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class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Storja"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Storja</span> </div> </a> <ul id="toc-Storja-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Analisi_Matematika" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Analisi_Matematika"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Analisi Matematika</span> </div> </a> <button aria-controls="toc-Analisi_Matematika-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>Uri jew aħbi s-sottosezzjoni Analisi Matematika</span> </button> <ul id="toc-Analisi_Matematika-sublist" class="vector-toc-list"> <li id="toc-Għaliex_l-Analisi_Astratta?" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Għaliex_l-Analisi_Astratta?"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Għaliex l-Analisi Astratta?</span> </div> </a> <ul id="toc-Għaliex_l-Analisi_Astratta?-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Storja_tal-Analisi_Matematika" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Storja_tal-Analisi_Matematika"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Storja tal-Analisi Matematika</span> </div> </a> <ul id="toc-Storja_tal-Analisi_Matematika-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Oqsma_ta'_l-Analisi" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Oqsma_ta'_l-Analisi"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Oqsma ta' l-Analisi</span> </div> </a> <ul id="toc-Oqsma_ta'_l-Analisi-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Alġebra" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Alġebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Alġebra</span> </div> </a> <button aria-controls="toc-Alġebra-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>Uri jew aħbi s-sottosezzjoni Alġebra</span> </button> <ul id="toc-Alġebra-sublist" class="vector-toc-list"> <li id="toc-Klassifikazzjoni" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Klassifikazzjoni"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Klassifikazzjoni</span> </div> </a> <ul id="toc-Klassifikazzjoni-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-L-Alġebra_Elementari" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#L-Alġebra_Elementari"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>L-Alġebra Elementari</span> </div> </a> <ul id="toc-L-Alġebra_Elementari-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-X'inhi_l-Alġebra_Astratta" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#X'inhi_l-Alġebra_Astratta"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>X'inhi l-Alġebra Astratta</span> </div> </a> <ul id="toc-X'inhi_l-Alġebra_Astratta-sublist" class="vector-toc-list"> <li id="toc-Gruppi—strutturi_ta’_sett_b’operazzjoni_binarja_waħda" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Gruppi—strutturi_ta’_sett_b’operazzjoni_binarja_waħda"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.1</span> <span>Gruppi—strutturi ta’ sett b’operazzjoni binarja waħda</span> </div> </a> <ul id="toc-Gruppi—strutturi_ta’_sett_b’operazzjoni_binarja_waħda-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Ċrieki_u_Kampi—strutturi_ta’_sett_b’żewġ_operazzjonijiet_binarji,_(+)_u_(×)" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Ċrieki_u_Kampi—strutturi_ta’_sett_b’żewġ_operazzjonijiet_binarji,_(+)_u_(×)"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3.2</span> <span>Ċrieki u Kampi—strutturi ta’ sett b’żewġ operazzjonijiet binarji, (+) u (×)</span> </div> </a> <ul id="toc-Ċrieki_u_Kampi—strutturi_ta’_sett_b’żewġ_operazzjonijiet_binarji,_(+)_u_(×)-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Alġebriet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Alġebriet"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.4</span> <span>Alġebriet</span> </div> </a> <ul id="toc-Alġebriet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Storja_ta'_l-alġebra" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Storja_ta'_l-alġebra"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Storja ta' l-alġebra</span> </div> </a> <ul id="toc-Storja_ta'_l-alġebra-sublist" class="vector-toc-list"> </ul> </li> </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="Kontenut" 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="Aħbi jew uri l-werrej" > <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">Aħbi jew uri l-werrej</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">Matematika</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="Żur artiklu f'lingwa differenti. Disponibbli fi 254 lingwi" > <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 lingwi</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 – Afrikans" lang="af" hreflang="af" data-title="Wiskunde" data-language-autonym="Afrikaans" data-language-local-name="Afrikans" 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 – Ġermaniż tal-Iżvizzera" lang="gsw" hreflang="gsw" data-title="Mathematik" data-language-autonym="Alemannisch" data-language-local-name="Ġermaniż tal-Iżvizzera" 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 – Amhariku" lang="am" hreflang="am" data-title="ትምህርተ ሂሳብ" data-language-autonym="አማርኛ" data-language-local-name="Amhariku" 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 – Aragoniż" lang="an" hreflang="an" data-title="Matematicas" data-language-autonym="Aragonés" data-language-local-name="Aragoniż" 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 – Ingliż Antik" lang="ang" hreflang="ang" data-title="Rīmcræft" data-language-autonym="Ænglisc" data-language-local-name="Ingliż Antik" 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 – Angika" lang="anp" hreflang="anp" data-title="गणित" data-language-autonym="अंगिका" data-language-local-name="Angika" 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 – Għarbi" lang="ar" hreflang="ar" data-title="رياضيات" data-language-autonym="العربية" data-language-local-name="Għarbi" 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 – Assamiż" lang="as" hreflang="as" data-title="গণিত" data-language-autonym="অসমীয়া" data-language-local-name="Assamiż" 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 – Asturian" lang="ast" hreflang="ast" data-title="Matemátiques" data-language-autonym="Asturianu" data-language-local-name="Asturian" 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 – Awadhi" lang="awa" hreflang="awa" data-title="गणित" data-language-autonym="अवधी" data-language-local-name="Awadhi" 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 – Aymara" lang="ay" hreflang="ay" data-title="Jakhu" data-language-autonym="Aymar aru" data-language-local-name="Aymara" 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 – Ażerbajġani" lang="az" hreflang="az" data-title="Riyaziyyat" data-language-autonym="Azərbaycanca" data-language-local-name="Ażerbajġani" 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 – Bashkir" lang="ba" hreflang="ba" data-title="Математика" data-language-autonym="Башҡортса" data-language-local-name="Bashkir" 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 – Belarussu" lang="be" hreflang="be" data-title="Матэматыка" data-language-autonym="Беларуская" data-language-local-name="Belarussu" 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 – Bulgaru" lang="bg" hreflang="bg" data-title="Математика" data-language-autonym="Български" data-language-local-name="Bulgaru" 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 – Bislama" lang="bi" hreflang="bi" data-title="Matematikis" data-language-autonym="Bislama" data-language-local-name="Bislama" 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 – Bambara" lang="bm" hreflang="bm" data-title="Matematiki" data-language-autonym="Bamanankan" data-language-local-name="Bambara" 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 – Bengali" lang="bn" hreflang="bn" data-title="গণিত" data-language-autonym="বাংলা" data-language-local-name="Bengali" 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 – Tibetjan" lang="bo" hreflang="bo" data-title="རྩིས་རིག" data-language-autonym="བོད་ཡིག" data-language-local-name="Tibetjan" 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 – Breton" lang="br" hreflang="br" data-title="Matematik" data-language-autonym="Brezhoneg" data-language-local-name="Breton" 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 – Bożnijaku" lang="bs" hreflang="bs" data-title="Matematika" data-language-autonym="Bosanski" data-language-local-name="Bożnijaku" 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 – Buginese" lang="bug" hreflang="bug" data-title="ᨆᨈᨛᨆᨈᨗᨀ" data-language-autonym="Basa Ugi" data-language-local-name="Buginese" 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 – Katalan" lang="ca" hreflang="ca" data-title="Matemàtiques" data-language-autonym="Català" data-language-local-name="Katalan" 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 – Chechen" lang="ce" hreflang="ce" data-title="Математика" data-language-autonym="Нохчийн" data-language-local-name="Chechen" 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 – Cebuano" lang="ceb" hreflang="ceb" data-title="Isip" data-language-autonym="Cebuano" data-language-local-name="Cebuano" 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 – Chamorro" lang="ch" hreflang="ch" data-title="Matematika" data-language-autonym="Chamoru" data-language-local-name="Chamorro" 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 – Kurd Ċentrali" lang="ckb" hreflang="ckb" data-title="ماتماتیک" data-language-autonym="کوردی" data-language-local-name="Kurd Ċentrali" 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 – Korsiku" lang="co" hreflang="co" data-title="Matematica" data-language-autonym="Corsu" data-language-local-name="Korsiku" 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 – Tork tal-Krimea" lang="crh" hreflang="crh" data-title="Riyaziyat" data-language-autonym="Qırımtatarca" data-language-local-name="Tork tal-Krimea" 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 – Ċek" lang="cs" hreflang="cs" data-title="Matematika" data-language-autonym="Čeština" data-language-local-name="Ċek" 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 – Slaviku tal-Knisja" lang="cu" hreflang="cu" data-title="Маѳиматїка" data-language-autonym="Словѣньскъ / ⰔⰎⰑⰂⰡⰐⰠⰔⰍⰟ" data-language-local-name="Slaviku tal-Knisja" 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 – Chuvash" lang="cv" hreflang="cv" data-title="Математика" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" 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 – Welsh" lang="cy" hreflang="cy" data-title="Mathemateg" data-language-autonym="Cymraeg" data-language-local-name="Welsh" 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 – Daniż" lang="da" hreflang="da" data-title="Matematik" data-language-autonym="Dansk" data-language-local-name="Daniż" 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 – Ġermaniż" lang="de" hreflang="de" data-title="Mathematik" data-language-autonym="Deutsch" data-language-local-name="Ġermaniż" 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 – Sorbjan Komuni" lang="dsb" hreflang="dsb" data-title="Matematika" data-language-autonym="Dolnoserbski" data-language-local-name="Sorbjan Komuni" 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 – Divehi" lang="dv" hreflang="dv" data-title="ރިޔާޟިއްޔާތު" data-language-autonym="ދިވެހިބަސް" data-language-local-name="Divehi" 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 – Grieg" lang="el" hreflang="el" data-title="Μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="Grieg" 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 – Ingliż" lang="en" hreflang="en" data-title="Mathematics" data-language-autonym="English" data-language-local-name="Ingliż" 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 – Esperanto" lang="eo" hreflang="eo" data-title="Matematiko" data-language-autonym="Esperanto" data-language-local-name="Esperanto" 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 – Spanjol" lang="es" hreflang="es" data-title="Matemáticas" data-language-autonym="Español" data-language-local-name="Spanjol" 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 – Estonjan" lang="et" hreflang="et" data-title="Matemaatika" data-language-autonym="Eesti" data-language-local-name="Estonjan" 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 – Bask" lang="eu" hreflang="eu" data-title="Matematika" data-language-autonym="Euskara" data-language-local-name="Bask" 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 – Persjan" lang="fa" hreflang="fa" data-title="ریاضیات" data-language-autonym="فارسی" data-language-local-name="Persjan" 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 – Finlandiż" lang="fi" hreflang="fi" data-title="Matematiikka" data-language-autonym="Suomi" data-language-local-name="Finlandiż" 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 – Fiġjan" lang="fj" hreflang="fj" data-title="Fika" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="Fiġjan" 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 – Faroese" lang="fo" hreflang="fo" data-title="Støddfrøði" data-language-autonym="Føroyskt" data-language-local-name="Faroese" 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 – Franċiż" lang="fr" hreflang="fr" data-title="Mathématiques" data-language-autonym="Français" data-language-local-name="Franċiż" 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 – Northern Frisian" lang="frr" hreflang="frr" data-title="Matematiik" data-language-autonym="Nordfriisk" data-language-local-name="Northern Frisian" 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 – Frijuljan" lang="fur" hreflang="fur" data-title="Matematiche" data-language-autonym="Furlan" data-language-local-name="Frijuljan" 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 – Frisian tal-Punent" lang="fy" hreflang="fy" data-title="Wiskunde" data-language-autonym="Frysk" data-language-local-name="Frisian tal-Punent" 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 – Irlandiż" lang="ga" hreflang="ga" data-title="Matamaitic" data-language-autonym="Gaeilge" data-language-local-name="Irlandiż" 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 – Galliku Skoċċiż" lang="gd" hreflang="gd" data-title="Matamataig" data-language-autonym="Gàidhlig" data-language-local-name="Galliku Skoċċiż" 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 – Galiċjan" lang="gl" hreflang="gl" data-title="Matemáticas" data-language-autonym="Galego" data-language-local-name="Galiċjan" 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 – Guarani" lang="gn" hreflang="gn" data-title="Papapykuaa" data-language-autonym="Avañe'ẽ" data-language-local-name="Guarani" 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 – Gorontalo" lang="gor" hreflang="gor" data-title="Matematika" data-language-autonym="Bahasa Hulontalo" data-language-local-name="Gorontalo" 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 – Gujarati" lang="gu" hreflang="gu" data-title="ગણિત" data-language-autonym="ગુજરાતી" data-language-local-name="Gujarati" 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 – Manx" lang="gv" hreflang="gv" data-title="Maddaght" data-language-autonym="Gaelg" data-language-local-name="Manx" 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 – Hausa" lang="ha" hreflang="ha" data-title="Lissafi" data-language-autonym="Hausa" data-language-local-name="Hausa" 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 – Ħawajjan" lang="haw" hreflang="haw" data-title="Makemakika" data-language-autonym="Hawaiʻi" data-language-local-name="Ħawajjan" 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 – Ebrajk" lang="he" hreflang="he" data-title="מתמטיקה" data-language-autonym="עברית" data-language-local-name="Ebrajk" 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 – Hindi" lang="hi" hreflang="hi" data-title="गणित" data-language-autonym="हिन्दी" data-language-local-name="Hindi" 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 – Kroat" lang="hr" hreflang="hr" data-title="Matematika" data-language-autonym="Hrvatski" data-language-local-name="Kroat" 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 – Creole ta’ Haiti" lang="ht" hreflang="ht" data-title="Matematik" data-language-autonym="Kreyòl ayisyen" data-language-local-name="Creole ta’ Haiti" 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 – Ungeriż" lang="hu" hreflang="hu" data-title="Matematika" data-language-autonym="Magyar" data-language-local-name="Ungeriż" 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 – Armen" lang="hy" hreflang="hy" data-title="Մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="Armen" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><a href="https://ia.wikipedia.org/wiki/Mathematica" title="Mathematica – Interlingua" lang="ia" hreflang="ia" data-title="Mathematica" data-language-autonym="Interlingua" data-language-local-name="Interlingua" 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 – Iban" lang="iba" hreflang="iba" data-title="Matematik" data-language-autonym="Jaku Iban" data-language-local-name="Iban" 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 – Indoneżjan" lang="id" hreflang="id" data-title="Matematika" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indoneżjan" 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 – Interlingue" lang="ie" hreflang="ie" data-title="Matematica" data-language-autonym="Interlingue" data-language-local-name="Interlingue" 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 – Igbo" lang="ig" hreflang="ig" data-title="Ọmúmú-ónúọgụgụ" data-language-autonym="Igbo" data-language-local-name="Igbo" 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 – Iloko" lang="ilo" hreflang="ilo" data-title="Matematika" data-language-autonym="Ilokano" data-language-local-name="Iloko" 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 – Ingush" lang="inh" hreflang="inh" data-title="Математика" data-language-autonym="ГӀалгӀай" data-language-local-name="Ingush" 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 – Ido" lang="io" hreflang="io" data-title="Matematiko" data-language-autonym="Ido" data-language-local-name="Ido" 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 – Iżlandiż" lang="is" hreflang="is" data-title="Stærðfræði" data-language-autonym="Íslenska" data-language-local-name="Iżlandiż" 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 – Taljan" lang="it" hreflang="it" data-title="Matematica" data-language-autonym="Italiano" data-language-local-name="Taljan" 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 – Ġappuniż" lang="ja" hreflang="ja" data-title="数学" data-language-autonym="日本語" data-language-local-name="Ġappuniż" 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 – Lojban" lang="jbo" hreflang="jbo" data-title="cmaci" data-language-autonym="La .lojban." data-language-local-name="Lojban" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><a href="https://jv.wikipedia.org/wiki/Mat%C3%A9matika" title="Matématika – Ġavaniż" lang="jv" hreflang="jv" data-title="Matématika" data-language-autonym="Jawa" data-language-local-name="Ġavaniż" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><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 – Ġorġjan" lang="ka" hreflang="ka" data-title="მათემატიკა" data-language-autonym="ქართული" data-language-local-name="Ġorġjan" 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 – Kabuljan" lang="kab" hreflang="kab" data-title="Tusnakt" data-language-autonym="Taqbaylit" data-language-local-name="Kabuljan" 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 – Każak" lang="kk" hreflang="kk" data-title="Математика" data-language-autonym="Қазақша" data-language-local-name="Każak" 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 – Kalallisut" lang="kl" hreflang="kl" data-title="Matematikki" data-language-autonym="Kalaallisut" data-language-local-name="Kalallisut" 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 – Khmer" lang="km" hreflang="km" data-title="គណិតវិទ្យា" data-language-autonym="ភាសាខ្មែរ" data-language-local-name="Khmer" 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 – Kannada" lang="kn" hreflang="kn" data-title="ಗಣಿತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" 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 – Korean" lang="ko" hreflang="ko" data-title="수학" data-language-autonym="한국어" data-language-local-name="Korean" 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 – Karachay-Balkar" lang="krc" hreflang="krc" data-title="Математика" data-language-autonym="Къарачай-малкъар" data-language-local-name="Karachay-Balkar" 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 – Kashmiri" lang="ks" hreflang="ks" data-title="گرٛؠندُت" data-language-autonym="कॉशुर / کٲشُر" data-language-local-name="Kashmiri" 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 – Kurd" lang="ku" hreflang="ku" data-title="Matematîk" data-language-autonym="Kurdî" data-language-local-name="Kurd" 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 – Korniku" lang="kw" hreflang="kw" data-title="Awgrym" data-language-autonym="Kernowek" data-language-local-name="Korniku" 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 – Kirgiż" lang="ky" hreflang="ky" data-title="Википедия:Сомо/Математика" data-language-autonym="Кыргызча" data-language-local-name="Kirgiż" class="interlanguage-link-target"><span>Кыргызча</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><a href="https://la.wikipedia.org/wiki/Mathematica" title="Mathematica – Latin" lang="la" hreflang="la" data-title="Mathematica" data-language-autonym="Latina" data-language-local-name="Latin" 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 – Ladino" lang="lad" hreflang="lad" data-title="Matemátika" data-language-autonym="Ladino" data-language-local-name="Ladino" 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 – Lussemburgiż" lang="lb" hreflang="lb" data-title="Mathematik" data-language-autonym="Lëtzebuergesch" data-language-local-name="Lussemburgiż" 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 – Leżgjan" lang="lez" hreflang="lez" data-title="Математика" data-language-autonym="Лезги" data-language-local-name="Leżgjan" 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 – Ganda" lang="lg" hreflang="lg" data-title="Ekibalangulo" data-language-autonym="Luganda" data-language-local-name="Ganda" 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 – Limburgish" lang="li" hreflang="li" data-title="Mathematiek" data-language-autonym="Limburgs" data-language-local-name="Limburgish" 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 – Ligurian" lang="lij" hreflang="lij" data-title="Matematica" data-language-autonym="Ligure" data-language-local-name="Ligurian" 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 – Laosjan" lang="lo" hreflang="lo" data-title="ຄະນິດສາດ" data-language-autonym="ລາວ" data-language-local-name="Laosjan" 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 – Litwan" lang="lt" hreflang="lt" data-title="Matematika" data-language-autonym="Lietuvių" data-language-local-name="Litwan" 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 – Latvjan" lang="lv" hreflang="lv" data-title="Matemātika" data-language-autonym="Latviešu" data-language-local-name="Latvjan" 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 – Maduriż" lang="mad" hreflang="mad" data-title="Matematika" data-language-autonym="Madhurâ" data-language-local-name="Maduriż" 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 – Maithili" lang="mai" hreflang="mai" data-title="गणित" data-language-autonym="मैथिली" data-language-local-name="Maithili" 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 – Malagasy" lang="mg" hreflang="mg" data-title="Matematika" data-language-autonym="Malagasy" data-language-local-name="Malagasy" 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 – Minangkabau" lang="min" hreflang="min" data-title="Matematika" data-language-autonym="Minangkabau" data-language-local-name="Minangkabau" 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 – Maċedonjan" lang="mk" hreflang="mk" data-title="Математика" data-language-autonym="Македонски" data-language-local-name="Maċedonjan" 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 – Malayalam" lang="ml" hreflang="ml" data-title="ഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><a href="https://mn.wikipedia.org/wiki/%D0%9C%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA" title="Математик – Mongoljan" lang="mn" hreflang="mn" data-title="Математик" data-language-autonym="Монгол" data-language-local-name="Mongoljan" class="interlanguage-link-target"><span>Монгол</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 – Manipuri" lang="mni" hreflang="mni" data-title="ꯆꯩꯁꯤꯡꯂꯣꯟ" data-language-autonym="ꯃꯤꯇꯩ ꯂꯣꯟ" data-language-local-name="Manipuri" 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 – Marathi" lang="mr" hreflang="mr" data-title="गणित" data-language-autonym="मराठी" data-language-local-name="Marathi" 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 – Malay" lang="ms" hreflang="ms" data-title="Matematik" data-language-autonym="Bahasa Melayu" data-language-local-name="Malay" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mwl mw-list-item"><a href="https://mwl.wikipedia.org/wiki/Matem%C3%A1tica" title="Matemática – Mirandiż" lang="mwl" hreflang="mwl" data-title="Matemática" data-language-autonym="Mirandés" data-language-local-name="Mirandiż" 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 – Burmiż" lang="my" hreflang="my" data-title="သင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="Burmiż" 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 – Erzya" lang="myv" hreflang="myv" data-title="Математика" data-language-autonym="Эрзянь" data-language-local-name="Erzya" 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 – Mazanderani" lang="mzn" hreflang="mzn" data-title="رقم" data-language-autonym="مازِرونی" data-language-local-name="Mazanderani" 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 – Ġermaniż Komuni" lang="nds" hreflang="nds" data-title="Mathematik" data-language-autonym="Plattdüütsch" data-language-local-name="Ġermaniż Komuni" 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 – Sassonu Komuni" lang="nds-NL" hreflang="nds-NL" data-title="Wiskunde" data-language-autonym="Nedersaksies" data-language-local-name="Sassonu Komuni" 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 – Nepaliż" lang="ne" hreflang="ne" data-title="गणित" data-language-autonym="नेपाली" data-language-local-name="Nepaliż" 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 – Newari" lang="new" hreflang="new" data-title="ल्याःज्या" data-language-autonym="नेपाल भाषा" data-language-local-name="Newari" 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 – Nijas" lang="nia" hreflang="nia" data-title="Matematika" data-language-autonym="Li Niha" data-language-local-name="Nijas" 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 – Olandiż" lang="nl" hreflang="nl" data-title="Wiskunde" data-language-autonym="Nederlands" data-language-local-name="Olandiż" 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 – Ninorsk Norveġiż" lang="nn" hreflang="nn" data-title="Matematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="Ninorsk Norveġiż" 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 – Bokmal Norveġiż" lang="nb" hreflang="nb" data-title="Matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmal Norveġiż" 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 – Navajo" lang="nv" hreflang="nv" data-title="Ałhiiʼnínáʼiidzóóh" data-language-autonym="Diné bizaad" data-language-local-name="Navajo" 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 – Oċċitan" lang="oc" hreflang="oc" data-title="Matematicas" data-language-autonym="Occitan" data-language-local-name="Oċċitan" 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 – Oromo" lang="om" hreflang="om" data-title="Herrega" data-language-autonym="Oromoo" data-language-local-name="Oromo" 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 – Odia" lang="or" hreflang="or" data-title="ଗଣିତ" data-language-autonym="ଓଡ଼ିଆ" data-language-local-name="Odia" 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 – Ossettiku" lang="os" hreflang="os" data-title="Математикæ" data-language-autonym="Ирон" data-language-local-name="Ossettiku" 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 – Punjabi" lang="pa" hreflang="pa" data-title="ਗਣਿਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="Punjabi" 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 – Pangasinjan" lang="pag" hreflang="pag" data-title="Matematiks" data-language-autonym="Pangasinan" data-language-local-name="Pangasinjan" 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 – Pampanga" lang="pam" hreflang="pam" data-title="Matematica" data-language-autonym="Kapampangan" data-language-local-name="Pampanga" 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 – Papiamento" lang="pap" hreflang="pap" data-title="Matemátika" data-language-autonym="Papiamentu" data-language-local-name="Papiamento" 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 – Pollakk" lang="pl" hreflang="pl" data-title="Matematyka" data-language-autonym="Polski" data-language-local-name="Pollakk" 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 – Pashto" lang="ps" hreflang="ps" data-title="شمېرپوهنه" data-language-autonym="پښتو" data-language-local-name="Pashto" 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 – Portugiż" lang="pt" hreflang="pt" data-title="Matemática" data-language-autonym="Português" data-language-local-name="Portugiż" 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 – Quechua" lang="qu" hreflang="qu" data-title="Yupay yachay" data-language-autonym="Runa Simi" data-language-local-name="Quechua" 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 – Rumen" lang="ro" hreflang="ro" data-title="Matematică" data-language-autonym="Română" data-language-local-name="Rumen" 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 – Aromanjan" lang="rup" hreflang="rup" data-title="Mathematicâ" data-language-autonym="Armãneashti" data-language-local-name="Aromanjan" 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 – Russu" lang="ru" hreflang="ru" data-title="Математика" data-language-autonym="Русский" data-language-local-name="Russu" 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 – Sanskrit" lang="sa" hreflang="sa" data-title="गणितम्" data-language-autonym="संस्कृतम्" data-language-local-name="Sanskrit" 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 – Sakha" lang="sah" hreflang="sah" data-title="Математика" data-language-autonym="Саха тыла" data-language-local-name="Sakha" 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 – Santali" lang="sat" hreflang="sat" data-title="ᱮᱞᱠᱷᱟ" data-language-autonym="ᱥᱟᱱᱛᱟᱲᱤ" data-language-local-name="Santali" class="interlanguage-link-target"><span>ᱥᱟᱱᱛᱟᱲᱤ</span></a></li><li class="interlanguage-link interwiki-sc badge-Q17437796 badge-featuredarticle mw-list-item" title="vetrina"><a href="https://sc.wikipedia.org/wiki/Matem%C3%A0tica" title="Matemàtica – Sardinjan" lang="sc" hreflang="sc" data-title="Matemàtica" data-language-autonym="Sardu" data-language-local-name="Sardinjan" 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 – Sqalli" lang="scn" hreflang="scn" data-title="Matimàtica" data-language-autonym="Sicilianu" data-language-local-name="Sqalli" 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 – Skoċċiż" lang="sco" hreflang="sco" data-title="Mathematics" data-language-autonym="Scots" data-language-local-name="Skoċċiż" 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 – Sindhi" lang="sd" hreflang="sd" data-title="رياضي" data-language-autonym="سنڌي" data-language-local-name="Sindhi" 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 – Serbo-Kroat" lang="sh" hreflang="sh" data-title="Matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="Serbo-Kroat" 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 – Tachelhit" lang="shi" hreflang="shi" data-title="Tusnakt" data-language-autonym="Taclḥit" data-language-local-name="Tachelhit" 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 – Sinhala" lang="si" hreflang="si" data-title="ගණිතය" data-language-autonym="සිංහල" data-language-local-name="Sinhala" 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 – Slovakk" lang="sk" hreflang="sk" data-title="Matematika" data-language-autonym="Slovenčina" data-language-local-name="Slovakk" 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 – Sloven" lang="sl" hreflang="sl" data-title="Matematika" data-language-autonym="Slovenščina" data-language-local-name="Sloven" 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 – Samoan" lang="sm" hreflang="sm" data-title="Matematika" data-language-autonym="Gagana Samoa" data-language-local-name="Samoan" 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 – Shona" lang="sn" hreflang="sn" data-title="Masvomhu" data-language-autonym="ChiShona" data-language-local-name="Shona" 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 – Somali" lang="so" hreflang="so" data-title="Tiromaal" data-language-autonym="Soomaaliga" data-language-local-name="Somali" 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 – Albaniż" lang="sq" hreflang="sq" data-title="Matematika" data-language-autonym="Shqip" data-language-local-name="Albaniż" 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 – Serb" lang="sr" hreflang="sr" data-title="Математика" data-language-autonym="Српски / srpski" data-language-local-name="Serb" 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 – Sranan Tongo" lang="srn" hreflang="srn" data-title="Sabi fu Teri" data-language-autonym="Sranantongo" data-language-local-name="Sranan Tongo" 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 – Swati" lang="ss" hreflang="ss" data-title="Tekubala" data-language-autonym="SiSwati" data-language-local-name="Swati" 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 – Sundaniż" lang="su" hreflang="su" data-title="Matematika" data-language-autonym="Sunda" data-language-local-name="Sundaniż" 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 – Żvediż" lang="sv" hreflang="sv" data-title="Matematik" data-language-autonym="Svenska" data-language-local-name="Żvediż" 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 – Swahili" lang="sw" hreflang="sw" data-title="Hisabati" data-language-autonym="Kiswahili" data-language-local-name="Swahili" 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 – Tamil" lang="ta" hreflang="ta" data-title="கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="Tamil" 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 – Telugu" lang="te" hreflang="te" data-title="గణితం" data-language-autonym="తెలుగు" data-language-local-name="Telugu" 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 – Tetum" lang="tet" hreflang="tet" data-title="Matemátika" data-language-autonym="Tetun" data-language-local-name="Tetum" 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 – Taġik" lang="tg" hreflang="tg" data-title="Риёзиёт" data-language-autonym="Тоҷикӣ" data-language-local-name="Taġik" 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 – Tajlandiż" lang="th" hreflang="th" data-title="คณิตศาสตร์" data-language-autonym="ไทย" data-language-local-name="Tajlandiż" 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 – Turkmeni" lang="tk" hreflang="tk" data-title="Matematika" data-language-autonym="Türkmençe" data-language-local-name="Turkmeni" 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 – Tswana" lang="tn" hreflang="tn" data-title="Dipalo" data-language-autonym="Setswana" data-language-local-name="Tswana" 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 – Tok Pisin" lang="tpi" hreflang="tpi" data-title="Ol matematik" data-language-autonym="Tok Pisin" data-language-local-name="Tok Pisin" 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 – Tork" lang="tr" hreflang="tr" data-title="Matematik" data-language-autonym="Türkçe" data-language-local-name="Tork" 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 – Tsonga" lang="ts" hreflang="ts" data-title="Dyondzo-Tinhlayo" data-language-autonym="Xitsonga" data-language-local-name="Tsonga" 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 – Tatar" lang="tt" hreflang="tt" data-title="Математика" data-language-autonym="Татарча / tatarça" data-language-local-name="Tatar" 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 – Udmurt" lang="udm" hreflang="udm" data-title="Математика" data-language-autonym="Удмурт" data-language-local-name="Udmurt" 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 – Ukren" lang="uk" hreflang="uk" data-title="Математика" data-language-autonym="Українська" data-language-local-name="Ukren" 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 – Urdu" lang="ur" hreflang="ur" data-title="ریاضی" data-language-autonym="اردو" data-language-local-name="Urdu" 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 – Uzbek" lang="uz" hreflang="uz" data-title="Matematika" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" 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 – Venetian" lang="vec" hreflang="vec" data-title="Matemàtega" data-language-autonym="Vèneto" data-language-local-name="Venetian" 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 – Vjetnamiż" lang="vi" hreflang="vi" data-title="Toán học" data-language-autonym="Tiếng Việt" data-language-local-name="Vjetnamiż" 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="vetrina"><a href="https://vo.wikipedia.org/wiki/Matemat" title="Matemat – Volapuk" lang="vo" hreflang="vo" data-title="Matemat" data-language-autonym="Volapük" data-language-local-name="Volapuk" 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 – Walloon" lang="wa" hreflang="wa" data-title="Matematike" data-language-autonym="Walon" data-language-local-name="Walloon" 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 – Waray" lang="war" hreflang="war" data-title="Matematika" data-language-autonym="Winaray" data-language-local-name="Waray" 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 – Wolof" lang="wo" hreflang="wo" data-title="Xayma" data-language-autonym="Wolof" data-language-local-name="Wolof" 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 – Wu" lang="wuu" hreflang="wuu" data-title="数学" data-language-autonym="吴语" data-language-local-name="Wu" 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 – Kalmyk" lang="xal" hreflang="xal" data-title="Математика" data-language-autonym="Хальмг" data-language-local-name="Kalmyk" 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 – Xhosa" lang="xh" hreflang="xh" data-title="I-Mathematics" data-language-autonym="IsiXhosa" data-language-local-name="Xhosa" 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 – Yiddish" lang="yi" hreflang="yi" data-title="מאטעמאטיק" data-language-autonym="ייִדיש" data-language-local-name="Yiddish" 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 – Yoruba" lang="yo" hreflang="yo" data-title="Mathimátíkì" data-language-autonym="Yorùbá" data-language-local-name="Yoruba" 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 – Tamazight Standard tal-Marokk" lang="zgh" hreflang="zgh" data-title="ⵜⵓⵙⵏⴰⴽⵜ" data-language-autonym="ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ" data-language-local-name="Tamazight Standard tal-Marokk" class="interlanguage-link-target"><span>ⵜⴰⵎⴰⵣⵉⵖⵜ ⵜⴰⵏⴰⵡⴰⵢⵜ</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B0%E5%AD%A6" title="数学 – Ċiniż" lang="zh" hreflang="zh" data-title="数学" data-language-autonym="中文" data-language-local-name="Ċiniż" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="數學" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C3%B2%CD%98-ha%CC%8Dk" title="Sò͘-ha̍k – Minnan" lang="nan" hreflang="nan" data-title="Sò͘-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B8%E5%AD%B8" title="數學 – Kantoniż" lang="yue" hreflang="yue" data-title="數學" data-language-autonym="粵語" data-language-local-name="Kantoniż" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zu mw-list-item"><a href="https://zu.wikipedia.org/wiki/Umchazazibalo" title="Umchazazibalo – Zulu" lang="zu" hreflang="zu" data-title="Umchazazibalo" 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class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q395" title="Ħolqa għall-element konness tal-arkivju tad-dejta [g]" accesskey="g"><span>Element ta' Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Għodda tal-paġna"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Dehra"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Dehra</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">mexxi għall-ġenb</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">aħbi</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Minn Wikipedija, l-enċiklopedija l-ħielsa</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="mt" dir="ltr"><p>Il-kelma <b>Matematika</b> ġejja mill-<a href="/wiki/Lingwa_Griega" title="Lingwa Griega">Grieg</a> μάθημα (<i>máthema</i>), li tfisser "tgħalim", jew "xjenza"; μαθηματικός (<i>mathematikós</i>) tfisser "wieħed li jrid jitgħallem". </p><p>Fid-dixxiplina tal-Matematika nistudjaw problemi dwar il-kwantità, estensjoni u figuri spazjali, moviment tal-korpi, u l-istrutturi kollha fejn nistgħu neżaminaw dawn l-aspetti b'mod ġenerali. </p><p>Il-<b>Matematika</b> għandha tradizzjoni qadima fil-ġnus kollha; kienet l-ewwel dixxiplina li adottat metodi rigorużi ħafna, u b'hekk laħqet l-istatus ta’ <a href="/wiki/Xjenza" title="Xjenza">xjenza</a>; progressivament il-metodi tagħha żviluppaw u nfirxu ma ħafna oqsma fejn jistgħu ikunu ta’ għajnuna fil-komputazzjoni u l-immudellar. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Storja">Storja</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=1" title="Editja s-sezzjoni: Storja" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=1" title="Edit section's source code: Storja"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dd><i>Biex tapprofondixxi, ara l-artiklu: <a href="/wiki/Kronolo%C4%A1ija_tal-matematika" title="Kronoloġija tal-matematika">Kronoloġija tal-matematika</a></i>.</dd></dl> <div class="plainlinks" style="margin-left:2em; margin-bottom:0.5em; border-top:1px solid #ccc; border-bottom:1px solid #ccc; padding:2px; text-align:left; font-size:95%;"><span typeof="mw:File"><a href="/wiki/Stampa:Fairytale_warning.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/15px-Fairytale_warning.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/23px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/30px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span> Din is-sezzjoni għadha vojta. <span class="plainlinks"><a class="external text" href="https://mt.wikipedia.org/w/index.php?title=Matematika&action=edit&section=1">Għinna</a></span> biex niktbuha!</div> <div class="mw-heading mw-heading2"><h2 id="Analisi_Matematika">Analisi Matematika</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=2" title="Editja s-sezzjoni: Analisi Matematika" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=2" title="Edit section's source code: Analisi Matematika"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-<b>analisi matematika</b> bdiet mill-formulazzjoni rigoruża tal-<a href="/w/index.php?title=Kalkulu_infinite%C5%BCmali&action=edit&redlink=1" class="new" title="Kalkulu infiniteżmali (il-paġna ma teżistix)">kalkulu infiniteżmali</a>. Hija fergħa tal-<a class="mw-selflink selflink">matematika</a> li tikkonċentra fuq l-ideja tal-<a href="/w/index.php?title=Limitu_(matematika)&action=edit&redlink=1" class="new" title="Limitu (matematika) (il-paġna ma teżistix)">limitu</a>: il-<a href="/w/index.php?title=Limitu_ta%E2%80%99_su%C4%8B%C4%8Bessjoni&action=edit&redlink=1" class="new" title="Limitu ta’ suċċessjoni (il-paġna ma teżistix)">limitu ta’ suċċessjoni</a> jew il-<a href="/w/index.php?title=Limitu_ta%E2%80%99_funzjoni&action=edit&redlink=1" class="new" title="Limitu ta’ funzjoni (il-paġna ma teżistix)">limitu ta’ funzjoni</a>. Tinkludi wkoll it-teoriji tad-<a href="/wiki/Derivata" title="Derivata">differenzazzjoni</a>, <a href="/wiki/Integral" class="mw-redirect" title="Integral">integrazzjoni</a> u <a href="/w/index.php?title=Me%C5%BCura_(matematika)&action=edit&redlink=1" class="new" title="Meżura (matematika) (il-paġna ma teżistix)">meżura</a>, <a href="/w/index.php?title=Serje_(matematika)&action=edit&redlink=1" class="new" title="Serje (matematika) (il-paġna ma teżistix)">serji infiniti</a>, u <a href="/w/index.php?title=Funzjoni_analitika&action=edit&redlink=1" class="new" title="Funzjoni analitika (il-paġna ma teżistix)">funzjonijiet analitiċi</a>. L-istudju ta’ dawn it-teoriji ħafna drabi jsir fil-kuntest tan-<a href="/w/index.php?title=Numru_reali&action=edit&redlink=1" class="new" title="Numru reali (il-paġna ma teżistix)">numri reali</a>, <a href="/w/index.php?title=Numru_kompless&action=edit&redlink=1" class="new" title="Numru kompless (il-paġna ma teżistix)">numri komplessi</a>, u <a href="/w/index.php?title=Funzjoni_(matematika)&action=edit&redlink=1" class="new" title="Funzjoni (matematika) (il-paġna ma teżistix)">funzjonijiet</a> reali u komplessi. Madankollu, nistgħu niddefinixxu u nistudjaw dawn it-teoriji f’kull <a href="/w/index.php?title=Spazju&action=edit&redlink=1" class="new" title="Spazju (il-paġna ma teżistix)">spazju</a> ta’ oġġetti matematiċi li fih hu possibbli li nagħtu definizzjoni ta’ "distanza" (<a href="/w/index.php?title=Spazju_metriku&action=edit&redlink=1" class="new" title="Spazju metriku (il-paġna ma teżistix)">spazju metriku</a>) jew iżjed ġenerali ta’ "qrubija" (<a href="/w/index.php?title=Spazju_topolo%C4%A1iku&action=edit&redlink=1" class="new" title="Spazju topoloġiku (il-paġna ma teżistix)">spazju topoloġiku</a>). </p> <div class="mw-heading mw-heading3"><h3 id="Għaliex_l-Analisi_Astratta?"><span id="G.C4.A7aliex_l-Analisi_Astratta.3F"></span>Għaliex l-Analisi Astratta?</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=3" title="Editja s-sezzjoni: Għaliex l-Analisi Astratta?" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=3" title="Edit section's source code: Għaliex l-Analisi Astratta?"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Stampa:Hilbert.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/200px-Hilbert.jpg" decoding="async" width="200" height="271" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/300px-Hilbert.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/79/Hilbert.jpg/400px-Hilbert.jpg 2x" data-file-width="437" data-file-height="592" /></a><figcaption> David Hilbert t.1862 m.1943</figcaption></figure> <p>Għandna nistudjaw l-analisi matematika fil-kuntest iżjed wiesa' ta’ l-ispazji topologiċi jew spazji metriċi għal żewġ raġunijiet: </p> <ul><li>l-ewwel, għax l-istess metodi bażiċi ħafna drabi japplikaw għal klassi ta’ problemi li hi ħafna usa’ (pereżempju, l-istudju ta’ <a href="/w/index.php?title=Analisi_Funzjonali&action=edit&redlink=1" class="new" title="Analisi Funzjonali (il-paġna ma teżistix)">spazji ta’ funzjonijiet</a>).</li></ul> <ul><li>it-tieni, u mhux inqas importanti, għax meta nifhmu l-analisi fi spazji aktar astratti sikwit nsibu li nistgħu napplikawha direttament għal problemi klassiċi. Pereżempju, fl-<a href="/wiki/Analisi_armonika" title="Analisi armonika">analisi ta’ Fourier</a>, nistgħu nesprimu kull funzjoni bħala ċerta serje infinita (ta’ funzjonijiet trigonometriċi jew esponenzjali komplessi). Fiżikament, b’din id-dekompożizzjoni nirriduċu mewġa (tal-ħoss) arbitrarja fil-frekwenzi li jikkomponuha. Il "piżijiet" jew koeffiċjenti tat-termini fl-espansjoni ta’ Fourier ta’ funzjoni, jistgħu jitqiesu bħala l-komponenti ta’ vettur fi spazju ta’ dimensjoni infinita li nsibuh bħala <a href="/w/index.php?title=Spazju_ta%E2%80%99_Hilbert&action=edit&redlink=1" class="new" title="Spazju ta’ Hilbert (il-paġna ma teżistix)">spazju ta’ Hilbert</a>. Mela l-istudju tal-funzjonijiet definiti f’dil-qagħda iżjed ġenerali jipprovdi metodu konvenjenti għad-derivazzjoni ta’ riżultati fuq kif il-funzjonijiet ivarjaw fl-ispazju u mal-ħin, jew f’termini aktar matematiċi fuq l-<a href="/wiki/Ekwazzjoni_differenzjali" title="Ekwazzjoni differenzjali">ekwazzjonijiet differenzjali parzjali</a>, fejn din it-teknika nafuha bħala separazzjoni tal-<a href="/wiki/Varjabbli" title="Varjabbli">varjabbli</a>.</li></ul> <div class="mw-heading mw-heading3"><h3 id="Storja_tal-Analisi_Matematika">Storja tal-Analisi Matematika</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=4" title="Editja s-sezzjoni: Storja tal-Analisi Matematika" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=4" title="Edit section's source code: Storja tal-Analisi Matematika"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il-<a href="/w/index.php?title=MatematikuGrieg&action=edit&redlink=1" class="new" title="MatematikuGrieg (il-paġna ma teżistix)">matematiċi Griegi</a> bħal <a href="/w/index.php?title=Ewdossu_ta%E2%80%99_Knidu&action=edit&redlink=1" class="new" title="Ewdossu ta’ Knidu (il-paġna ma teżistix)">Ewdossu</a> u <a href="/wiki/Arkimede" title="Arkimede">Arkimede</a> meta applikaw il-<a href="/w/index.php?title=Metodu_ta%E2%80%99_l-e%C5%BCawriment&action=edit&redlink=1" class="new" title="Metodu ta’ l-eżawriment (il-paġna ma teżistix)">metodu ta’ l-eżawriment</a> biex jikkalkulaw l-arja u l-volum ta’ xi reġjuni u solidi użaw il-kunċetti tal-limiti u l-konvergenza b’mod informali. Fl-<a href="/w/index.php?title=Matematiku_Indjan&action=edit&redlink=1" class="new" title="Matematiku Indjan (il-paġna ma teżistix)">Indja</a>, il-matematiku tas-<a href="/w/index.php?title=Seklu_12&action=edit&redlink=1" class="new" title="Seklu 12 (il-paġna ma teżistix)">seklu 12</a>, <a href="/w/index.php?title=Bhaskara&action=edit&redlink=1" class="new" title="Bhaskara (il-paġna ma teżistix)">Bhaskara</a> ġa kellu l-ideja tal-<a href="/w/index.php?title=Kalkulu_differenzjali&action=edit&redlink=1" class="new" title="Kalkulu differenzjali (il-paġna ma teżistix)">kalkulu differenzjali</a> u ta eżempji tad-<a href="/wiki/Derivata" title="Derivata">derivata</a>, flimkien mal-propożizzjoni ta’ dik li nsejħulu llum it-<a href="/w/index.php?title=Teorema_ta%E2%80%99_Rolle&action=edit&redlink=1" class="new" title="Teorema ta’ Rolle (il-paġna ma teżistix)">Teorema ta’ Rolle</a>. </p><p>Fis-<a href="/w/index.php?title=Seklu_14&action=edit&redlink=1" class="new" title="Seklu 14 (il-paġna ma teżistix)">seklu 14</a>, l-analisi matematika bdiha <a href="/w/index.php?title=Madhava_ta%E2%80%99_Sangamagrama&action=edit&redlink=1" class="new" title="Madhava ta’ Sangamagrama (il-paġna ma teżistix)">Madhava ta’ Sangamagrama</a>, meqjus bħala l-"<a href="/w/index.php?title=Fundatur_ta%E2%80%99l-analisi_matematika&action=edit&redlink=1" class="new" title="Fundatur ta’l-analisi matematika (il-paġna ma teżistix)">fundatur ta’l-analisi matematika</a>". Hu żviluppa idejat fundamentali: l-iżvilupp ta’ funzjoni f’<a href="/w/index.php?title=Serje_infinita&action=edit&redlink=1" class="new" title="Serje infinita (il-paġna ma teżistix)">serje infinita</a>, <a href="/w/index.php?title=Serje_ta%E2%80%99_potenzi&action=edit&redlink=1" class="new" title="Serje ta’ potenzi (il-paġna ma teżistix)">serje ta’ potenzi</a>, is-<a href="/w/index.php?title=Serje_ta%E2%80%99_Taylor&action=edit&redlink=1" class="new" title="Serje ta’ Taylor (il-paġna ma teżistix)">serje ta’ Taylor</a>, u l-approssimazzjoni razzjonali ta’ serje infinita. Żviluppa wkoll is-serje ta’ Taylor għall-<a href="/w/index.php?title=Funzjonijiet_trigonometri%C4%8Bi&action=edit&redlink=1" class="new" title="Funzjonijiet trigonometriċi (il-paġna ma teżistix)">funzjonijiet trigonometriċi</a> tas-<a href="/w/index.php?title=Senu&action=edit&redlink=1" class="new" title="Senu (il-paġna ma teżistix)">senu</a>, <a href="/w/index.php?title=Kosenu&action=edit&redlink=1" class="new" title="Kosenu (il-paġna ma teżistix)">kosenu</a>, <a href="/w/index.php?title=Tan%C4%A1enti&action=edit&redlink=1" class="new" title="Tanġenti (il-paġna ma teżistix)">tanġenti</a> u <a href="/w/index.php?title=Arktan%C4%A1enti&action=edit&redlink=1" class="new" title="Arktanġenti (il-paġna ma teżistix)">arktanġenti</a>, u stima l-iżbal li nagħmlu meta naqtgħu is-serje. Żviluppa l-<a href="/w/index.php?title=Frazzjonijiet_kontinwati&action=edit&redlink=1" class="new" title="Frazzjonijiet kontinwati (il-paġna ma teżistix)">frazzjonijiet kontinwati</a> infiniti, l-<a href="/wiki/Integral" class="mw-redirect" title="Integral">integrazzjoni</a> b’termini wara termini, l-approssimazzjoni b’serje ta’ Taylor tas-senu u kosenu, u s-serje f’potenzi tar-<a href="/w/index.php?title=Ra%C4%A1%C4%A1&action=edit&redlink=1" class="new" title="Raġġ (il-paġna ma teżistix)">raġġ</a>, <a href="/w/index.php?title=Diametru&action=edit&redlink=1" class="new" title="Diametru (il-paġna ma teżistix)">diametru</a>, <a href="/w/index.php?title=%C4%8Airkonferenza&action=edit&redlink=1" class="new" title="Ċirkonferenza (il-paġna ma teżistix)">ċirkonferenza</a>, <a href="/w/index.php?title=%CE%A0&action=edit&redlink=1" class="new" title="Π (il-paġna ma teżistix)">π</a>, π/4 u l-anglu <a href="/w/index.php?title=%CE%98&action=edit&redlink=1" class="new" title="Θ (il-paġna ma teżistix)">θ</a>. Id-dixxipli tiegħu fl-i<a href="/w/index.php?title=Skola_ta%E2%80%99_Kerala&action=edit&redlink=1" class="new" title="Skola ta’ Kerala (il-paġna ma teżistix)">Skola ta’ Kerala</a> baqgħu ikkabru x-xogħol tiegħu sas-<a href="/w/index.php?title=Seklu_16&action=edit&redlink=1" class="new" title="Seklu 16 (il-paġna ma teżistix)">seklu 16</a>. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Stampa:Gottfried_Wilhelm_von_Leibniz.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg/200px-Gottfried_Wilhelm_von_Leibniz.jpg" decoding="async" width="200" height="253" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg/300px-Gottfried_Wilhelm_von_Leibniz.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/6/6a/Gottfried_Wilhelm_von_Leibniz.jpg 2x" data-file-width="316" data-file-height="400" /></a><figcaption>Gottfried Leibniz t.1646 m.1716</figcaption></figure> <p>Fl-Ewropa, fit-tieni nofs tas-<a href="/wiki/Seklu_17" title="Seklu 17">seklu 17</a>, <a href="/wiki/Isaac_Newton" title="Isaac Newton">Newton</a> u <a href="/w/index.php?title=Gottfried_Leibniz&action=edit&redlink=1" class="new" title="Gottfried Leibniz (il-paġna ma teżistix)">Leibniz</a> independement minn xulxien żviluppaw il-kalkulu, li bl-istimulu ta’ l-applikazzjonijiet matul is-<a href="/w/index.php?title=Seklu_18&action=edit&redlink=1" class="new" title="Seklu 18 (il-paġna ma teżistix)">seklu 18</a> rabba ħafna friegħi bħall-<a href="/wiki/Kalkulu_tal-varjazzjonijiet" title="Kalkulu tal-varjazzjonijiet">kalkulu tal-varjazzjonijiet</a>, l-<a href="/w/index.php?title=Ekwazzjonijiet_differenzjali_ordinarji&action=edit&redlink=1" class="new" title="Ekwazzjonijiet differenzjali ordinarji (il-paġna ma teżistix)">ekwazzjonijiet differenzjali ordinarji</a> u <a href="/w/index.php?title=Parzjali&action=edit&redlink=1" class="new" title="Parzjali (il-paġna ma teżistix)">parzjali</a> u l-<a href="/w/index.php?title=Analisi_ta%E2%80%99_Fourier&action=edit&redlink=1" class="new" title="Analisi ta’ Fourier (il-paġna ma teżistix)">analisi ta’ Fourier</a> . F’dal-perijodu, il-metodi tal-kalkulu ġew applikati biex japprossimaw <a href="/w/index.php?title=Problemi_diskreti&action=edit&redlink=1" class="new" title="Problemi diskreti (il-paġna ma teżistix)">problemi diskreti</a> b’oħrajn kontinwi. </p><p>Fis-<a href="/w/index.php?title=Seklu18&action=edit&redlink=1" class="new" title="Seklu18 (il-paġna ma teżistix)">seklu18</a>, <a href="/w/index.php?title=Leonard_Euler&action=edit&redlink=1" class="new" title="Leonard Euler (il-paġna ma teżistix)">Euler</a> introduċa il-kunċett ta’ <a href="/wiki/Funzjonijiet_(matematika)" title="Funzjonijiet (matematika)">funzjoni matematika</a>. Fis-<a href="/w/index.php?title=Seklu19&action=edit&redlink=1" class="new" title="Seklu19 (il-paġna ma teżistix)">seklu19</a>, <a href="/w/index.php?title=Augustin_Louis_Cauchy&action=edit&redlink=1" class="new" title="Augustin Louis Cauchy (il-paġna ma teżistix)">Cauchy</a> kien l-ewwel li stabbilixa l-kalkulu fuq pedament loġiku sod bl-introduzzjoni ta’ l-ideja tas-<a href="/w/index.php?title=Su%C4%8B%C4%8Bessjoni_ta%E2%80%99_Cauchy&action=edit&redlink=1" class="new" title="Suċċessjoni ta’ Cauchy (il-paġna ma teżistix)">suċċessjoni ta’ Cauchy</a>. Beda wkoll it-teorija formali ta’ l-<a href="/wiki/Analisi_komplessa" title="Analisi komplessa">analisi komplessa</a>. <a href="/w/index.php?title=Simeon_Poisson&action=edit&redlink=1" class="new" title="Simeon Poisson (il-paġna ma teżistix)">Poisson</a>, <a href="/w/index.php?title=Liouville&action=edit&redlink=1" class="new" title="Liouville (il-paġna ma teżistix)">Liouville</a>, <a href="/w/index.php?title=Jean-Baptiste_Joseph_Fourier&action=edit&redlink=1" class="new" title="Jean-Baptiste Joseph Fourier (il-paġna ma teżistix)">Fourier</a> u oħrajn studjaw l-ekwazzjonijiet differenzjali parzjali u l-<a href="/wiki/Analisi_armonika" title="Analisi armonika">analisi armonika</a>. </p><p>F’nofs is-seklu <a href="/w/index.php?title=Bernhard_Riemann&action=edit&redlink=1" class="new" title="Bernhard Riemann (il-paġna ma teżistix)">Riemann</a> introduċa t-teorija tiegħu tal-<a href="/wiki/Integral" class="mw-redirect" title="Integral">integrazzjoni</a>. F’l-aħħar terz tas-seklu 19, <a href="/wiki/Karl_Weierstrass" title="Karl Weierstrass">Weierstrass</a> li l-fehma tiegħu kienet li l-argumenti ġometriċi jistgħu iqarqu bina, daħħal l-aritmetizzazzjoni ta’ l-analisi u introduċa id-definizzjoni "epsilon-delta" tal-<a href="/w/index.php?title=Limitu&action=edit&redlink=1" class="new" title="Limitu (il-paġna ma teżistix)">limitu</a>. Wara, il-matematiċi bdew jinkwietaw li kienu qegħdin jassumu l-eżistenza tal-<a href="/w/index.php?title=Kontinwu&action=edit&redlink=1" class="new" title="Kontinwu (il-paġna ma teżistix)">kontinwu</a> tan-<a href="/w/index.php?title=Numri_reali&action=edit&redlink=1" class="new" title="Numri reali (il-paġna ma teżistix)">numri reali</a> mingħajr prova. <a href="/w/index.php?title=Dedekind&action=edit&redlink=1" class="new" title="Dedekind (il-paġna ma teżistix)">Dedekind</a> imbagħad ta kostruzzjoni tan-numri reali bil-methodu tal-<a href="/w/index.php?title=Qtug%C4%A7_ta%E2%80%99_Dedekind&action=edit&redlink=1" class="new" title="Qtugħ ta’ Dedekind (il-paġna ma teżistix)">qtugħ ta’ Dedekind</a>, li bih il-matematiċi jikkrejaw numri rrazzjonali li jimlew il-"vojt" bejn in-numri razzjonali, u hekk joħolqu sett <a href="/w/index.php?title=Komplet&action=edit&redlink=1" class="new" title="Komplet (il-paġna ma teżistix)">komplet</a>: il-kontinwu tan-numri reali. Madwar dak iż-żmien l-isforzi għar-raffinar tat-<a href="/w/index.php?title=Teoremi&action=edit&redlink=1" class="new" title="Teoremi (il-paġna ma teżistix)">teoremi</a> ta’ l-<a href="/w/index.php?title=Integrazzjoni_ta%E2%80%99_Riemann&action=edit&redlink=1" class="new" title="Integrazzjoni ta’ Riemann (il-paġna ma teżistix)">integrazzjoni ta’ Riemann</a> wasslu għall-istudju tal-"qies" tas-sett tad-<a href="/w/index.php?title=Diskontinwitajiet&action=edit&redlink=1" class="new" title="Diskontinwitajiet (il-paġna ma teżistix)">diskontinwitajiet</a> tal-funzjonijiet reali. </p><p>Fl-istess ħin, bdew jinħolqu "<a href="/w/index.php?title=Mostri&action=edit&redlink=1" class="new" title="Mostri (il-paġna ma teżistix)">mostri</a>" (funzjonijiet <a href="/w/index.php?title=Mkien_kontinwi&action=edit&redlink=1" class="new" title="Mkien kontinwi (il-paġna ma teżistix)">mkien kontinwi</a>, funzjonijiet kontinwi imma mkien differenzjabbli, <a href="/w/index.php?title=Kurvi_li_jimlew_l-ispazju&action=edit&redlink=1" class="new" title="Kurvi li jimlew l-ispazju (il-paġna ma teżistix)">kurvi li jimlew l-ispazju</a>). F’dal-kuntest, <a href="/w/index.php?title=Camille_Jordan&action=edit&redlink=1" class="new" title="Camille Jordan (il-paġna ma teżistix)">Jordan</a> żviluppa t-teorija tiegħu tal-<a href="/w/index.php?title=Me%C5%BCura&action=edit&redlink=1" class="new" title="Meżura (il-paġna ma teżistix)">meżura</a>, <a href="/w/index.php?title=Georg_Cantor&action=edit&redlink=1" class="new" title="Georg Cantor (il-paġna ma teżistix)">Cantor</a> żviluppa dik li daż-żmien insejħulha it-<a href="/w/index.php?title=Teorija_sempli%C4%8Bi_tas-settijiet&action=edit&redlink=1" class="new" title="Teorija sempliċi tas-settijiet (il-paġna ma teżistix)">teorija sempliċi tas-settijiet</a>, u <a href="/w/index.php?title=Baire&action=edit&redlink=1" class="new" title="Baire (il-paġna ma teżistix)">Baire</a> ipprova it-<a href="/w/index.php?title=Teorema_tal-kategoriji_ta%E2%80%99_Baire&action=edit&redlink=1" class="new" title="Teorema tal-kategoriji ta’ Baire (il-paġna ma teżistix)">teorema tal-kategoriji ta’ Baire</a>. Fil-bidu tas-<a href="/w/index.php?title=Seklu_20&action=edit&redlink=1" class="new" title="Seklu 20 (il-paġna ma teżistix)">seklu 20</a>, il-kalkulu ġie formalizzat b’l-użu tat-<a href="/w/index.php?title=Teorija_assjomatika_tas-settijiet&action=edit&redlink=1" class="new" title="Teorija assjomatika tas-settijiet (il-paġna ma teżistix)">teorija assjomatika tas-settijiet</a>. <a href="/w/index.php?title=Henri_Leon_Lebesgue&action=edit&redlink=1" class="new" title="Henri Leon Lebesgue (il-paġna ma teżistix)">Lebesgue</a> irriżolva l-problema tal-miżura, u <a href="/w/index.php?title=David_Hilbert&action=edit&redlink=1" class="new" title="David Hilbert (il-paġna ma teżistix)">Hilbert</a> introduċa l-i<a href="/w/index.php?title=Spazji_ta%E2%80%99_Hilbert&action=edit&redlink=1" class="new" title="Spazji ta’ Hilbert (il-paġna ma teżistix)">spazji ta’ Hilbert</a> biex jirriżolvi l-<a href="/w/index.php?title=Ekwazzjonijiet_integrali&action=edit&redlink=1" class="new" title="Ekwazzjonijiet integrali (il-paġna ma teżistix)">ekwazzjonijiet integrali</a>. L-ideja ta’ l-i<a href="/w/index.php?title=Spazji_vettorjali_normati&action=edit&redlink=1" class="new" title="Spazji vettorjali normati (il-paġna ma teżistix)">spazji vettorjali normati</a> kienet infirxet, u f’l-20ijiet tas-seklu <a href="/w/index.php?title=Stefan_Banach&action=edit&redlink=1" class="new" title="Stefan Banach (il-paġna ma teżistix)">Banach</a> ħoloq l-<a href="/w/index.php?title=Analisi_funzjonali&action=edit&redlink=1" class="new" title="Analisi funzjonali (il-paġna ma teżistix)">analisi funzjonali</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Oqsma_ta'_l-Analisi"><span id="Oqsma_ta.27_l-Analisi"></span>Oqsma ta' l-Analisi</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=5" title="Editja s-sezzjoni: Oqsma ta' l-Analisi" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=5" title="Edit section's source code: Oqsma ta' l-Analisi"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-Analsi Matematika tinkludi dawn l-oqsma: </p> <ul><li><a href="/w/index.php?title=Analisi_Reali&action=edit&redlink=1" class="new" title="Analisi Reali (il-paġna ma teżistix)">Analisi Reali</a>, l-istudju <a href="/w/index.php?title=Rigoru%C5%BC&action=edit&redlink=1" class="new" title="Rigoruż (il-paġna ma teżistix)">rigoruż</a> tad-<a href="/wiki/Derivata" title="Derivata">derivati</a> u l-<a href="/wiki/Integral" class="mw-redirect" title="Integral">integrali</a> ta’ funzjonijiet b’varjabbli reali. Dan jinkludi l-istudju tas-<a href="/w/index.php?title=Su%C4%8B%C4%8Bessjonijiet&action=edit&redlink=1" class="new" title="Suċċessjonijiet (il-paġna ma teżistix)">suċċessjonijiet</a> u l-<a href="/w/index.php?title=Limiti&action=edit&redlink=1" class="new" title="Limiti (il-paġna ma teżistix)">limiti</a> tagħhom, is-<a href="/w/index.php?title=Serji&action=edit&redlink=1" class="new" title="Serji (il-paġna ma teżistix)">serji</a>, u l-<a href="/w/index.php?title=Me%C5%BCuri&action=edit&redlink=1" class="new" title="Meżuri (il-paġna ma teżistix)">meżuri</a>.</li> <li><a href="/wiki/Analisi_komplessa" title="Analisi komplessa">Analisi Komplessa</a>, l-istudju ta’ funzjonijiet mill-<a href="/w/index.php?title=Pjan_kompless&action=edit&redlink=1" class="new" title="Pjan kompless (il-paġna ma teżistix)">pjan kompless</a> għall-pjan kompless li huma komplessament differenzjabbli.</li> <li><a href="/w/index.php?title=Analisi_Funzjonali&action=edit&redlink=1" class="new" title="Analisi Funzjonali (il-paġna ma teżistix)">Analisi Funzjonali</a>, l-istudju ta’ spazji ta’ funzjonijiet b’l-użu ta’ kunċetti bħal <a href="/w/index.php?title=Spazji_ta%E2%80%99_Banach&action=edit&redlink=1" class="new" title="Spazji ta’ Banach (il-paġna ma teżistix)">spazji ta’ Banach</a> u <a href="/w/index.php?title=Spazji_ta%E2%80%99_Hilbert&action=edit&redlink=1" class="new" title="Spazji ta’ Hilbert (il-paġna ma teżistix)">spazji ta’ Hilbert</a>.</li> <li><a href="/wiki/Analisi_armonika" title="Analisi armonika">Analisi Armonika</a> l-istudju tas-<a href="/wiki/Serje_ta%27_Fourier" title="Serje ta' Fourier">serji ta' Fourier</a> u l-astrazzjonijiet tagħhom..</li> <li><a href="/w/index.php?title=%C4%A0ometrija_Differenzjali_u_Topolo%C4%A1ija&action=edit&redlink=1" class="new" title="Ġometrija Differenzjali u Topoloġija (il-paġna ma teżistix)">Ġometrija Differenzjali u Topoloġija</a>, l-applicazzjoni tal-kalkulu għal spazji matematiċi astratti li għandhom struttura interna komplikata.</li> <li><a href="/w/index.php?title=Analisi_Numerika&action=edit&redlink=1" class="new" title="Analisi Numerika (il-paġna ma teżistix)">Analisi Numerika</a>, l-istudju ta’ l-algoritmi użati għall-approssimazzjoni ta’ problemi tal-matematika kontinwa.</li></ul> <p>Il-kelma <b>Analisi Klassika</b> s-soltu tfisser analisi mingħajr l-użu tal-metodi tal-analisi funzjonali. L-istudju tal-<a href="/wiki/Ekwazzjoni_differenzjali" title="Ekwazzjoni differenzjali">ekwazzjonijiet differenzjali</a> issa huwa mferrex ma friegħi oħra bħas-<a href="/w/index.php?title=Sistemi_dinami%C4%8Bi&action=edit&redlink=1" class="new" title="Sistemi dinamiċi (il-paġna ma teżistix)">sistemi dinamiċi</a>, imma ġħadu mportanti ħafna fl-analisi konvenzjonali. </p> <div class="mw-heading mw-heading2"><h2 id="Alġebra"><span id="Al.C4.A1ebra"></span>Alġebra</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=6" title="Editja s-sezzjoni: Alġebra" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=6" title="Edit section's source code: Alġebra"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-<b>alġebra</b> hi waħda mill-friegħi prinċipali tal-<a class="mw-selflink selflink">matematika</a> u titratta l-istudju ta’ <a href="/w/index.php?title=Strutturi_al%C4%A1ebrin&action=edit&redlink=1" class="new" title="Strutturi alġebrin (il-paġna ma teżistix)">strutturi alġebrin</a>, <a href="/w/index.php?title=Relazzjonijiet&action=edit&redlink=1" class="new" title="Relazzjonijiet (il-paġna ma teżistix)">relazzjonijiet</a> u <a href="/w/index.php?title=Kwantit%C3%A0&action=edit&redlink=1" class="new" title="Kwantità (il-paġna ma teżistix)">kwantità</a>. </p><p>Il-kelma alġebra (mill-Għarbi الجبر, <i>al-ġabr</i> li tfisser "ġabra") ġejja mill-isem tal-ktieb tal-matematiku <a href="/w/index.php?title=Persjan&action=edit&redlink=1" class="new" title="Persjan (il-paġna ma teżistix)">Persjan</a> <a href="/wiki/G%C4%A7arbi" class="mw-redirect" title="Għarbi">Għarbi</a> <a href="/w/index.php?title=Mu%C4%A7ammad_ibn_Musa_al-Khwari%C5%BCmi&action=edit&redlink=1" class="new" title="Muħammad ibn Musa al-Khwariżmi (il-paġna ma teżistix)">Muħammad ibn Musa al-Khwariżmi</a>, intitolat <i>Al-Kitab al-Ġabr wa-l-Muqabala</i> ("Il-Ktieb tal-Ġabra u t-Tqabbil"), li jittratta ir-riżoluzzjoni tal-<a href="/w/index.php?title=Ekwazzjonijiet_linjari&action=edit&redlink=1" class="new" title="Ekwazzjonijiet linjari (il-paġna ma teżistix)">ekwazzjonijiet linjari</a> u <a href="/w/index.php?title=Kwadrati%C4%8Bi&action=edit&redlink=1" class="new" title="Kwadratiċi (il-paġna ma teżistix)">kwadratiċi</a>. </p><p>L-<a href="/w/index.php?title=Al%C4%A1ebra_elementari&action=edit&redlink=1" class="new" title="Alġebra elementari (il-paġna ma teżistix)">alġebra elementari</a> li normalment tifforma parti mill-kurrikulu ta’ l-iskejjel sekondarji, tintroduċi l-ideja ta’ <a href="/w/index.php?title=Simboli&action=edit&redlink=1" class="new" title="Simboli (il-paġna ma teżistix)">simboli</a> jew <a href="/wiki/Varjabbli" title="Varjabbli">varjabbli</a> li jirrepreżentaw kwantitajiet mhux magħrufa. Nitgħalmu wkoll kif ngħoddu u nimmoltiplikaw dawn il varjabbli, fuq il-polinomji mibnija minnhom u l-fattorizzazzjoni u l-kalkulazzjoni tar-<a href="/w/index.php?title=Radi%C4%8Bi&action=edit&redlink=1" class="new" title="Radiċi (il-paġna ma teżistix)">radiċi</a>. Però, l-alġebra hi ħafn’ usa’ minn hekk. L-għadd u l-moltiplikazzjoni nistgħu nqisuhom bħala <a href="/w/index.php?title=Operazzjoniet&action=edit&redlink=1" class="new" title="Operazzjoniet (il-paġna ma teżistix)">operazzjoniet</a> ġenerali u d-definizzjoni eżatta tagħhom twassalna għal strutturi ġodda bħal <a href="/w/index.php?title=Gruppi&action=edit&redlink=1" class="new" title="Gruppi (il-paġna ma teżistix)">gruppi</a>, <a href="/w/index.php?title=%C4%8Arieki&action=edit&redlink=1" class="new" title="Ċrieki (il-paġna ma teżistix)">ċrieki</a> u <a href="/w/index.php?title=Kampi&action=edit&redlink=1" class="new" title="Kampi (il-paġna ma teżistix)">kampi</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Klassifikazzjoni">Klassifikazzjoni</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=7" title="Editja s-sezzjoni: Klassifikazzjoni" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=7" title="Edit section's source code: Klassifikazzjoni"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="plainlinks" style="margin-left:2em; margin-bottom:0.5em; border-top:1px solid #ccc; border-bottom:1px solid #ccc; padding:2px; text-align:left; font-size:95%;"><span typeof="mw:File"><a href="/wiki/Stampa:Fairytale_warning.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/15px-Fairytale_warning.png" decoding="async" width="15" height="15" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/23px-Fairytale_warning.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Fairytale_warning.png/30px-Fairytale_warning.png 2x" data-file-width="64" data-file-height="64" /></a></span> Din is-sezzjoni għadha vojta. <span class="plainlinks"><a class="external text" href="https://mt.wikipedia.org/w/index.php?title=Matematika&action=edit&section=7">Għinna</a></span> biex niktbuha!</div> <div class="mw-heading mw-heading3"><h3 id="L-Alġebra_Elementari"><span id="L-Al.C4.A1ebra_Elementari"></span>L-Alġebra Elementari</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=8" title="Editja s-sezzjoni: L-Alġebra Elementari" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=8" title="Edit section's source code: L-Alġebra Elementari"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-<b>Alġebra elementari</b> hija l-forma l-iżjed bażika ta’ l-alġebra. Jitgħalmuha l-istudenti li m’għandhomx tgħalim tal-mathematika iżjed avvanzat mill-prinċipji bażiċi ta’ l-aritmetika. Fl-aritmetika, nsibu biss in-numri u l-operazzjonijiet aritmetiċi fuqhom (bħal +, −, ×, ÷). Fl-alġebra, in-numri spiss nirripreżentawhom bis-simboli (bħal <i>a</i>, <i>x</i>, <i>y</i>). Din ir-repreżentazzjoni għandha dawn il-vantaġġi: </p> <ul><li>Biha nistgħu nagħtu formulazzjoni ġenerali tar-regoli aritmetiċi (pereżempju <i>a</i> + <i>b</i> = <i>b</i> + <i>a</i> għal kull <i>a</i> u <i>b</i>), u hekk nistgħu nagħmlu l-ewwel pass fl-esplorazzjoni sistematika tal-propjetajiet tas-sistema tan-numri reali.</li> <li>Biha nistgħu nirreferu għan-numri "mhux magħrufin", nifformulaw ekwazzjonijiet u nistudjaw kif nirriżolvuhom (pereżempju, "Sib numru <i>x</i> sabiex 3<i>x</i> + 1 = 10").</li> <li>Biha nistgħu nagħmlu formulazzjoni ta’ relazzjonijiet funzjonali (bħal "Jekk tbigħ <i>x</i> biljetti, jkollok qligħ ta’ 3<i>x</i> - 10 ewri, jew <i>f</i>(<i>x</i>) = 3<i>x</i> - 10, fejn <i>f</i> hija l-funzjoni u <i>x</i> huwa n-numru li taġixxi fuqu l-funzjoni .").</li></ul> <div class="mw-heading mw-heading3"><h3 id="X'inhi_l-Alġebra_Astratta"><span id="X.27inhi_l-Al.C4.A1ebra_Astratta"></span>X'inhi l-Alġebra Astratta</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=9" title="Editja s-sezzjoni: X'inhi l-Alġebra Astratta" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=9" title="Edit section's source code: X'inhi l-Alġebra Astratta"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-'<i>alġebra astratta’</i> testendi il-kunċetti li nsibu fl-alġebra elementari għal oħrajn iżjed ġenerali. </p><p><b><a href="/w/index.php?title=Settijiet&action=edit&redlink=1" class="new" title="Settijiet (il-paġna ma teżistix)">Settijiet</a></b>: Minnflok nikkunsidraw biss it-tipi ta’ <a href="/w/index.php?title=Numri&action=edit&redlink=1" class="new" title="Numri (il-paġna ma teżistix)">numri</a> differenti, fl-alġebra astratta nqisu il-kunċett iżjed ġenerali ta’ <i>sett</i> li hu ġabra ta’ oġġetti (li jgħidulhom <a href="/w/index.php?title=Elementi&action=edit&redlink=1" class="new" title="Elementi (il-paġna ma teżistix)">elementi</a>) li għandhom ċerta propjetà speċifika għas-sett. Pereżempju in-numri reali jiffurmaw sett u n-numri komplessi sett ieħor. Eżempji oħra ta’ settijiet jinkludu is-sett tal-<a href="/w/index.php?title=Matri%C4%8Bi&action=edit&redlink=1" class="new" title="Matriċi (il-paġna ma teżistix)">matriċi</a> ta’ tnejn-bi-tnejn, is-sett tal-<a href="/w/index.php?title=Polinomji&action=edit&redlink=1" class="new" title="Polinomji (il-paġna ma teżistix)">polinomji</a> tat-tieni ordni (<i>ax</i><sup>2</sup> + <i>bx</i> + <i>c</i>), is-sett tal-<a href="/w/index.php?title=Vetturi&action=edit&redlink=1" class="new" title="Vetturi (il-paġna ma teżistix)">vetturi</a> bi-dimensjonali, u <a href="/w/index.php?title=Gruppi_finiti&action=edit&redlink=1" class="new" title="Gruppi finiti (il-paġna ma teżistix)">gruppi finiti</a> varji bħall-<a href="/w/index.php?title=Gruppi_%C4%8Bikli%C4%8Bi&action=edit&redlink=1" class="new" title="Gruppi ċikliċi (il-paġna ma teżistix)">gruppi ċikliċi</a>, jiġifieri l-gruppi tan-numri interi <a href="/w/index.php?title=Modulo&action=edit&redlink=1" class="new" title="Modulo (il-paġna ma teżistix)">modulo</a> <i>n</i>. It-<a href="/w/index.php?title=Teorija_tas-settijiet&action=edit&redlink=1" class="new" title="Teorija tas-settijiet (il-paġna ma teżistix)">Teorija tas-settijiet</a> hija fergħa tal-<a href="/w/index.php?title=Lo%C4%A1ika&action=edit&redlink=1" class="new" title="Loġika (il-paġna ma teżistix)">loġika</a> u teknikament mhux fergħa ta’ l-alġebra. </p><p><b><a href="/w/index.php?title=Operazzjonijiet_binarji&action=edit&redlink=1" class="new" title="Operazzjonijiet binarji (il-paġna ma teżistix)">Operazzjonijiet binarji</a></b>: L-ideja ta’ l-<a href="/w/index.php?title=G%C4%A7add&action=edit&redlink=1" class="new" title="Għadd (il-paġna ma teżistix)">għadd</a> (+) nistgħu nagħmluha iżjed astratta biex ittina <i>operazzjoni binarja</i>, * ngħidu aħna. Il-kunċett ta’ operazzjoni binarja ma jfisser xejn jekk ma nagħtux is-sett li fuqu qed niddefinixxu l-operazzjoni. Għal żewġ elementi <i>a</i> u <i>b</i> f’sett <i>S</i> <i>a</i>*<i>b</i> ittina element ieħor fis-sett, (dil-kundizzjoni ngħidulha <a href="/w/index.php?title=G%C4%A7eluq&action=edit&redlink=1" class="new" title="Għeluq (il-paġna ma teżistix)">għeluq</a> taħt l-operazzjoni). L-<a href="/w/index.php?title=G%C4%A7ad&action=edit&redlink=1" class="new" title="Għad (il-paġna ma teżistix)">Għad</a> (+), it-<a href="/wiki/Tnaqqis" title="Tnaqqis">Tnaqqis</a> (-), il-<a href="/w/index.php?title=Moltiplikazzjoni&action=edit&redlink=1" class="new" title="Moltiplikazzjoni (il-paġna ma teżistix)">moltiplikazzjoni</a> (×), u d-<a href="/w/index.php?title=Matematika_divi%C5%BCjoni&action=edit&redlink=1" class="new" title="Matematika diviżjoni (il-paġna ma teżistix)">diviżjoni</a> (÷) huma operazzjonijiet binarji meta niddefinuhom fuq settijiet addattati, kif ukoll l-għadd u l-moltiplikazzjoni tal-matriċi, vetturi u polinomji. </p><p><b><a href="/w/index.php?title=Elementi_ta%E2%80%99_l-identit%C3%A0&action=edit&redlink=1" class="new" title="Elementi ta’ l-identità (il-paġna ma teżistix)">Elementi ta’ l-identità</a></b>: Il-kunċett ta’ l-“element ta’ l-identità” huwa l-astrazzjoni tan-numri żero u wieħed. Żero huwa l-element ta’ l-identità għall-għadd and u wieħed l-element ta’ l-identità għall-moltiplikazzjoni. Għal operazzjoni binarja ġenerali * l-element ta’ l-identità <i>e</i> irid jissodisfa <i>a</i> * <i>e</i> = <i>a</i> u <i>e</i> * <i>a</i> = <i>a</i>. Għall-għadd din hi sodisfatta billi <i>a</i> + 0 = <i>a</i> u 0 + <i>a</i> = <i>a</i> u għall-moltiplikazzjini wkoll għax <i>a</i> × 1 = <i>a</i> u 1 × <i>a</i> = <i>a</i>. Imma, jekk nieħdu in-numri naturali pożitivi u l-operazzjoni ta’ l-għadd, m’hemmx element ta’ l-identità. </p><p><b><a href="/w/index.php?title=Elementi_inversi&action=edit&redlink=1" class="new" title="Elementi inversi (il-paġna ma teżistix)">Elementi inversi</a></b>: Minn-numri negattivi noħolqu l-kunċett ta’ <i>element invers</i> jew sempliċiment l-<i>invers</i>. Għall-għadd, l-invers ta’ <i>a</i> huwa <i>-a</i>, u għall-moltiplikazzjoni l-invers hu 1/<i>a</i>. L-element invers ġenerali <i>a</i><sup>-1</sup> jrid jissodifa r-relazzjoni <i>a</i> * <i>a</i><sup>-1</sup> = <i>e</i> u <i>a</i><sup>-1</sup> * <i>a</i> = <i>e</i>. </p><p><b><a href="/w/index.php?title=Asso%C4%8Bjattivit%C3%A0&action=edit&redlink=1" class="new" title="Assoċjattività (il-paġna ma teżistix)">Assoċjattività</a></b>: L-għadd tan-numri interi għandu propjetà li nsejħulha assoċjattività. Jiġifieri, l-kumbinazzjoni tan-numri li nkunu qed nogħdu ma tbiddilx is-somma tagħhom. Pereżempju: (2+3)+4=2+(3+4). Fil-kuntest generali, din issir (<i>a</i> * <i>b</i>) * <i>c</i> = <i>a</i> * (<i>b</i> * <i>c</i>). Il-biċċa kbira ta’ l-operazzjonijiet binarji għandhom din il-propjetà imma t-tnaqqis u d-diviżjoni le. </p><p><b><a href="/w/index.php?title=Kommutattivit%C3%A0&action=edit&redlink=1" class="new" title="Kommutattività (il-paġna ma teżistix)">Kommutattività</a></b>: L-għadd tan-numri interi għandu wkoll propjetà oħra li ngħidulha kommutattività. Jiġifieri, l-ordni tan-numri li nkunu qed nogħdu ma tbiddilx is-somma tagħhom. Pereżempju: 2+3=3+2. Fil-kuntest generali, din issir <i>a</i> * <i>b</i> = <i>b</i> * <i>a</i>. Mhux l-operazzjonijiet binarji kollha għandhom din il-propjetà. L-għadd u l-moltiplikazzjoni tan-numri interi għandhom din il-propjetà imma l-<a href="/w/index.php?title=Moltiplikazzjoni_tal-matri%C4%8Bi&action=edit&redlink=1" class="new" title="Moltiplikazzjoni tal-matriċi (il-paġna ma teżistix)">moltiplikazzjoni tal-matriċi</a> le. </p> <div class="mw-heading mw-heading4"><h4 id="Gruppi—strutturi_ta’_sett_b’operazzjoni_binarja_waħda"><span id="Gruppi.E2.80.94strutturi_ta.E2.80.99_sett_b.E2.80.99operazzjoni_binarja_wa.C4.A7da"></span>Gruppi—strutturi ta’ sett b’operazzjoni binarja waħda</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=10" title="Editja s-sezzjoni: Gruppi—strutturi ta’ sett b’operazzjoni binarja waħda" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=10" title="Edit section's source code: Gruppi—strutturi ta’ sett b’operazzjoni binarja waħda"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Meta niġbru flimkien il-kunċetti li rajna qabel, ikollna waħda mill-iżjed strutturi mportanti fil-matematika: il- <b><a href="/wiki/Grupp_(Matematika)" class="mw-redirect" title="Grupp (Matematika)">grupp</a></b>. Grupp jikkonsisti f’sett <i>S</i> u <a href="/w/index.php?title=Operazzjoni_wa%C4%A7da&action=edit&redlink=1" class="new" title="Operazzjoni waħda (il-paġna ma teżistix)">operazzjoni waħda</a> li rridu, li niktbuha '*', imma li jrid ikolla dawn il-propjetajiet: </p> <ul><li>Irid ikun hemm element ta’ l-identità <i>e</i>, li għal kull membru ieħor <i>a</i> ta’ <i>S</i>, <i>e</i> * <i>a</i> u <i>a</i> * <i>e</i> huma t-tnejn ugwali għal <i>a</i>.</li> <li>Kull element irid ikollu invers: għal kull membru ieħor <i>a</i> ta’ <i>S</i>, irid jeżisti membru <i>a</i><sup>-1</sup> sabiex <i>a</i> * <i>a</i><sup>-1</sup> u <i>a</i><sup>-1</sup> * <i>a</i> huma t-tnejn ugwali għall-element ta’ l-identità.</li> <li>L-operazzjoni hi assoċjattiva: għal <i>a</i>, <i>b</i> u <i>c</i> membri ta’ <i>S</i>, (<i>a</i> * <i>b</i>) * <i>c</i> hija ugwali għal <i>a</i> * (<i>b</i> * <i>c</i>).</li></ul> <p>Jekk grupp hu anki <a href="/w/index.php?title=Kommutattiv&action=edit&redlink=1" class="new" title="Kommutattiv (il-paġna ma teżistix)">kommutattiv</a> - jiġifieri, għal kull żewg membri <i>a</i> u <i>b</i> ta’ <i>S</i>, <i>a</i> * <i>b</i> hija ugwali għal <i>b</i> * <i>a</i> – il-grupp ngħidu li hu <a href="/w/index.php?title=Abeljan&action=edit&redlink=1" class="new" title="Abeljan (il-paġna ma teżistix)">Abeljan</a>. </p><p>Pereżempju, is-sett tan-numri interi bl-operazzjoni ta’ l-għadd huwa grupp. F’dal grupp, l-identità hija 0 u l-invers ta’ kull element <i>a</i> huwa n-negativ tiegħu, -<i>a</i>. Il-kundizzjoni ta’ assoċjattività hi sodisfatta, għax għal kull tliet numri interi <i>a</i>, <i>b</i> u <i>c</i>, (<i>a</i> + <i>b</i>) + <i>c</i> = <i>a</i> + (<i>b</i> + <i>c</i>). </p><p>Imma l-interi bl-operazzjoni tal-moltiplikazzjoni ma jiffurmawx grupp. Dan jiġri għax, in ġenerali, l-invers moltiplikattiv ta’ numru interu mhuwiex interu. Pereżempju, 4 huwa interu, imma l-invers moltiplikattiv tiegħu hu 1/4, li mhux interu. </p><p>L-istudju tal-gruppi jsir fit-<a href="/w/index.php?title=Teorija_tal-gruppi&action=edit&redlink=1" class="new" title="Teorija tal-gruppi (il-paġna ma teżistix)">teorija tal-gruppi</a>. Wieħed mir-riżultati l-iżjed importanti f’din it-teorija kien il-<a href="/w/index.php?title=Klassifikazzjoni_tal-gruppi_finiti_sempli%C4%8Bi&action=edit&redlink=1" class="new" title="Klassifikazzjoni tal-gruppi finiti sempliċi (il-paġna ma teżistix)">klassifikazzjoni tal-gruppi finiti sempliċi</a> li l-ikbar parti tagħha ġiet ippublikata bejn xi l-1955 u l-1983. Din tqassam il-<a href="/w/index.php?title=Gruppi_sempli%C4%8Bi&action=edit&redlink=1" class="new" title="Gruppi sempliċi (il-paġna ma teżistix)">gruppi sempliċi</a> <a href="/w/index.php?title=Finiti&action=edit&redlink=1" class="new" title="Finiti (il-paġna ma teżistix)">finiti</a> f’xi 30 tip bażiku. </p> <table class="toccolours" border="1" cellpadding="4" cellspacing="0" style="border-collapse: collapse; margin:0 ;"> <tbody><tr> <td colspan="11"><b>Eżempji</b> (MA = Mhux Applikabbli, bż = bla żero) </td></tr> <tr> <th>Sett: </th> <th colspan="2"><a href="/w/index.php?title=Numri_naturali&action=edit&redlink=1" class="new" title="Numri naturali (il-paġna ma teżistix)">Numri naturali</a> <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 \mathbb {N} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">N</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {N} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdf9a96b565ea202d0f4322e9195613fb26a9bed" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {N} }"></span> </th> <th colspan="2"><a href="/w/index.php?title=Numri_interi&action=edit&redlink=1" class="new" title="Numri interi (il-paġna ma teżistix)">Numri interi</a> <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 \mathbb {Z} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449494a083e0a1fda2b61c62b2f09b6bee4633dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.55ex; height:2.176ex;" alt="{\displaystyle \mathbb {Z} }"></span> </th> <th colspan="4"><a href="/w/index.php?title=Numri_razzjonali&action=edit&redlink=1" class="new" title="Numri razzjonali (il-paġna ma teżistix)">Numri razzjonali</a> <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 \mathbb {Q} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Q</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Q} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c5909f0b54e4718fa24d5fd34d54189d24a66e9a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.808ex; height:2.509ex;" alt="{\displaystyle \mathbb {Q} }"></span>, <a href="/w/index.php?title=Numri_reali&action=edit&redlink=1" class="new" title="Numri reali (il-paġna ma teżistix)">Numri reali</a> <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 \mathbb {R} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">R</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {R} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/786849c765da7a84dbc3cce43e96aad58a5868dc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {R} }"></span> u <a href="/w/index.php?title=Numri_komplessi&action=edit&redlink=1" class="new" title="Numri komplessi (il-paġna ma teżistix)">Numri komplessi</a> <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 \mathbb {C} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">C</mi> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {C} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f9add4085095b9b6d28d045fd9c92c2c09f549a7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.678ex; height:2.176ex;" alt="{\displaystyle \mathbb {C} }"></span> </th> <th colspan="2">Interi mod 3: {0,1,2} </th></tr> <tr> <th>Operazzjoni </th> <td>+ </td> <td>× (bż) </td> <td>+ </td> <td>× (bż) </td> <td>+ </td> <td>− </td> <td>× (bż) </td> <td>÷ (bż) </td> <td>+ </td> <td>× (bż) </td></tr> <tr> <td>Magħluq </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td></tr> <tr> <td>Identità </td> <td>0 </td> <td>1 </td> <td>0 </td> <td>1 </td> <td>0 </td> <td>MA </td> <td>1 </td> <td>MA </td> <td>0 </td> <td>1 </td></tr> <tr> <td>Invers </td> <td>MA </td> <td>MA </td> <td>-a </td> <td>MA </td> <td>-a </td> <td>a </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 {\begin{matrix}{\frac {1}{a}}\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> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mi>a</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{matrix}{\frac {1}{a}}\end{matrix}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/13409529cf4d4ca2672ff0c0646b3581712eaf14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:2.457ex; height:3.509ex;" alt="{\displaystyle {\begin{matrix}{\frac {1}{a}}\end{matrix}}}"></span> </td> <td>a </td> <td>0,2,1, respettivament </td> <td>MA, 1, 2, respettivament </td></tr> <tr> <td>Assoċjattiv </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Le </td> <td>Iva </td> <td>Le </td> <td>Iva </td> <td>Iva </td></tr> <tr> <td>Kommutativ </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Iva </td> <td>Le </td> <td>Iva </td> <td>Le </td> <td>Iva </td> <td>Iva </td></tr> <tr> <td>Struttura </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (il-paġna ma teżistix)">monoid</a> </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (il-paġna ma teżistix)">monoid</a> </td> <td>grupp Abeljan </td> <td><a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (il-paġna ma teżistix)">monoid</a> </td> <td>grupp Abeljan </td> <td><a href="/w/index.php?title=Kwa%C5%BCigrupp&action=edit&redlink=1" class="new" title="Kważigrupp (il-paġna ma teżistix)">kważigrupp</a> </td> <td>grupp Abeljan </td> <td><a href="/w/index.php?title=Kwa%C5%BCigrupp&action=edit&redlink=1" class="new" title="Kważigrupp (il-paġna ma teżistix)">kważigrupp</a> </td> <td>grupp Abeljan </td> <td>grupp Abeljan (<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 \mathbb {Z} _{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathbb {Z} _{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/92aedfb5c02eff978ab963421ce930f46801657e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.605ex; height:2.509ex;" alt="{\displaystyle \mathbb {Z} _{2}}"></span>) </td></tr></tbody></table> <p><a href="/w/index.php?title=Semigruppi&action=edit&redlink=1" class="new" title="Semigruppi (il-paġna ma teżistix)">Semigruppi</a>, <a href="/w/index.php?title=Kwa%C5%BCigruppi&action=edit&redlink=1" class="new" title="Kważigruppi (il-paġna ma teżistix)">kważigruppi</a>, u <a href="/w/index.php?title=Monoidi&action=edit&redlink=1" class="new" title="Monoidi (il-paġna ma teżistix)">monoidi</a> huma strutturi simili għall-gruppi, imma iżjed ġenerali. Jikkonsistu f’sett u operazzjoni binarja magħluqa, imma ma jissodisfawx il-kondizzjonijiet l-oħra neċessarjament. <a href="/w/index.php?title=Semigrupp&action=edit&redlink=1" class="new" title="Semigrupp (il-paġna ma teżistix)">Semigrupp</a> għandu operazzjoni binarja <i>assoċjattiva</i>, imma jista’ jkun li m’għandux element ta’ l-identità. <a href="/w/index.php?title=Monoid&action=edit&redlink=1" class="new" title="Monoid (il-paġna ma teżistix)">Monoid</a> huwa semigrupp li għandu identità imma jista’ jkun li m’għandux invers għal kull element. <a href="/w/index.php?title=Kwa%C5%BCigrupp&action=edit&redlink=1" class="new" title="Kważigrupp (il-paġna ma teżistix)">Kważigrupp</a> għandu l-propjetà li kull element jista’ jinbidel f’kull ieħor bi pre- jew post-operazzjoni unika; imma l-operazzjoni binarja jista’ jkun li mhux assoċjattiva. </p><p>Il-gruppi kollha huma monoidi, u l-monoidi kollha huma semigruppi. </p> <div class="mw-heading mw-heading4"><h4 id="Ċrieki_u_Kampi—strutturi_ta’_sett_b’żewġ_operazzjonijiet_binarji,_(+)_u_(×)"><span id=".C4.8Arieki_u_Kampi.E2.80.94strutturi_ta.E2.80.99_sett_b.E2.80.99.C5.BCew.C4.A1_operazzjonijiet_binarji.2C_.28.2B.29_u_.28.C3.97.29"></span>Ċrieki u Kampi—strutturi ta’ sett b’żewġ operazzjonijiet binarji, (+) u (×)</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=11" title="Editja s-sezzjoni: Ċrieki u Kampi—strutturi ta’ sett b’żewġ operazzjonijiet binarji, (+) u (×)" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=11" title="Edit section's source code: Ċrieki u Kampi—strutturi ta’ sett b’żewġ operazzjonijiet binarji, (+) u (×)"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il-gruppi għandhom operazzjoni binarja waħda biss. Biex nispjegaw il-mekkaniżmu tat-tipi ta’ numri differenti kompletament, hemm bżonn li nistudjaw strutturi b’żewġ operazzjonijiet. L-iżjed importanti fost dawn huma ċ-<a href="/w/index.php?title=%C4%8Arieki&action=edit&redlink=1" class="new" title="Ċrieki (il-paġna ma teżistix)">Ċrieki</a>, u l-<a href="/w/index.php?title=Kampi&action=edit&redlink=1" class="new" title="Kampi (il-paġna ma teżistix)">Kampi</a>. </p><p>Id-<b><a href="/w/index.php?title=Distributtivit%C3%A0&action=edit&redlink=1" class="new" title="Distributtività (il-paġna ma teżistix)">Distributtività</a></b> tiġġeneralizza l-<i>liġi distributtiva</i> tan-numri u tiffissa f’liema ordni għandna napplikaw l-operazzjonijiet, (ngħidulha l-<a href="/w/index.php?title=Pre%C4%8Bedenza&action=edit&redlink=1" class="new" title="Preċedenza (il-paġna ma teżistix)">preċedenza</a>). Għall-interi (<i>a</i> + <i>b</i>) × c = <i>a</i>×<i>c</i>+ <i>b</i>×<i>c</i> u <i>c</i> × (<i>a</i> + <i>b</i>) = <i>c</i>×<i>a</i> + <i>c</i>×<i>b</i>, u ngħidu li × hija <i> distributtiva </i> fuq +. </p><p><b><a href="/w/index.php?title=%C4%8Airku&action=edit&redlink=1" class="new" title="Ċirku (il-paġna ma teżistix)">Ċirku</a></b> għandu żewġ operazzjonijiet (+) u (×), fejn × hu distributtiv fuq +. Taħt l-ewwel operazzjoni (+) jifforma <i>grupp Abeljan</i>. Taħt it-tieni operazzjoni (×) hu assoċjattiv, imma m’hemmx bżonn ta' identità jew ta' invers, u allura ma nistgħux niddividu. L-element ta’ l-identità ta’ l-għadd (+) niktbuha bħala 0 u l-inverse ta’ l-għadd ta’ <i>a</i> jinkiteb -<i>a</i>. </p><p>In-numri interi huma eżempju ta’ ċirku. </p><p><b><a href="/w/index.php?title=Kamp&action=edit&redlink=1" class="new" title="Kamp (il-paġna ma teżistix)">Kamp</a></b> hu <i>ċirku</i> b’propjetà oħra miżjuda li l-elementi kollha barra 0 jiffurmaw <i>grupp Abeljan</i> taħt ×. L-identità moltiplikattiva (×) niktbuha bħala 1 u l-invers moltiplikattiv ta’ <i>a</i> jinkiteb <i>a</i><sup>-1</sup>. </p><p>In-numri razzjonali, in-numri reali u n-numri komplessi huma kollha eżempji ta’ kampi. </p> <div class="mw-heading mw-heading3"><h3 id="Alġebriet"><span id="Al.C4.A1ebriet"></span>Alġebriet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=12" title="Editja s-sezzjoni: Alġebriet" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=12" title="Edit section's source code: Alġebriet"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Il-kelma <i><b>alġebra</b></i> nużawha wkoll għal xi <a href="/w/index.php?title=Strutturi_al%C4%A1ebrin&action=edit&redlink=1" class="new" title="Strutturi alġebrin (il-paġna ma teżistix)">strutturi alġebrin</a>: </p> <ul><li><a href="/w/index.php?title=Al%C4%A1ebra_fuq_kamp&action=edit&redlink=1" class="new" title="Alġebra fuq kamp (il-paġna ma teżistix)">Alġebra fuq kamp</a></li> <li><a href="/w/index.php?title=Al%C4%A1ebra_fuq_sett&action=edit&redlink=1" class="new" title="Alġebra fuq sett (il-paġna ma teżistix)">Alġebra fuq sett</a></li> <li><a href="/w/index.php?title=Al%C4%A1ebra_Boolejana&action=edit&redlink=1" class="new" title="Alġebra Boolejana (il-paġna ma teżistix)">Alġebra Boolejana</a></li> <li><a href="/w/index.php?title=F-al%C4%A1ebra&action=edit&redlink=1" class="new" title="F-alġebra (il-paġna ma teżistix)">F-alġebra</a> u <a href="/w/index.php?title=F-koal%C4%A1ebra&action=edit&redlink=1" class="new" title="F-koalġebra (il-paġna ma teżistix)">F-koalġebra</a> fit-<a href="/w/index.php?title=Teorija_tal-kategoriji&action=edit&redlink=1" class="new" title="Teorija tal-kategoriji (il-paġna ma teżistix)">teorija tal-kategoriji</a></li> <li><a href="/w/index.php?title=Sigma-al%C4%A1ebra&action=edit&redlink=1" class="new" title="Sigma-alġebra (il-paġna ma teżistix)">Sigma-alġebra</a></li></ul> <div class="mw-heading mw-heading3"><h3 id="Storja_ta'_l-alġebra"><span id="Storja_ta.27_l-al.C4.A1ebra"></span>Storja ta' l-alġebra</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Matematika&veaction=edit&section=13" title="Editja s-sezzjoni: Storja ta' l-alġebra" class="mw-editsection-visualeditor"><span>immodifika</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Matematika&action=edit&section=13" title="Edit section's source code: Storja ta' l-alġebra"><span>immodifika s-sors</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>L-alġebra nistgħu nsibu l-oriġini tagħha fil-<a href="/wiki/Babilonja" title="Babilonja">Babilonja</a> antika. Il-Babilonjani żviluppaw <a href="/w/index.php?title=Sistema_aritmetiku&action=edit&redlink=1" class="new" title="Sistema aritmetiku (il-paġna ma teżistix)">sistema aritmetiku</a> avvanzat li bih setgħu jagħmlu kalkulazzjonijiet b’metodu alġebri. Permezz ta’ dan is-sistema, setgħu japplikaw formoli u jikkalkulaw valuri mhux magħrufa għal klassi ta’ problemi li daż-żmien nirriżolvuhom bl-użu ta’ <a href="/w/index.php?title=Ekwazzjonijiet_linjari&action=edit&redlink=1" class="new" title="Ekwazzjonijiet linjari (il-paġna ma teżistix)">ekwazzjonijiet linjari</a>, <a href="/w/index.php?title=Ekwazzjonijiet_kwadrati%C4%8Bi&action=edit&redlink=1" class="new" title="Ekwazzjonijiet kwadratiċi (il-paġna ma teżistix)">ekwazzjonijiet kwadratiċi</a> u <a href="/w/index.php?title=Ekwazzjonijiet_linjari_indeterminati&action=edit&redlink=1" class="new" title="Ekwazzjonijiet linjari indeterminati (il-paġna ma teżistix)">ekwazzjonijiet linjari indeterminati</a>. Għall-kontrarju, il-biċċa kbira tal-matematiċi <a href="/w/index.php?title=E%C4%A1izzjani&action=edit&redlink=1" class="new" title="Eġizzjani (il-paġna ma teżistix)">Eġizzjani</a> ta’ dak iż-żmien, u l-biċċa kbira tal-matematiċi <a href="/w/index.php?title=Indjani&action=edit&redlink=1" class="new" title="Indjani (il-paġna ma teżistix)">Indjani</a>, <a href="/w/index.php?title=Griegi&action=edit&redlink=1" class="new" title="Griegi (il-paġna ma teżistix)">Griegi</a> u <a href="/w/index.php?title=%C4%8Aini%C5%BCi&action=edit&redlink=1" class="new" title="Ċiniżi (il-paġna ma teżistix)">Ċiniżi</a> f’l-<a href="/w/index.php?title=Ewwel_millennju_QK&action=edit&redlink=1" class="new" title="Ewwel millennju QK (il-paġna ma teżistix)">ewwel millennju QK</a>, is-soltu kienu jirriżolvu dawn il-problemi b’metodi <a href="/w/index.php?title=%C4%A0ometri%C4%8Bi&action=edit&redlink=1" class="new" title="Ġometriċi (il-paġna ma teżistix)">ġometriċi</a>, bħal dawk imfissra fil-<i><a href="/w/index.php?title=Papiru_Matematiku_ta%E2%80%99_Rhind&action=edit&redlink=1" class="new" title="Papiru Matematiku ta’ Rhind (il-paġna ma teżistix)">Papiru Matematiku ta’ Rhind</a></i>, <i><a href="/w/index.php?title=Sulba_Sutras&action=edit&redlink=1" class="new" title="Sulba Sutras (il-paġna ma teżistix)">Sulba Sutras</a></i>, <i><a href="/w/index.php?title=L-Elementi_ta%E2%80%99_Ewklidi&action=edit&redlink=1" class="new" title="L-Elementi ta’ Ewklidi (il-paġna ma teżistix)">L-Elementi ta’ Ewklidi</a></i>, u <i><a href="/w/index.php?title=Id-Disg%C4%A7a_Kapitli_fuq%E2%80%99_l-Arti_Matematika&action=edit&redlink=1" class="new" title="Id-Disgħa Kapitli fuq’ l-Arti Matematika (il-paġna ma teżistix)">Id-Disgħa Kapitli fuq’ l-Arti Matematika</a></i>. Ix-xogħol ġometriku tal-Griegi, li l-Elementi huwa eżempju tajjeb ħafna tiegħu, ipprovda s-sisien għall-ġeneralizzazzjoni tal-formuli mis-soluzzjoni ta’ problemi partikulari għal sistemi iżjed ġenerali li jistgħu jintużaw għall-formulazzjoni u s-soluzzjoni tal-ekwazzjonijiet. </p> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Stampa:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg/200px-Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg" decoding="async" width="200" height="317" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/2/23/Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg 1.5x" data-file-width="240" data-file-height="380" /></a><figcaption>L-ewwel paġna tal-ktieb ta' al-Khwariżmi</figcaption></figure> <p>Il-kelma "<i>alġebra</i>" ġejja mill-Għarbi "<i>al-ġabr</i>" fit-titlu tal-ktieb "<i>al-Kitab al-muhtasar fi ħisab al-ġabr wa-l-muqabala</i>", li jfisser <i>Il-ktieb fil-qosor fi ħsib il-ġbir u tqassim</i>. Dan kitbu il-matematiku Persjan <a href="/w/index.php?title=Mu%C4%A7ammad_ibn_Musa_al-Khwari%C5%BCmi&action=edit&redlink=1" class="new" title="Muħammad ibn Musa al-Khwariżmi (il-paġna ma teżistix)">Muħammad ibn Musa al-Khwariżmi</a> (Għarbi: محمد بن موسى الخوارزميّ المجوسيّ القطربّليّ) fit-820. Il-matematiku Grieg <a href="/w/index.php?title=Diofantu&action=edit&redlink=1" class="new" title="Diofantu (il-paġna ma teżistix)">Diofantu</a> (Grieg: Διόφαντος ὁ Ἀλεξανδρεύς t. bejn <a href="/w/index.php?title=200&action=edit&redlink=1" class="new" title="200 (il-paġna ma teżistix)">200</a> u <a href="/w/index.php?title=214&action=edit&redlink=1" class="new" title="214 (il-paġna ma teżistix)">214</a>, m. bejn <a href="/w/index.php?title=284&action=edit&redlink=1" class="new" title="284 (il-paġna ma teżistix)">284</a> u <a href="/w/index.php?title=298&action=edit&redlink=1" class="new" title="298 (il-paġna ma teżistix)">298</a> AD) hu tradizzjonalment magħruf bħala “missier l-alġebra” imma hemm argument jekk Al-Khwariżmi għandux joħodlu dan it-titlu. Dawk li jżommu ma Al-Khwariżmi jsossnu li ħafna mix-xogħol tiegħu fuq “il-ġbir” jew riduzzjoni għadu użat sa llum u li hu ta spjegazzjoni kompleta fuq is-soluzzjoni ta’ l-ekwazzjonijiet kwadratiċi. Dawk li jżommu ma <a href="/w/index.php?title=Diofantu&action=edit&redlink=1" class="new" title="Diofantu (il-paġna ma teżistix)">Diofantu</a> jgħidu li l-alġebra li nsibu f’<i>Al-Ġabr</i> hi iżjed elementari mill-alġebra fl- <i>Aritmetika</i> ta’ Diofantu u li l-<i>Aritmetika</i> hi miktuba fi stil sinkopat waqt li <i>Al-Ġabr</i> hi kollha fi stil retoriku. Matematiku Persjan ieħor, <a href="/w/index.php?title=Omar_Khajjam&action=edit&redlink=1" class="new" title="Omar Khajjam (il-paġna ma teżistix)">Omar Khajjam</a> (Persjan: غیاث الدین ابو الفتح عمر بن ابراهیم خیام نیشابوری t. 18 ta’ Mejju, 1048, m. 4 ta’ Diċembru, 1131), żviluppa l-<a href="/w/index.php?title=%C4%A0ometrija_al%C4%A1ebrija&action=edit&redlink=1" class="new" title="Ġometrija alġebrija (il-paġna ma teżistix)">ġometrija alġebrija</a> u sab soluzzjoni ġenerali ġometrika ta’ l-<a href="/w/index.php?title=Ekwazzjonijiet_kubi%C4%8Bi&action=edit&redlink=1" class="new" title="Ekwazzjonijiet kubiċi (il-paġna ma teżistix)">ekwazzjonijiet kubiċi</a>. Il-matematiċi Indjani <a href="/w/index.php?title=Ma%C4%A7avira&action=edit&redlink=1" class="new" title="Maħavira (il-paġna ma teżistix)">Maħavira</a> u <a href="/w/index.php?title=Baskara_II&action=edit&redlink=1" class="new" title="Baskara II (il-paġna ma teżistix)">Baskara II</a>, u l-matematiku Ċiniż <a href="/w/index.php?title=%C5%BBu_Xi%C4%A1je&action=edit&redlink=1" class="new" title="Żu Xiġje (il-paġna ma teżistix)">Żu Xiġje</a>, irriżolvew xi każi ta’ ekwazzjonijiet kubiċi, <a href="/w/index.php?title=Kwarti%C4%8Bi&action=edit&redlink=1" class="new" title="Kwartiċi (il-paġna ma teżistix)">kwartiċi</a>, <a href="/w/index.php?title=Kwinti%C4%8Bi&action=edit&redlink=1" class="new" title="Kwintiċi (il-paġna ma teżistix)">kwintiċi</a> u <a href="/w/index.php?title=Polinomjali&action=edit&redlink=1" class="new" title="Polinomjali (il-paġna ma teżistix)">polinomjali</a> ta’ ordni ogħla. </p><p>F’nofs is-seklu 16 kien hemm żvilupp importanti ieħor ta' l-alġebra. Dan kien is-soluzzjoni alġebrija ġenerali tal-ekwazzjonijiet kubiċi u kwartiċi. L-ideja ta’ <a href="/w/index.php?title=Determinant&action=edit&redlink=1" class="new" title="Determinant (il-paġna ma teżistix)">determinant</a> żviluppha l-matematiku Ġappuniż <a href="/w/index.php?title=Kowa_Seki&action=edit&redlink=1" class="new" title="Kowa Seki (il-paġna ma teżistix)">Kowa Seki</a> fis-seklu 17, u għaxar snin wara <a href="/w/index.php?title=Gottfried_Leibniz&action=edit&redlink=1" class="new" title="Gottfried Leibniz (il-paġna ma teżistix)">Gottfried Leibniz</a> uża d-determinanti biex jirriżolvi sistemi ta’ ekwazzjonijiet linjari simultanji premezz tal-<a href="/w/index.php?title=Matri%C4%8Bi&action=edit&redlink=1" class="new" title="Matriċi (il-paġna ma teżistix)">matriċi</a>. Fis-seklu 18, <a href="/w/index.php?title=Gabriel_Cramer&action=edit&redlink=1" class="new" title="Gabriel Cramer (il-paġna ma teżistix)">Gabriel Cramer</a> ukoll ħadem fuq il-matriċi u d-determinanti. L-iżvilupp ta’ l-<a href="/wiki/Al%C4%A1ebra_astratta" title="Alġebra astratta">Alġebra astratta</a> sar fis-seklu 19. Fil-bidu dan ix-xogħol ikkonċentra fuq li daż-żmien insejħulha it-<a href="/w/index.php?title=Teorija_ta%E2%80%99_Galois&action=edit&redlink=1" class="new" title="Teorija ta’ Galois (il-paġna ma teżistix)">teorija ta’ Galois</a> u fuq kwistjonijiet tal-<a href="/w/index.php?title=Kostruttibbilt%C3%A0&action=edit&redlink=1" class="new" title="Kostruttibbiltà (il-paġna ma teżistix)">kostruttibbiltà</a>. </p><p>L-istadji ta’ l-iżvilupp ta’ l-alġebra simbolika kienu bejn wieħed u ieħor dawn: </p> <ul><li>Alġebra retorika, li żviluppawha l-Babilonjani u baqet dominanti sas-seklu 16;</li> <li>Alġebra ġometrika kostruttiva, li tawha ħafna mportanza il-matematiċi Indjani u l-matematiċi klassiċi Griegi;</li> <li>Alġebra sinkopata, li kienet żviluppata minn <a href="/w/index.php?title=Diofantu&action=edit&redlink=1" class="new" title="Diofantu (il-paġna ma teżistix)">Diofantu</a> u fil-<i><a href="/w/index.php?title=Manuskritt_Bakxali&action=edit&redlink=1" class="new" title="Manuskritt Bakxali (il-paġna ma teżistix)">Manuskritt Bakxali</a></i>;</li> <li>Alġebra simbolika, li laħqet il-quċċata fix-xogħol ta’ <a href="/w/index.php?title=Leibniz&action=edit&redlink=1" class="new" title="Leibniz (il-paġna ma teżistix)">Leibniz</a>.</li></ul> <p>Kronoloġija ta’ żviluppi kritiċi fl-alġebra: </p> <ul><li>Ċirka 1800 QK: Fit-<a href="/w/index.php?title=Tavletta_ta%E2%80%99_Strassburg&action=edit&redlink=1" class="new" title="Tavletta ta’ Strassburg (il-paġna ma teżistix)">tavletta ta’ Strassburg</a> il-Babilonjani jfittxu s-soluzzjoni ta’ ekwazzjoni ellittika kwadratika.</li> <li>Ċirka 1600 QK: It-tavletta ta’ <i><a href="/w/index.php?title=Plimpton_322&action=edit&redlink=1" class="new" title="Plimpton 322 (il-paġna ma teżistix)">Plimpton 322</a></i> tagħti tavola ta’ <a href="/w/index.php?title=Trippli_Pitagori%C4%8Bi&action=edit&redlink=1" class="new" title="Trippli Pitagoriċi (il-paġna ma teżistix)">trippli Pitagoriċi</a> fi skritt <a href="/w/index.php?title=Kuneiformi&action=edit&redlink=1" class="new" title="Kuneiformi (il-paġna ma teżistix)">Kuneiformi</a> Babilonjan</li> <li>Ċirka 800 QK: Il-matematiku Indjan <a href="/w/index.php?title=Bawdajana&action=edit&redlink=1" class="new" title="Bawdajana (il-paġna ma teżistix)">Bawdajana</a>, fix-xogħol tiegħu <i><a href="/w/index.php?title=Sulba_Sutra&action=edit&redlink=1" class="new" title="Sulba Sutra (il-paġna ma teżistix)">Sulba Sutra</a></i>, jiskopri trippli Pitagoriċi b’metodi alġebrin, jsib soluzzjonijiet ġometriċi ta’ ekwazzjonijiet linjari u ekwazzjonijiet kwadratiċi tal-forma ax<sup>2</sup> = c u ax<sup>2</sup> + bx = c, u jsib żewġ settijiet ta’ soluzzjonijiet integrali pożittivi għal sett ta’ ekwazzjonijiet simultanji Diofantini.</li> <li>Ċirka 600 QK: Il-matematiku Indjan <a href="/w/index.php?title=Apastamba&action=edit&redlink=1" class="new" title="Apastamba (il-paġna ma teżistix)">Apastamba</a>, fix-xogħol tiegħu <i>Apastamba Sulba Sutra</i>, jirriżolvi l-ekwazzjoni linjari ġenerali u juża ekwazzjonijiet simultanji Diofantini b’sa ħames kwantitajiet mhux magħrufa.</li> <li>Ċirka 300 QK: Fit-tieni ktieb ta’ l-Elementi, <a href="/wiki/Ewklide" title="Ewklide">Ewklidi</a> jagħti kostruzzjoni ġometrika b’metodi Ewklidej għas-soluzzjoni ta’ l-ekwazzjoni kwadratika għal radiċi posittivi reali. Il-kostruzzjoni hi dovuta għall-iSkola Pitagorika tal-ġometrija.</li> <li>Ċirka 300 QK: Titfittex kostruzzjoni ġometrika għas-soluzzjoni ta’ l-ekwazzjoni kubika. Issa nafu li bil-metodi Ewklidej ma nistgħux insibu soluzzjoni għall-ekwazzjoni kubika ġenerali.</li> <li>Ċirka 100 QK: Il-ktieb tal-matematika Ċiniż <i><a href="/w/index.php?title=%C4%A0ju%C5%BCang_Suwanxu&action=edit&redlink=1" class="new" title="Ġjużang Suwanxu (il-paġna ma teżistix)">Ġjużang Suwanxu</a></i> (<i>Id-Disgħa Kapitli fuq l-Arti Matematika</i>), jittratta Ekwazzjonijiet alġebrin. Dal-ktieb fih soluzzjonijiet ta’ ekwazzjonijiet linjari bl-użu tar-<a href="/w/index.php?title=Regola_tal-po%C5%BCizzjoni_falza_doppja&action=edit&redlink=1" class="new" title="Regola tal-pożizzjoni falza doppja (il-paġna ma teżistix)">regola tal-pożizzjoni falza doppja</a>, soluzzjonijiet gometriċi ta’ ekwazzjonijiet kwadratiċi, u soluzzjonijiet ta’ matriċi, ekwivalenti għall-metodi moderni, għas-soluzzjoni tas-sistemi ta’ ekwazzjonijiet linjari simultanji.</li> <li>Ċirka 100 QK: Il-<i><a href="/w/index.php?title=Manuskritt_ta%E2%80%99_Bakxali&action=edit&redlink=1" class="new" title="Manuskritt ta’ Bakxali (il-paġna ma teżistix)">Manuskritt ta’ Bakxali</a></i>, miktub fl-Indja, juża forma ta’ notazzjoni alġebrija bl-ittri u sinjali oħra, u fih ekwazzjonijiet kubiċi u kwartiċi, soluzzjonijiet alġebrin ta’ <a href="/w/index.php?title=Ekwazzjonijiet_linjari&action=edit&redlink=1" class="new" title="Ekwazzjonijiet linjari (il-paġna ma teżistix)">ekwazzjonijiet linjari</a> b’sa ħames kwantitajiet mhux magħrufa, il-formula alġebrija ġenerali għall-ekwazzjoni kwadratiċi, u soluzzjonijiet ta’ ekwazzjonijiet kwadratiċi indeterminati u ekwazzjonijiet simultanji.</li></ul> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Stampa:Diophantus-cover.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Diophantus-cover.jpg/200px-Diophantus-cover.jpg" decoding="async" width="200" height="328" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/60/Diophantus-cover.jpg/300px-Diophantus-cover.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/6/60/Diophantus-cover.jpg 2x" data-file-width="360" data-file-height="591" /></a><figcaption> Paġna titulari ta’ l-edizzjoni ta’ 1621 ta’ l-<i>Arithmetica</i> ta’ Diofantu, maqluba għall-Latin minn de Méziriac</figcaption></figure> <ul><li>Ċirka 150 AD: Il-matematiku Eġizzjan Ellenistiku <a href="/w/index.php?title=Eroni_ta%E2%80%99_Lixandra&action=edit&redlink=1" class="new" title="Eroni ta’ Lixandra (il-paġna ma teżistix)">Eroni ta’ Lixandra</a>, jittratta l-ekwazzjonijiet alġebrin fi tliet volumi tal-matematika.</li> <li>Ċirka 200: Il-matematiku Babilonjan Ellenistiku, <a href="/w/index.php?title=Diofantu&action=edit&redlink=1" class="new" title="Diofantu (il-paġna ma teżistix)">Diofantu</a> li għex fl-Eġittu u li ħafna jikkunsidrawh bħala "missier l-alġebra", jikteb l-opra famuża tiegħu, l-<i>Aritmetika</i>, li fiha soluzzjonijiet ta’ ekwazzjonijiet alġebrin u xogħol fuq it-teorija tan-numri.</li> <li>499: Il-matematiku Indjan <a href="/w/index.php?title=Arjabata&action=edit&redlink=1" class="new" title="Arjabata (il-paġna ma teżistix)">Arjabata</a>, fit-trattat tiegħu <i>Arjabatija</i>, jsib soluzzjonijiet interi għal xi ekwazzjonijiet linjari b’metodu ekwivalenti għal dak li nużaw illum, jiddeskrivi s-soluzzjoni integrali ġenerali ta’ l-ekwazzjoni linjari indeterminata u jagħti soluzzjonijiet integrali ta’ xi ekwazzjonijiet linjari simultanji indeterminati.</li> <li>Ċirka 625: Il-matematiku Ċiniż, Wang <a href="/w/index.php?title=Ksijaotong&action=edit&redlink=1" class="new" title="Ksijaotong (il-paġna ma teżistix)">Ksijaotong</a>, jsib soluzzjonijiet numeriċi ta’ ekwazzjonijiet kubiċi.</li> <li>628: Il-matematiku Indjan, <a href="/w/index.php?title=Brahmagupta&action=edit&redlink=1" class="new" title="Brahmagupta (il-paġna ma teżistix)">Brahmagupta</a>, fit-trattat tiegħu <i>Brahma Sputa Siddhanta</i>, jivvinta l-metodu <i>ċakravala</i> għas-soluzzjoni ta’ xi ekwazzjonijiet kwadratiċi simultanji indeterminati, fosthom l-ekwazzjoni ta’ Pell, u jagħti regoli għas-soluzzjoni ta’ l-ekwazzjonijiet linjari u kwadratiċi.</li> <li>820: Il-matematiku Persjan, Muhammad ibn Musa <a href="/w/index.php?title=Al-Khwari%C5%BCmi&action=edit&redlink=1" class="new" title="Al-Khwariżmi (il-paġna ma teżistix)">al-Khwariżmi</a>, jikteb it-trattat intitolat <i>Al-Kitab al-Ġabr wa-l-Muqabala</i> (li tfisser "Il-Ktieb tal-ġbir u t-tqabbil") fuq is-soluzzjoni sistematika ta’ l-ekwazzjonijiet linjari u kwadratiċi. Il-kelma <i>alġebra</i> ġejja minn <i>al-Ġabr</i> fit-titlu ta’ dal-ktieb. Al-Khwariżmi hu kkunsidrat minn bosta bħala "missier l-alġebra" u ħafna mill-metodi tiegħu ta’ riduzzjoni jew ‘’ġbir’’ għadna nużawhom fl-alġebra sa llum.</li> <li>Ċirka 850: Il-matematiku Persjan, <a href="/w/index.php?title=Al-Ma%C4%A7ani&action=edit&redlink=1" class="new" title="Al-Maħani (il-paġna ma teżistix)">al-Maħani</a>, jaħseb fl-ideja ta’ riduzzjoni ta’ problemi ġometriċi, bħad-duplikazzjoni tal-kubu, għal problemi fl-alġebra.</li> <li>Ċirka 850 Il-matematiku, <a href="/w/index.php?title=Mahavira&action=edit&redlink=1" class="new" title="Mahavira (il-paġna ma teżistix)">Mahavira</a>, jirriżolvi bosta ekwazzjonijiet kwadratiċi, kubiċi, kwartiċi, kwintiċi u ta’ ordni ogħla kif ukoll xi ekwazzjonijiet indeterminati. kwadratiċi, kubiċi u ta’ ordni ogħla.</li> <li>Ċirka 990: Il-Persjan <a href="/w/index.php?title=Abu_Bakr_al-Kara%C4%A1i&action=edit&redlink=1" class="new" title="Abu Bakr al-Karaġi (il-paġna ma teżistix)">Abu Bakr al-Karaġi</a>, fit-trattat tiegħu <i>al-Fakhri</i>, jiżviluppa l-alġebra iżjed billi jestendi l-metodoloġija ta’ Al-Khwariżmi biex tinkludi poteri integrali u radiċi integrali ta’ kwantitajiet mhux magħrufa. Jissostwixxi l-operazzjonijiet gometriċi ta’ l-alġebra b’operazzjonijiet aritmetiċi moderni, u jiddefinixxi il-monomjali x, x<sup>2</sup>, x<sup>3</sup>, ... u 1/x, 1/x<sup>2</sup>, 1/x<sup>3</sup>, ... u jagħti l-prodott ta’ kull par minn dawn.</li> <li>Ċirka 1050: Il-matematiku Ċiniż, <a href="/w/index.php?title=%C4%A0ija_Ksijan&action=edit&redlink=1" class="new" title="Ġija Ksijan (il-paġna ma teżistix)">Ġija Ksijan</a>, jsib soluzzjonijiet numeriċi ta’ ekwazzjonijiet polinomjali.</li> <li>1072: Il-matematiku Persjan, <a href="/w/index.php?title=Omar_Khajjam&action=edit&redlink=1" class="new" title="Omar Khajjam (il-paġna ma teżistix)">Omar Khajjam</a>, jiżviluppa l-ġometrija alġebrija, u fit-<i>Trattat fuq Dimostrazzjoni ta’ Problemi fl-Alġebra</i>, jagħti klassifikazzjoni ta’ ekwazzjonijiet kubiċi permezz ta’soluzzjonijiet ġometriċi ġenerali misjuba bis-sezzjonijiet koniċi ntlaqqin.</li> <li>1114: Il-matematiku Indjan, <a href="/w/index.php?title=Bhaskara&action=edit&redlink=1" class="new" title="Bhaskara (il-paġna ma teżistix)">Bhaskara</a>, fil- <i>Biġaganita</i> (<i>Alġebra</i>), jinduna li numru pożittiv għandu radiċi kwadrata pożittiva u oħra negattiva, u jirriżolvi bosta ekwazzjonijiet kubiċi, kwartiċi, kwintiċi u ta’ ordni polinomjali, kif ukoll l-ekwazzjoni kwadratika ġenerali indeterminata.</li> <li>1202: L-alġebra tidħol l-Ewropa l-iktar imħabba x-xogħol ta’ <a href="/w/index.php?title=Leonardo_Fibonacci&action=edit&redlink=1" class="new" title="Leonardo Fibonacci (il-paġna ma teżistix)">Leonardo Fibonacci</a> ta’ Pisa fil-ktieb tiegħu <i><a href="/w/index.php?title=Liber_Abaci&action=edit&redlink=1" class="new" title="Liber Abaci (il-paġna ma teżistix)">Liber Abaci</a></i>.</li> <li>Ċirka 1300: Il-matematiku Ċiniż, <a href="/w/index.php?title=%C5%BBhu_Xi%C4%A1je&action=edit&redlink=1" class="new" title="Żhu Xiġje (il-paġna ma teżistix)">Żhu Xiġje</a>, jittratta l-alġebra polinomjali, jirriżolvi ekwazzjonijiet kwadratiċi, ekwazzjonijiet simultanji u ekwazzjonijiet b’sa erbgħa kwantitajiet mhux magħrufa, u jirriżolvi numerikament xi ekwazzjonijiet kwartiċi, kwintiċi u polinomjali ta’ ordni ogħla.</li></ul> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Stampa:Evariste_galois.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/200px-Evariste_galois.jpg" decoding="async" width="200" height="259" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/300px-Evariste_galois.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/53/Evariste_galois.jpg/400px-Evariste_galois.jpg 2x" data-file-width="792" data-file-height="1024" /></a><figcaption> Évariste Galois t.1811 m.1832</figcaption></figure> <ul><li>Ċirka 1400: Il-matematiku Indjan, <a href="/w/index.php?title=Madhava_ta%E2%80%99_Sangamagramma&action=edit&redlink=1" class="new" title="Madhava ta’ Sangamagramma (il-paġna ma teżistix)">Madhava ta’ Sangamagramma</a>, jiskopri metodi iterattivi għas-soluzzjoni approssima ta’ ekwazzjonijiet mhux linjari.</li> <li>1535: Nicolo Fontana <a href="/w/index.php?title=Tartaglia&action=edit&redlink=1" class="new" title="Tartaglia (il-paġna ma teżistix)">Tartaglia</a> u matematiċi oħra fl-Italja independentement jirriżolvu l-ekwazzjoni kubika ġenerali.</li> <li>1545: Girolamo <a href="/w/index.php?title=Cardano&action=edit&redlink=1" class="new" title="Cardano (il-paġna ma teżistix)">Cardano</a> jippublika <i>Ars magna</i> (<i>L-Arti l-Kbira</i>) fejn jagħti s-soluzzjoni ta’ Fontana għall-ekwazzjoni kwartika ġenerali.</li> <li>1572: Rafael <a href="/w/index.php?title=Bombelli&action=edit&redlink=1" class="new" title="Bombelli (il-paġna ma teżistix)">Bombelli</a> jsib ir-radiċi komplessa tal-kubiku u jtejjeb in-notazzjoni kurrenti.</li> <li>1591: <a href="/w/index.php?title=Fran%C3%A7ois_Vi%C3%A8te&action=edit&redlink=1" class="new" title="François Viète (il-paġna ma teżistix)">François Viète</a> jiżviluppa u jtejjeb in-notazzjoni simbolika għall-poteri fil-ktieb <i>In artem analyticam isagoge</i>.</li> <li>1682: <a href="/w/index.php?title=Gottfried_Leibniz&action=edit&redlink=1" class="new" title="Gottfried Leibniz (il-paġna ma teżistix)">Gottfried Wilhelm Leibniz</a> jiżviluppa l-manipulazzjoni simbolika b’regoli formali li jgħidilhom <i>characteristica generalis</i>.</li> <li>1680s: Il-matematiku Ġappuniż, <a href="/w/index.php?title=Kowa_Seki&action=edit&redlink=1" class="new" title="Kowa Seki (il-paġna ma teżistix)">Kowa Seki</a>, fil-<i>Metodu għas-soluzzjoni ta’ problemi dissimulati</i>, jiskopri d-determinant u n-<a href="/w/index.php?title=Numri_ta%E2%80%99_Bernoulli&action=edit&redlink=1" class="new" title="Numri ta’ Bernoulli (il-paġna ma teżistix)">numri ta’ Bernoulli</a>.</li> <li>1750: <a href="/w/index.php?title=Gabriel_Cramer&action=edit&redlink=1" class="new" title="Gabriel Cramer (il-paġna ma teżistix)">Gabriel Cramer</a>, fit-trattat tiegħu <i>Introduzzjoni għall-analisi ta’ kurvi alġebrin</i>, jipproponi r-<a href="/w/index.php?title=Regola_ta%E2%80%99_Cramer&action=edit&redlink=1" class="new" title="Regola ta’ Cramer (il-paġna ma teżistix)">regola ta’ Cramer</a> u jistudja l-kurvi alġebrin, il-matriċi u d-determinanti.</li> <li>1824: <a href="/w/index.php?title=Niels_Henrik_Abel&action=edit&redlink=1" class="new" title="Niels Henrik Abel (il-paġna ma teżistix)">Niels Henrik Abel</a> jipprova li ma nistgħux nirriżolvu l-ekwazzjoni kwintika ġenerali bir-radiċi.</li> <li>1832: It-teorija ta’ Galois jiżviluppha <a href="/w/index.php?title=%C3%89variste_Galois&action=edit&redlink=1" class="new" title="Évariste Galois (il-paġna ma teżistix)">Évariste Galois</a> fix-xogħol tiegħu fuq l-alġebra astratta.</li></ul> <p><br /> </p> <div style="border: 1px solid #99b3ff; text-align: center; padding: 2px; background-color: #D8D9EB; font-size:125%; font-weight:bolder;"><span typeof="mw:File"><a href="/wiki/Stampa:P_math.png" 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