B0%D1%84%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Графын онол">Графын онол</a> </td></tr></tbody></table></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Хэрэглээний_математик"><span id=".D0.A5.D1.8D.D1.80.D1.8D.D0.B3.D0.BB.D1.8D.D1.8D.D0.BD.D0.B8.D0.B9_.D0.BC.D0.B0.D1.82.D0.B5.D0.BC.D0.B0.D1.82.D0.B8.D0.BA"></span>Хэрэглээний математик</h3><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&veaction=edit&section=11" title="Хэсгийг засварлах: Хэрэглээний математик" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=11" title="Edit section's source code: Хэрэглээний математик"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/%D0%A8%D0%B8%D0%BD%D0%B6%D0%BB%D1%8D%D1%85_%D1%83%D1%85%D0%B0%D0%B0%D0%BD" title="Шинжлэх ухаан">Шинжлэх ухаан</a>, <a href="/wiki/%D0%91%D0%B8%D0%B7%D0%BD%D0%B5%D1%81" title="Бизнес">бизнес</a> болон бусад салбарт математикийн абстракт аппаратыг ашиглах явдлыг хэрэглээний математикт авч үздэг. Хэрэглээний математикийн нэг чухал салбар нь <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA" title="Статистик">статистик</a> бөгөөд энд <a href="/wiki/%D0%9C%D0%B0%D0%B3%D0%B0%D0%B4%D0%BB%D0%B0%D0%BB%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Магадлалын онол">магадлалын онолыг</a> ашиглан тохиолдох эсэх нь тодорхойгүй үзэгдлүүдийг тайлбарлах, шинжлэх, урьдчилсан таамаг гаргах талаар судална. Ихэнх туршилт, хайгуул, болон ажиглалтууд статистикийн ядаж анхан шатны мэдлэг шаарддаг. Ерөнхийдөө хүний тооцон бодох чадвараас хэт давсан төрөл бүрийн математикийн бодлогуудыг хэмнэлттэйгээр тооцоолох аргуудыг <a href="/wiki/%D0%A2%D0%BE%D0%BE%D0%BD_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Тоон анализ">тоон анализ</a> судалдаг. Энд тухайлбал <a href="/w/index.php?title=%D0%A2%D0%BE%D0%B9%D0%BC%D0%BB%D0%BE%D0%BB%D1%8B%D0%BD_%D0%B0%D0%BB%D0%B4%D0%B0%D0%B0&action=edit&redlink=1" class="new" title="Тоймлолын алдаа (ийм хуудас байхгүй)">тоймлолын алдаа</a> болон бусад алдааны эх үүсвэрүүдийг шинжлэх явдал орно. </p> <dl><dd><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA_%D1%84%D0%B8%D0%B7%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Математик физик (ийм хуудас байхгүй)">Математик физик</a> • <a href="/w/index.php?title=%D0%90%D0%BD%D0%B0%D0%BB%D0%B8%D1%82%D0%B8%D0%BA_%D0%BC%D0%B5%D1%85%D0%B0%D0%BD%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Аналитик механик (ийм хуудас байхгүй)">Аналитик механик</a> • <a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA_%D1%88%D0%B8%D0%BD%D0%B3%D1%8D%D0%BD%D0%B8%D0%B9_%D0%B4%D0%B8%D0%BD%D0%B0%D0%BC%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Математик шингэний динамик (ийм хуудас байхгүй)">Математик шингэний динамик</a> • <a href="/wiki/%D0%A2%D0%BE%D0%BE%D0%BD_%D0%B0%D0%BD%D0%B0%D0%BB%D0%B8%D0%B7" title="Тоон анализ">Тоон анализ</a> • <a href="/w/index.php?title=%D0%9E%D0%BF%D1%82%D0%B8%D0%BC%D0%B8%D0%B7%D0%B0%D1%86%D0%B8&action=edit&redlink=1" class="new" title="Оптимизаци (ийм хуудас байхгүй)">Оптимизаци</a> • <a href="/w/index.php?title=%D0%9C%D0%B0%D0%B3%D0%B0%D0%B4%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Магадлал (ийм хуудас байхгүй)">Магадлал</a> • <a href="/wiki/%D0%A1%D1%82%D0%B0%D1%82%D0%B8%D1%81%D1%82%D0%B8%D0%BA" title="Статистик">Статистик</a> • <a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA_%D1%8D%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B7%D0%B0%D1%81%D0%B0%D0%B3&action=edit&redlink=1" class="new" title="Математик эдийн засаг (ийм хуудас байхгүй)">Математик эдийн засаг</a> • <a href="/w/index.php?title=%D0%A1%D0%B0%D0%BD%D1%85%D2%AF%D2%AF%D0%B3%D0%B8%D0%B9%D0%BD_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA&action=edit&redlink=1" class="new" title="Санхүүгийн математик (ийм хуудас байхгүй)">Санхүүгийн математик</a> • <a href="/wiki/%D0%A2%D0%BE%D0%B3%D0%BB%D0%BE%D0%BE%D0%BC%D1%8B%D0%BD_%D0%BE%D0%BD%D0%BE%D0%BB" title="Тоглоомын онол">Тоглоомын онол</a> • <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%B1%D0%B8%D0%BE%D0%BB%D0%BE%D0%B3%D0%B8&action=edit&redlink=1" class="new" title="Математик биологи (ийм хуудас байхгүй)">Математик биологи</a> • <a href="/wiki/%D0%9A%D1%80%D0%B8%D0%BF%D1%82%D0%BE%D0%B3%D1%80%D0%B0%D1%84" title="Криптограф">Криптограф</a> • <a href="/w/index.php?title=%D2%AE%D0%B9%D0%BB%D0%B4%D0%BB%D0%B8%D0%B9%D0%BD_%D1%88%D0%B8%D0%BD%D0%B6%D0%B8%D0%BB%D0%B3%D1%8D%D1%8D&action=edit&redlink=1" class="new" title="Үйлдлийн шинжилгээ (ийм хуудас байхгүй)">Үйлдлийн шинжилгээ</a></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Мөн_үзэх"><span id=".D0.9C.D3.A9.D0.BD_.D2.AF.D0.B7.D1.8D.D1.85"></span>Мөн үзэх</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&veaction=edit&section=12" title="Хэсгийг засварлах: Мөн үзэх" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=12" title="Edit section's source code: Мөн үзэх"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D1%82%D0%B0%D0%B9_%D1%85%D0%BE%D0%BB%D0%B1%D0%BE%D0%BE%D1%82%D0%BE%D0%B9_%D0%BD%D0%B8%D0%B9%D1%82%D0%BB%D1%8D%D0%BB%D2%AF%D2%AF%D0%B4%D0%B8%D0%B9%D0%BD_%D0%B6%D0%B0%D0%B3%D1%81%D0%B0%D0%B0%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Математиктай холбоотой нийтлэлүүдийн жагсаалт (ийм хуудас байхгүй)">Математиктай холбоотой нийтлэлүүдийн жагсаалт</a></li> <li><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%B8%D0%B9%D0%BD_%D1%84%D0%B8%D0%BB%D0%BE%D1%81%D0%BE%D1%84%D0%B8&action=edit&redlink=1" class="new" title="Математикийн философи (ийм хуудас байхгүй)">Математикийн философи</a></li> <li><a href="/wiki/%D0%91%D0%BE%D0%BB%D0%BE%D0%B2%D1%81%D1%80%D0%BE%D0%BB" title="Боловсрол">Боловсрол</a></li> <li><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%B8%D0%B9%D0%BD_%D0%B1%D0%BE%D0%B4%D0%BB%D0%BE%D0%B3%D0%BE&action=edit&redlink=1" class="new" title="Математикийн бодлого (ийм хуудас байхгүй)">Математикийн бодлого</a></li> <li><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%B8%D0%B9%D0%BD_%D1%83%D1%80%D0%B0%D0%BB%D0%B4%D0%B0%D0%B0%D0%BD_%D1%82%D1%8D%D0%BC%D1%86%D1%8D%D1%8D%D0%BD%D2%AF%D2%AF%D0%B4&action=edit&redlink=1" class="new" title="Математикийн уралдаан тэмцээнүүд (ийм хуудас байхгүй)">Математикийн уралдаан тэмцээнүүд</a></li> <li><a href="/w/index.php?title=%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D1%87%D0%B4%D1%8B%D0%BD_%D0%B6%D0%B0%D0%B3%D1%81%D0%B0%D0%B0%D0%BB%D1%82&action=edit&redlink=1" class="new" title="Математикчдын жагсаалт (ийм хуудас байхгүй)">Математикчдын жагсаалт</a></li> <li><a href="/w/index.php?title=%D0%9C%D0%BE%D0%BD%D0%B3%D0%BE%D0%BB%D1%8B%D0%BD_%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D1%87%D0%B4%D1%8B%D0%BD_%D0%A5%D0%BE%D0%BB%D0%B1%D0%BE%D0%BE&action=edit&redlink=1" class="new" title="Монголын Математикчдын Холбоо (ийм хуудас байхгүй)">Монголын Математикчдын Холбоо</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Тэмдэглэлүүд"><span id=".D0.A2.D1.8D.D0.BC.D0.B4.D1.8D.D0.B3.D0.BB.D1.8D.D0.BB.D2.AF.D2.AF.D0.B4"></span>Тэмдэглэлүүд</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&veaction=edit&section=13" title="Хэсгийг засварлах: Тэмдэглэлүүд" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=13" title="Edit section's source code: Тэмдэглэлүүд"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-size:92%"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">Peirce, хууд.97</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">Steen, L.A., (April 29, 1988). <i>The Science of Patterns.</i> Science, 240: 611–616. тойм: <a rel="nofollow" class="external text" href="https://web.archive.org/web/20070929010703/http://www.ascd.org/portal/site/ascd/template.chapter/menuitem.1889bf0176da7573127855b3e3108a0c/?chapterMgmtId=f97433df69abb010VgnVCM1000003d01a8c0RCRD">Association for Supervision and Curriculum Development.</a> (<a href="/w/index.php?title=%D0%A6%D0%B0%D1%85%D0%B8%D0%BC_%D0%B0%D1%80%D1%85%D0%B8%D0%B2%D1%87%D0%BB%D0%B0%D0%BB&action=edit&redlink=1" class="new" title="Цахим архивчлал (ийм хуудас байхгүй)">Memento</a> 29. Есдүгээр сар 2007 <i><a href="/wiki/%D0%A6%D0%B0%D1%85%D0%B8%D0%BC_%D0%B0%D1%80%D1%85%D0%B8%D0%B2" title="Цахим архив">цахим архивт</a></i>)<span style="display:none;"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text"> Devlin, Keith, <i>Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe</i> (Scientific American Paperback Library) 1996, ISBN-10: 0716760223 </span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Jourdain</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text">Eves</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Peterson</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Sevryuk</span> </li> </ol> </div> <div class="mw-heading mw-heading2"><h2 id="Ном_хэвлэл"><span id=".D0.9D.D0.BE.D0.BC_.D1.85.D1.8D.D0.B2.D0.BB.D1.8D.D0.BB"></span>Ном хэвлэл</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&veaction=edit&section=14" title="Хэсгийг засварлах: Ном хэвлэл" class="mw-editsection-visualeditor"><span>засварлах</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&action=edit&section=14" title="Edit section's source code: Ном хэвлэл"><span>кодоор засварлах</span></a><span class="mw-editsection-bracket">]</span></span></div> <div style="font-size:92%"> <ul><li>Eves, Howard, <i>An Introduction to the History of Mathematics</i>, Sixth Edition, Saunders, 1990, <a href="/wiki/%D0%A2%D1%83%D1%81%D0%B3%D0%B0%D0%B9:BookSources/0030295580" class="internal mw-magiclink-isbn">ISBN 0-03-029558-0</a>.</li> <li>Jourdain, Philip E. B., <i>The Nature of Mathematics</i>, in <i>The World of Mathematics</i>, James R. Newman, editor, Dover, 2003, <a href="/wiki/%D0%A2%D1%83%D1%81%D0%B3%D0%B0%D0%B9:BookSources/0486432688" class="internal mw-magiclink-isbn">ISBN 0-486-43268-8</a>.</li> <li><style data-mw-deduplicate="TemplateStyles:r793951">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#3a3;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFPeirce" class="citation journal cs1">Peirce, Benjamin. <a rel="nofollow" class="external text" href="http://links.jstor.org/sici?sici=0002-9327%281881%294%3A1%2F4%3C97%3ALAA%3E2.0.CO%3B2-X">"Linear Associative Algebra"</a>. <i>American Journal of Mathematics</i> (Vol. 4, No. 1/4. (1881).</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=American+Journal+of+Mathematics&rft.atitle=Linear+Associative+Algebra&rft.issue=Vol.+4%2C+No.+1%2F4.+%281881&rft.aulast=Peirce&rft.aufirst=Benjamin&rft_id=http%3A%2F%2Flinks.jstor.org%2Fsici%3Fsici%3D0002-9327%25281881%25294%253A1%252F4%253C97%253ALAA%253E2.0.CO%253B2-X&rfr_id=info%3Asid%2Fmn.wikipedia.org%3A%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/%D0%97%D0%B0%D0%B3%D0%B2%D0%B0%D1%80:Cite_journal" title="Загвар:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Unknown parameter <code class="cs1-code">|, pages=</code> ignored (<a href="/wiki/%D0%A2%D1%83%D1%81%D0%BB%D0%B0%D0%BC%D0%B6:CS1_errors#parameter_ignored" title="Тусламж:CS1 errors">help</a>)</span> JSTOR.</li> <li>Peterson, Ivars, <i>Mathematical Tourist, New and Updated Snapshots of Modern Mathematics</i>, Owl Books, 2001, <a href="/wiki/%D0%A2%D1%83%D1%81%D0%B3%D0%B0%D0%B9:BookSources/0805071598" class="internal mw-magiclink-isbn">ISBN 0-8050-7159-8</a>.</li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r793951"><cite id="CITEREFSevryuk2006" class="citation journal cs1">Sevryuk, Mikhail B. (2006). <a rel="nofollow" class="external text" href="http://www.ams.org/bull/2006-43-01/S0273-0979-05-01069-4/S0273-0979-05-01069-4.pdf">"Book Reviews"</a> <span class="cs1-format">(PDF)</span>. <i>Bulletin of the American Mathematical Society</i>. <b>43</b> (1): 101–109.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.jtitle=Bulletin+of+the+American+Mathematical+Society&rft.atitle=Book+Reviews&rft.volume=43&rft.issue=1&rft.pages=101-109&rft.date=2006&rft.aulast=Sevryuk&rft.aufirst=Mikhail+B.&rft_id=http%3A%2F%2Fwww.ams.org%2Fbull%2F2006-43-01%2FS0273-0979-05-01069-4%2FS0273-0979-05-01069-4.pdf&rfr_id=info%3Asid%2Fmn.wikipedia.org%3A%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA" class="Z3988"></span> <span class="cs1-visible-error citation-comment"><code class="cs1-code">{{<a href="/wiki/%D0%97%D0%B0%D0%B3%D0%B2%D0%B0%D1%80:Cite_journal" title="Загвар:Cite journal">cite journal</a>}}</code>: </span><span class="cs1-visible-error citation-comment">Unknown parameter <code class="cs1-code">|month=</code> ignored (<a href="/wiki/%D0%A2%D1%83%D1%81%D0%BB%D0%B0%D0%BC%D0%B6:CS1_errors#parameter_ignored" title="Тусламж:CS1 errors">help</a>)</span></li></ul> </div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r729770">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl ol,.mw-parser-output .hlist dl ul,.mw-parser-output .hlist ol dl,.mw-parser-output .hlist ol ol,.mw-parser-output .hlist ol ul,.mw-parser-output .hlist ul dl,.mw-parser-output .hlist ul ol,.mw-parser-output .hlist ul ul{display:inline}.mw-parser-output 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