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class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>博弈論</span> </div> </a> <ul id="toc-博弈論-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-睇埋" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#睇埋"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>睇埋</span> </div> </a> <ul id="toc-睇埋-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-引述" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#引述"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>引述</span> </div> </a> <ul id="toc-引述-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目錄" 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="開/收內容一覽" > <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">開/收內容一覽</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">應用數學</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="去睇另一種語文嘅文章。有79種語言版本。" > <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-79" 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">79種語言</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/Toegepaste_wiskunde" title="Toegepaste wiskunde – 南非荷蘭文" lang="af" hreflang="af" data-title="Toegepaste wiskunde" data-language-autonym="Afrikaans" data-language-local-name="南非荷蘭文" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A%D8%A7%D8%AA_%D8%AA%D8%B7%D8%A8%D9%8A%D9%82%D9%8A%D8%A9" title="رياضيات تطبيقية – 阿拉伯文" lang="ar" hreflang="ar" data-title="رياضيات تطبيقية" data-language-autonym="العربية" data-language-local-name="阿拉伯文" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Matem%C3%A1tiques_aplicaes" title="Matemátiques aplicaes – 阿斯圖里亞文" lang="ast" hreflang="ast" data-title="Matemátiques aplicaes" data-language-autonym="Asturianu" data-language-local-name="阿斯圖里亞文" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/T%C9%99tbiqi_riyaziyyat" title="Tətbiqi riyaziyyat – 亞塞拜然文" lang="az" hreflang="az" data-title="Tətbiqi riyaziyyat" data-language-autonym="Azərbaycanca" data-language-local-name="亞塞拜然文" 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%AA%D8%B7%D8%A8%DB%8C%D9%82%DB%8C_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA" title="تطبیقی ریاضیات – South Azerbaijani" lang="azb" hreflang="azb" data-title="تطبیقی 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-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%9F%D1%80%D1%8B%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Прыкладная матэматыка – 白俄羅斯文" lang="be" hreflang="be" data-title="Прыкладная матэматыка" data-language-autonym="Беларуская" data-language-local-name="白俄羅斯文" 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%9F%D1%80%D1%8B%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D1%8D%D0%BC%D0%B0%D1%82%D1%8B%D0%BA%D0%B0" title="Прыкладная матэматыка – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Прыкладная 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%9F%D1%80%D0%B8%D0%BB%D0%BE%D0%B6%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Приложна математика – 保加利亞文" lang="bg" hreflang="bg" data-title="Приложна математика" data-language-autonym="Български" data-language-local-name="保加利亞文" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%AB%E0%A6%B2%E0%A6%BF%E0%A6%A4_%E0%A6%97%E0%A6%A3%E0%A6%BF%E0%A6%A4" title="ফলিত গণিত – 孟加拉文" lang="bn" hreflang="bn" data-title="ফলিত গণিত" data-language-autonym="বাংলা" data-language-local-name="孟加拉文" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Primijenjena_matematika" title="Primijenjena matematika – 波士尼亞文" lang="bs" hreflang="bs" data-title="Primijenjena matematika" data-language-autonym="Bosanski" data-language-local-name="波士尼亞文" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Matem%C3%A0tiques_aplicades" title="Matemàtiques aplicades – 加泰羅尼亞文" lang="ca" hreflang="ca" data-title="Matemàtiques aplicades" data-language-autonym="Català" data-language-local-name="加泰羅尼亞文" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Aplikovan%C3%A1_matematika" title="Aplikovaná matematika – 捷克文" lang="cs" hreflang="cs" data-title="Aplikovaná matematika" data-language-autonym="Čeština" data-language-local-name="捷克文" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%9A%D0%B8%D0%BB%D1%82%D0%B5%D1%80%C4%95%D1%88_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Килтерĕш математика – 楚瓦什文" lang="cv" hreflang="cv" data-title="Килтерĕш математика" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什文" 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_gymhwysol" title="Mathemateg gymhwysol – 威爾斯文" lang="cy" hreflang="cy" data-title="Mathemateg gymhwysol" data-language-autonym="Cymraeg" data-language-local-name="威爾斯文" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Anvendt_matematik" title="Anvendt matematik – 丹麥文" lang="da" hreflang="da" data-title="Anvendt matematik" data-language-autonym="Dansk" data-language-local-name="丹麥文" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Angewandte_Mathematik" title="Angewandte Mathematik – 德文" lang="de" hreflang="de" data-title="Angewandte Mathematik" data-language-autonym="Deutsch" data-language-local-name="德文" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%95%CF%86%CE%B1%CF%81%CE%BC%CE%BF%CF%83%CE%BC%CE%AD%CE%BD%CE%B1_%CE%BC%CE%B1%CE%B8%CE%B7%CE%BC%CE%B1%CF%84%CE%B9%CE%BA%CE%AC" title="Εφαρμοσμένα μαθηματικά – 希臘文" lang="el" hreflang="el" data-title="Εφαρμοσμένα μαθηματικά" data-language-autonym="Ελληνικά" data-language-local-name="希臘文" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Applied_mathematics" title="Applied mathematics – 英文" lang="en" hreflang="en" data-title="Applied mathematics" data-language-autonym="English" data-language-local-name="英文" 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/Aplika_matematiko" title="Aplika matematiko – 世界文" lang="eo" hreflang="eo" data-title="Aplika matematiko" data-language-autonym="Esperanto" data-language-local-name="世界文" 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%A1tica_aplicada" title="Matemática aplicada – 西班牙文" lang="es" hreflang="es" data-title="Matemática aplicada" data-language-autonym="Español" data-language-local-name="西班牙文" 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/Rakendusmatemaatika" title="Rakendusmatemaatika – 愛沙尼亞文" lang="et" hreflang="et" data-title="Rakendusmatemaatika" data-language-autonym="Eesti" data-language-local-name="愛沙尼亞文" 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_aplikatuak" title="Matematika aplikatuak – 巴斯克文" lang="eu" hreflang="eu" data-title="Matematika aplikatuak" data-language-autonym="Euskara" data-language-local-name="巴斯克文" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C%D8%A7%D8%AA_%DA%A9%D8%A7%D8%B1%D8%A8%D8%B1%D8%AF%DB%8C" title="ریاضیات کاربردی – 波斯文" lang="fa" hreflang="fa" data-title="ریاضیات کاربردی" data-language-autonym="فارسی" data-language-local-name="波斯文" 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/Sovellettu_matematiikka" title="Sovellettu matematiikka – 芬蘭文" lang="fi" hreflang="fi" data-title="Sovellettu matematiikka" data-language-autonym="Suomi" data-language-local-name="芬蘭文" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Math%C3%A9matiques_appliqu%C3%A9es" title="Mathématiques appliquées – 法文" lang="fr" hreflang="fr" data-title="Mathématiques appliquées" data-language-autonym="Français" data-language-local-name="法文" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Matamaitic_fheidhmeach" title="Matamaitic fheidhmeach – 愛爾蘭文" lang="ga" hreflang="ga" data-title="Matamaitic fheidhmeach" data-language-autonym="Gaeilge" data-language-local-name="愛爾蘭文" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Matem%C3%A1tica_aplicada" title="Matemática aplicada – 加里西亞文" lang="gl" hreflang="gl" data-title="Matemática aplicada" data-language-autonym="Galego" data-language-local-name="加里西亞文" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%AA%D7%9E%D7%98%D7%99%D7%A7%D7%94_%D7%A9%D7%99%D7%9E%D7%95%D7%A9%D7%99%D7%AA" title="מתמטיקה שימושית – 希伯來文" lang="he" hreflang="he" data-title="מתמטיקה שימושית" data-language-autonym="עברית" data-language-local-name="希伯來文" 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%B5%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B5%E0%A4%B9%E0%A4%BE%E0%A4%B0%E0%A4%BF%E0%A4%95_%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4" title="व्यावहारिक गणित – 北印度文" lang="hi" hreflang="hi" data-title="व्यावहारिक गणित" data-language-autonym="हिन्दी" data-language-local-name="北印度文" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Primijenjena_matematika" title="Primijenjena matematika – 克羅埃西亞文" lang="hr" hreflang="hr" data-title="Primijenjena matematika" data-language-autonym="Hrvatski" data-language-local-name="克羅埃西亞文" 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_aplike" title="Matematik aplike – 海地文" lang="ht" hreflang="ht" data-title="Matematik aplike" data-language-autonym="Kreyòl ayisyen" data-language-local-name="海地文" class="interlanguage-link-target"><span>Kreyòl ayisyen</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%BF%D5%AB%D6%80%D5%A1%D5%BC%D5%A1%D5%AF%D5%A1%D5%B6_%D5%B4%D5%A1%D5%A9%D5%A5%D5%B4%D5%A1%D5%BF%D5%AB%D5%AF%D5%A1" title="Կիրառական մաթեմատիկա – 亞美尼亞文" lang="hy" hreflang="hy" data-title="Կիրառական մաթեմատիկա" data-language-autonym="Հայերեն" data-language-local-name="亞美尼亞文" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Mathematica_applicate" title="Mathematica applicate – 國際文" lang="ia" hreflang="ia" data-title="Mathematica applicate" data-language-autonym="Interlingua" data-language-local-name="國際文" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Matematika_terapan" title="Matematika terapan – 印尼文" lang="id" hreflang="id" data-title="Matematika terapan" data-language-autonym="Bahasa Indonesia" data-language-local-name="印尼文" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Aplikita_matematiko" title="Aplikita matematiko – 伊多文" lang="io" hreflang="io" data-title="Aplikita matematiko" data-language-autonym="Ido" data-language-local-name="伊多文" 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/Hagn%C3%BDtt_st%C3%A6r%C3%B0fr%C3%A6%C3%B0i" title="Hagnýtt stærðfræði – 冰島文" lang="is" hreflang="is" data-title="Hagnýtt stærðfræði" data-language-autonym="Íslenska" data-language-local-name="冰島文" 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_applicata" title="Matematica applicata – 義大利文" lang="it" hreflang="it" data-title="Matematica applicata" data-language-autonym="Italiano" data-language-local-name="義大利文" 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/%E5%BF%9C%E7%94%A8%E6%95%B0%E5%AD%A6" title="応用数学 – 日文" lang="ja" hreflang="ja" data-title="応用数学" data-language-autonym="日本語" data-language-local-name="日文" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/Mat%C3%A9matika_terapan" title="Matématika terapan – 爪哇文" lang="jv" hreflang="jv" data-title="Matématika terapan" data-language-autonym="Jawa" data-language-local-name="爪哇文" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%92%E1%83%90%E1%83%9B%E1%83%9D%E1%83%A7%E1%83%94%E1%83%9C%E1%83%94%E1%83%91%E1%83%98%E1%83%97%E1%83%98_%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="გამოყენებითი მათემატიკა – 喬治亞文" lang="ka" hreflang="ka" data-title="გამოყენებითი მათემატიკა" data-language-autonym="ქართული" data-language-local-name="喬治亞文" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D2%9A%D0%BE%D0%BB%D0%B4%D0%B0%D0%BD%D0%B1%D0%B0%D0%BB%D1%8B_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Қолданбалы математика – 哈薩克文" lang="kk" hreflang="kk" data-title="Қолданбалы математика" data-language-autonym="Қазақша" data-language-local-name="哈薩克文" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%91%EC%9A%A9%EC%88%98%ED%95%99" title="응용수학 – 韓文" lang="ko" hreflang="ko" data-title="응용수학" data-language-autonym="한국어" data-language-local-name="韓文" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-la mw-list-item"><a href="https://la.wikipedia.org/wiki/Mathematica_adhibita" title="Mathematica adhibita – 拉丁文" lang="la" hreflang="la" data-title="Mathematica adhibita" data-language-autonym="Latina" data-language-local-name="拉丁文" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lfn mw-list-item"><a href="https://lfn.wikipedia.org/wiki/Matematica_aplicada" title="Matematica aplicada – 新共同語言" lang="lfn" hreflang="lfn" data-title="Matematica aplicada" data-language-autonym="Lingua Franca Nova" data-language-local-name="新共同語言" class="interlanguage-link-target"><span>Lingua Franca Nova</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Lieti%C5%A1%C4%B7%C4%81_matem%C4%81tika" title="Lietišķā matemātika – 拉脫維亞文" lang="lv" hreflang="lv" data-title="Lietišķā matemātika" data-language-autonym="Latviešu" data-language-local-name="拉脫維亞文" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%BC%D0%B5%D0%BD%D0%B5%D1%82%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Применета математика – 馬其頓文" lang="mk" hreflang="mk" data-title="Применета математика" data-language-autonym="Македонски" data-language-local-name="馬其頓文" 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%AA%E0%B5%8D%E0%B4%B0%E0%B4%AF%E0%B5%8B%E0%B4%97_%E0%B4%97%E0%B4%A3%E0%B4%BF%E0%B4%A4%E0%B4%82" title="പ്രയോഗ ഗണിതം – 馬來亞拉姆文" lang="ml" hreflang="ml" data-title="പ്രയോഗ ഗണിതം" data-language-autonym="മലയാളം" data-language-local-name="馬來亞拉姆文" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Matematik_gunaan" title="Matematik gunaan – 馬來文" lang="ms" hreflang="ms" data-title="Matematik gunaan" data-language-autonym="Bahasa Melayu" data-language-local-name="馬來文" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%A1%E1%80%9E%E1%80%AF%E1%80%B6%E1%80%B8%E1%80%81%E1%80%BB%E1%80%9E%E1%80%84%E1%80%BA%E1%80%B9%E1%80%81%E1%80%BB%E1%80%AC" title="အသုံးချသင်္ချာ – 緬甸文" lang="my" hreflang="my" data-title="အသုံးချသင်္ချာ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="緬甸文" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Toegepaste_wiskunde" title="Toegepaste wiskunde – 荷蘭文" lang="nl" hreflang="nl" data-title="Toegepaste wiskunde" data-language-autonym="Nederlands" data-language-local-name="荷蘭文" 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/Bruksmatematikk" title="Bruksmatematikk – 耐諾斯克挪威文" lang="nn" hreflang="nn" data-title="Bruksmatematikk" data-language-autonym="Norsk nynorsk" data-language-local-name="耐諾斯克挪威文" 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/Anvendt_matematikk" title="Anvendt matematikk – 巴克摩挪威文" lang="nb" hreflang="nb" data-title="Anvendt matematikk" data-language-autonym="Norsk bokmål" data-language-local-name="巴克摩挪威文" 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/Aplikat_matematike" title="Aplikat matematike – 諾維亞文" lang="nov" hreflang="nov" data-title="Aplikat matematike" data-language-autonym="Novial" data-language-local-name="諾維亞文" class="interlanguage-link-target"><span>Novial</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Matematyka_stosowana" title="Matematyka stosowana – 波蘭文" lang="pl" hreflang="pl" data-title="Matematyka stosowana" data-language-autonym="Polski" data-language-local-name="波蘭文" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Matem%C3%A1tica_aplicada" title="Matemática aplicada – 葡萄牙文" lang="pt" hreflang="pt" data-title="Matemática aplicada" data-language-autonym="Português" data-language-local-name="葡萄牙文" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Matematic%C4%83_aplicat%C4%83" title="Matematică aplicată – 羅馬尼亞文" lang="ro" hreflang="ro" data-title="Matematică aplicată" data-language-autonym="Română" data-language-local-name="羅馬尼亞文" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0%D1%8F_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Прикладная математика – 俄文" lang="ru" hreflang="ru" data-title="Прикладная математика" data-language-autonym="Русский" data-language-local-name="俄文" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Applee%27d_mathematics" title="Applee'd mathematics – 蘇格蘭文" lang="sco" hreflang="sco" data-title="Applee'd mathematics" data-language-autonym="Scots" data-language-local-name="蘇格蘭文" 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%B9%D9%85%D9%84%D9%8A_%D8%B1%D9%8A%D8%A7%D8%B6%D9%8A" title="عملي رياضي – 信德文" lang="sd" hreflang="sd" data-title="عملي رياضي" data-language-autonym="سنڌي" data-language-local-name="信德文" 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/Primenjena_matematika" title="Primenjena matematika – 塞爾維亞克羅埃西亞文" lang="sh" hreflang="sh" data-title="Primenjena matematika" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞爾維亞克羅埃西亞文" 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_tisnsit" title="Tusnakt tisnsit – 希爾哈文" lang="shi" hreflang="shi" data-title="Tusnakt tisnsit" data-language-autonym="Taclḥit" data-language-local-name="希爾哈文" class="interlanguage-link-target"><span>Taclḥit</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Applied_mathematics" title="Applied mathematics – Simple English" lang="en-simple" hreflang="en-simple" data-title="Applied 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/Aplikovan%C3%A1_matematika" title="Aplikovaná matematika – 斯洛伐克文" lang="sk" hreflang="sk" data-title="Aplikovaná matematika" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克文" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Uporabna_matematika" title="Uporabna matematika – 斯洛維尼亞文" lang="sl" hreflang="sl" data-title="Uporabna matematika" data-language-autonym="Slovenščina" data-language-local-name="斯洛維尼亞文" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Matematika_aplikative" title="Matematika aplikative – 阿爾巴尼亞文" lang="sq" hreflang="sq" data-title="Matematika aplikative" data-language-autonym="Shqip" data-language-local-name="阿爾巴尼亞文" 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%9F%D1%80%D0%B8%D0%BC%D0%B5%D1%9A%D0%B5%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Примењена математика – 塞爾維亞文" lang="sr" hreflang="sr" data-title="Примењена математика" data-language-autonym="Српски / srpski" data-language-local-name="塞爾維亞文" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-su mw-list-item"><a href="https://su.wikipedia.org/wiki/Matematik_terapan" title="Matematik terapan – 巽他文" lang="su" hreflang="su" data-title="Matematik terapan" data-language-autonym="Sunda" data-language-local-name="巽他文" 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/Till%C3%A4mpad_matematik" title="Tillämpad matematik – 瑞典文" lang="sv" hreflang="sv" data-title="Tillämpad matematik" data-language-autonym="Svenska" data-language-local-name="瑞典文" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AA%E0%AE%AF%E0%AE%A9%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%8D%E0%AE%9F%E0%AF%81%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D" title="பயன்பாட்டுக் கணிதம் – 坦米爾文" lang="ta" hreflang="ta" data-title="பயன்பாட்டுக் கணிதம்" data-language-autonym="தமிழ்" data-language-local-name="坦米爾文" class="interlanguage-link-target"><span>தமிழ்</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%E0%B8%9B%E0%B8%A3%E0%B8%B0%E0%B8%A2%E0%B8%B8%E0%B8%81%E0%B8%95%E0%B9%8C" title="คณิตศาสตร์ประยุกต์ – 泰文" lang="th" hreflang="th" data-title="คณิตศาสตร์ประยุกต์" data-language-autonym="ไทย" data-language-local-name="泰文" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tl badge-Q70893996 mw-list-item" title=""><a href="https://tl.wikipedia.org/wiki/Matematikang_nalalapat" title="Matematikang nalalapat – 塔加路族文" lang="tl" hreflang="tl" data-title="Matematikang nalalapat" data-language-autonym="Tagalog" data-language-local-name="塔加路族文" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Matematik_m%C3%BChendisli%C4%9Fi" title="Matematik mühendisliği – 土耳其文" lang="tr" hreflang="tr" data-title="Matematik mühendisliği" data-language-autonym="Türkçe" data-language-local-name="土耳其文" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9F%D1%80%D0%B8%D0%BA%D0%BB%D0%B0%D0%B4%D0%BD%D0%B0_%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0" title="Прикладна математика – 烏克蘭文" lang="uk" hreflang="uk" data-title="Прикладна математика" data-language-autonym="Українська" data-language-local-name="烏克蘭文" 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%A7%D8%B7%D9%84%D8%A7%D9%82%DB%8C_%D8%B1%DB%8C%D8%A7%D8%B6%DB%8C" title="اطلاقی ریاضی – 烏都文" lang="ur" hreflang="ur" data-title="اطلاقی ریاضی" data-language-autonym="اردو" data-language-local-name="烏都文" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/To%C3%A1n_h%E1%BB%8Dc_%E1%BB%A9ng_d%E1%BB%A5ng" title="Toán học ứng dụng – 越南文" lang="vi" hreflang="vi" data-title="Toán học ứng dụng" data-language-autonym="Tiếng Việt" data-language-local-name="越南文" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Matemat_paj%C3%A4f%C3%BCk%C3%B6l" title="Matemat pajäfüköl – 沃拉普克文" lang="vo" hreflang="vo" data-title="Matemat pajäfüköl" data-language-autonym="Volapük" data-language-local-name="沃拉普克文" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E5%BA%94%E7%94%A8%E6%95%B0%E5%AD%A6" title="应用数学 – 吳語" lang="wuu" hreflang="wuu" data-title="应用数学" data-language-autonym="吴语" data-language-local-name="吳語" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E5%BA%94%E7%94%A8%E6%95%B0%E5%AD%A6" title="应用数学 – 中文" lang="zh" hreflang="zh" data-title="应用数学" data-language-autonym="中文" data-language-local-name="中文" class="interlanguage-link-target"><span>中文</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/%C3%88ng-i%C5%8Dng_s%C3%B2%CD%98-ha%CC%8Dk" title="Èng-iōng sò͘-ha̍k – 閩南語" lang="nan" hreflang="nan" data-title="Èng-iōng sò͘-ha̍k" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="閩南語" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q33521#sitelinks-wikipedia" title="改跨語言拎" class="wbc-editpage">改拎</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div 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class="vector-menu-content-list"> <li id="electron-print_pdf" class="mw-list-item"><a href="/w/index.php?title=Special:DownloadAsPdf&page=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=show-download-screen"><span>下載PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="javascript:print();" rel="alternate" title="呢一版印得嘅版本[p]" accesskey="p"><span>印得嘅版本</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> 第啲維基項目 </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:Applied_mathematics" hreflang="en"><span>維基同享</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q33521" title="連到接住資料儲存庫嘅項目[g]" accesskey="g"><span>維基數據項</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="頁面工具"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="閱讀設定"> <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">閱讀設定</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">移去側欄</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">收埋</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">出自維基百科，自由嘅百科全書</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="yue" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/File:Vehicle_Routing_Problem_Example.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Vehicle_Routing_Problem_Example.svg/300px-Vehicle_Routing_Problem_Example.svg.png" decoding="async" width="300" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Vehicle_Routing_Problem_Example.svg/450px-Vehicle_Routing_Problem_Example.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e0/Vehicle_Routing_Problem_Example.svg/600px-Vehicle_Routing_Problem_Example.svg.png 2x" data-file-width="548" data-file-height="535" /></a><figcaption>「揀邊條路行最快」涉及應用數學。</figcaption></figure> <p><b>應用數學</b>（<a href="/wiki/Wikipedia:%E7%B2%B5%E6%96%87%E6%8B%BC%E9%9F%B3" title="Wikipedia:粵文拼音">粵拼</a>：<span class="plainlinks" style="display:inline-block"><a rel="nofollow" class="external text" href="http://yue.forvo.com/word/yue/應用數學/#yue"><span>jing<span class="Jpingtone">3</span> jung<span class="Jpingtone">6</span> sou<span class="Jpingtone">3</span> hok<span class="Jpingtone">6</span></span></a></span>；<a href="/wiki/%E8%8B%B1%E6%96%87" title="英文">英文</a>：<span lang="en"><b>Applied Mathematics</b></span>）係<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>嘅分支，研究點樣將數學應用到其他範疇，同<a href="/wiki/%E7%B4%94%E7%B2%B9%E6%95%B8%E5%AD%B8" title="純粹數學">純粹數學</a>相反。應用數學方面嘅知識對於<a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a>、<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>同<a href="/wiki/%E5%B7%A5%E7%A8%8B%E5%AD%B8" title="工程學">工程學</a>方面嘅工作嚟講都好有用。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="數學分析"><span id=".E6.95.B8.E5.AD.B8.E5.88.86.E6.9E.90"></span>數學分析</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=1" title="編輯小節: 數學分析"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a></div> <p><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a>（mathematical analysis）重點在於研究<a href="/wiki/%E6%A5%B5%E9%99%90_(%E5%87%BD%E6%95%B8)" title="極限 (函數)">極限</a>（limit）同相關嘅概念：喺數學上，一個<a href="/wiki/%E5%87%BD%E6%95%B8" title="函數">函數</a>有極限值即係指，隨住個函數嘅輸入值趨近某個值，個函數嘅輸出值會趨近另外一個值，可以用<a href="/wiki/%E5%85%AC%E5%BC%8F" title="公式">公式</a>想像成<sup id="cite_ref-weisstein_1-0" class="reference"><a href="#cite_note-weisstein-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><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 \lim _{x\to c}f(x)=L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> <mo stretchy="false">→</mo> <mi>c</mi> </mrow> </munder> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{x\to c}f(x)=L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3f174c16cc9e61932ecc7eb71b27a4f10a44fc9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:12.781ex; height:3.843ex;" alt="{\displaystyle \lim _{x\to c}f(x)=L}"></span></dd></dl> <p>上述呢條式係指「隨住輸入值 <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 嘅值趨近 <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 c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86a67b81c2de995bd608d5b2df50cd8cd7d92455" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.007ex; height:1.676ex;" alt="{\displaystyle c}"></span>（<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 x\to c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo stretchy="false">→</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x\to c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7e550b4e2544dfce8c3b9e7af6344902e93f1c1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.951ex; height:1.843ex;" alt="{\displaystyle x\to c}"></span>），<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 f}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/132e57acb643253e7810ee9702d9581f159a1c61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.279ex; height:2.509ex;" alt="{\displaystyle f}"></span> 呢個以 <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 做輸入值嘅函數嘅輸出值（<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 f(x)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f(x)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/202945cce41ecebb6f643f31d119c514bec7a074" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.418ex; height:2.843ex;" alt="{\displaystyle f(x)}"></span>）會趨近 <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 L}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>L</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle L}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/103168b86f781fe6e9a4a87b8ea1cebe0ad4ede8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.583ex; height:2.176ex;" alt="{\displaystyle L}"></span>」<sup id="cite_ref-weisstein_1-1" class="reference"><a href="#cite_note-weisstein-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>。呢個概念可以用嚟分析<a href="/wiki/%E8%A4%87%E9%9B%9C" title="複雜">複雜</a>嘅函數，好似係附圖嗰條線噉，條線就噉望落似係<a href="/wiki/%E6%9B%B2%E7%B7%9A" class="mw-redirect" title="曲線">曲</a>嘅，而家將條線喺 <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 ({\text{c}},{\text{L}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\text{c}},{\text{L}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db3d6093546937c40646b116cff35cade92ae8c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle ({\text{c}},{\text{L}})}"></span> 嗰點斬開，<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 ({\text{c}}-\delta ,{\text{L}}-\epsilon )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> <mo>−</mo> <mi>δ</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mo>−</mo> <mi>ϵ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\text{c}}-\delta ,{\text{L}}-\epsilon )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/429622940e929701d2c0f18378bd566b844655f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.002ex; height:2.843ex;" alt="{\displaystyle ({\text{c}}-\delta ,{\text{L}}-\epsilon )}"></span> 同 <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 ({\text{c}},{\text{L}})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>c</mtext> </mrow> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>L</mtext> </mrow> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ({\text{c}},{\text{L}})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db3d6093546937c40646b116cff35cade92ae8c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.328ex; height:2.843ex;" alt="{\displaystyle ({\text{c}},{\text{L}})}"></span> 之間嗰一細橛望落比較似一條<a href="/wiki/%E7%9B%B4%E7%B7%9A" class="mw-redirect" title="直線">直線</a>，即係話－ </p> <dl><dd><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 \lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}=}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}=}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/62ea3c9f20107499aa688e1e81758e76921479ae" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:11.716ex; height:5.843ex;" alt="{\displaystyle \lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}=}"></span> <b>一個恆定嘅數值</b>；</dd></dl> <p>喺條式當中，<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 \Delta x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f3890eb866b6258d7a304fc34c70ee3fb3a81a70" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.266ex; height:2.176ex;" alt="{\displaystyle \Delta x}"></span> 係指 <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 x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> 喺某兩點之間變咗幾多，而 <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 \Delta y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7caae142d915be8ef4d8c423bf91d1f6ea10e8e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.091ex; height:2.509ex;" alt="{\displaystyle \Delta y}"></span> 同理係指 <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 y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> 喺嗰兩點之間變咗幾多。上述呢條式講嘅係，無論一條線幾咁曲都好，如果將條線斬到<a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">極細</a>，就可以將每一極細橛想像成直線（<a href="/wiki/%E6%96%9C%E7%8E%87" title="斜率">斜率</a>有個特定數值），而呢個諗頭亦係<a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a>（calculus）嘅理論基礎<sup id="cite_ref-wolfderiv_2-0" class="reference"><a href="#cite_note-wolfderiv-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-stewart2008_3-0" class="reference"><a href="#cite_note-stewart2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>。除咗微積分之外，數學分析仲會著手研究<a href="/wiki/%E5%AF%A6%E6%95%B8" title="實數">實數</a>函數、<a href="/wiki/%E8%A4%87%E6%95%B8" title="複數">複數</a>函數、<a href="/wiki/%E9%80%BC%E8%BF%91%E7%90%86%E8%AB%96" title="逼近理論">逼近理論</a>同埋<a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a>等等嘅課題<sup id="cite_ref-rudin1976_4-0" class="reference"><a href="#cite_note-rudin1976-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。 </p><p>數學分析嘅<a class="mw-selflink selflink">用途</a>廣泛得好交關：<a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a>上研究嘅各種<a href="/wiki/%E8%87%AA%E7%84%B6%E7%8F%BE%E8%B1%A1" title="自然現象">自然現象</a>同埋<a href="/wiki/%E5%B7%A5%E7%A8%8B%E5%AD%B8" title="工程學">工程學</a>上研究嘅人造<a href="/wiki/%E7%B3%BB%E7%B5%B1" title="系統">系統</a>都可以用函數嚟描述；例如<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8" title="物理學">物理學</a>就好興用函數嘅方法表達<a href="/wiki/%E7%89%A9%E7%90%86%E5%AE%9A%E5%BE%8B" title="物理定律">佢哋啲定律</a>，所以數學分析上嘅方法能夠幫到手理解呢啲函數同埋按呢啲定律設計出嚟嘅人造系統<sup id="cite_ref-jinjin2007_5-0" class="reference"><a href="#cite_note-jinjin2007-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="運算理論"><span id=".E9.81.8B.E7.AE.97.E7.90.86.E8.AB.96"></span>運算理論</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=2" title="編輯小節: 運算理論"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/File:Turing_Machine_Model_Davey_2012.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Turing_Machine_Model_Davey_2012.jpg/300px-Turing_Machine_Model_Davey_2012.jpg" decoding="async" width="300" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Turing_Machine_Model_Davey_2012.jpg/450px-Turing_Machine_Model_Davey_2012.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Turing_Machine_Model_Davey_2012.jpg/600px-Turing_Machine_Model_Davey_2012.jpg 2x" data-file-width="5066" data-file-height="3377" /></a><figcaption>圖靈機嘅大致實現；部機會一路讀取條帶上面嘅一格，並且對嗰個格作出運算，再決定<br /> <b>(1)</b> 使唔使改嗰格，同埋<br /> <b>(2)</b> 跟住要向左郁定向右郁。</figcaption></figure> <div role="note" class="hatnote">内文：<a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a></div> <p><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a>（theory of computation）專門研究<a href="/wiki/%E6%A9%9F%E6%A2%B0" title="機械">機械</a>點樣用<a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95" title="演算法">演算法</a>解難。運算理論會用<a href="/wiki/%E6%95%B8%E5%AD%B8%E8%AD%89%E6%98%8E" title="數學證明">數學證明</a>等嘅方法，嘗試思考唔同種類嘅理論性<a href="/wiki/%E9%81%8B%E7%AE%97%E6%A9%9F%E6%A2%B0" class="mw-redirect" title="運算機械">運算機械</a>喺解難能力上有乜差異（<a href="/wiki/%E8%87%AA%E5%8B%95%E6%A9%9F%E7%90%86%E8%AB%96" title="自動機理論">自動機理論</a>）、有啲乜嘢問題係能夠（或者唔能夠）用運算機械解嘅（<a href="/wiki/%E5%8F%AF%E9%81%8B%E7%AE%97%E6%80%A7%E7%90%86%E8%AB%96" class="mw-redirect" title="可運算性理論">可運算性理論</a>）以及一個運算上嘅問題最高嘅可能解決效率（<a href="/wiki/%E9%81%8B%E7%AE%97%E8%A4%87%E9%9B%9C%E5%BA%A6%E7%90%86%E8%AB%96" title="運算複雜度理論">運算複雜度理論</a>）等等嘅問題<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>。 </p><p>用一句嘢概括嘅話，運算理論主要思考嘅係呢個問題<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>： </p> <table align="center" style="border-collapse:collapse; border-style:none; background-color:transparent; margin: 5px auto;" class="cquote"> <tbody><tr> <td valign="top" style="width:20px; color:#B2B7F2; font-size:40px; font-family:Elephant,'Times New Roman',serif; font-weight:bold; text-align:left; padding:10px 10px;">「 </td> <td><div style="display: table-cell; text-align: left; padding: 1em; vertical-align: middle;"><a href="/wiki/%E9%9B%BB%E8%85%A6" title="電腦">電腦</a>（<a href="/wiki/%E9%81%8B%E7%AE%97%E6%A9%9F%E6%A2%B0" class="mw-redirect" title="運算機械">運算機械</a>）嘅基本能力同<a href="/wiki/%E9%81%8B%E7%AE%97%E5%98%85%E6%A5%B5%E9%99%90" title="運算嘅極限">極限</a>係乜？</div> </td> <td valign="bottom" style="width:20px; color:#B2B7F2; font-size:40px; font-family:Elephant,'Times New Roman',serif; font-weight:bold; text-align:right; padding:10px 10px;">」 </td></tr></tbody></table> <p>運算理論會攞一啲<a href="/wiki/%E9%81%8B%E7%AE%97%E6%A8%A1%E5%9E%8B" title="運算模型">運算模型</a>（一個運算模型會描述一部機械點由輸入嗰度計個輸出出嚟）嚟將運算機械概念化。當中喺廿一世紀最常用嘅運算模型係所謂嘅<a href="/wiki/%E5%9C%96%E9%9D%88%E6%A9%9F" title="圖靈機">圖靈機</a>（Turing machine；個名取自著名<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%AE%B6" title="數學家">數學家</a><a href="/wiki/%E4%BA%9E%E5%80%AB%E5%9C%96%E9%9D%88" class="mw-redirect" title="亞倫圖靈">亞倫圖靈</a>），圖靈機可以想像成一部噉嘅機械：部圖靈機會讀取一條分做若干個格嘅帶，每個格裏面都會有個<a href="/wiki/%E7%AC%A6%E8%99%9F" title="符號">符號</a>（1 同 0 等）；喺每一個時間點，部圖靈機個讀取器都讀住其中一格，並且會做以下三個基本作業嘅其中一個<sup id="cite_ref-hodges2012_10-0" class="reference"><a href="#cite_note-hodges2012-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>： </p> <ol><li>讀取讀取器下嗰格有乜符號；</li> <li>編輯嗰格－寫一個新嘅符號落去或者刪除咗嗰格佢；</li> <li>將條帶向左或者向右移一格，等個讀取器可以讀取打前嗰個格隔蘺嘅一個格。</li></ol> <p>圖靈機呢部<a href="/wiki/%E6%8A%BD%E8%B1%A1" class="mw-redirect" title="抽象">抽象</a>機械就噉睇好似好簡單，但查實可以計到好多嘢<sup id="cite_ref-rabin2012_11-0" class="reference"><a href="#cite_note-rabin2012-11"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>，好似簡單嘅<a href="/wiki/%E5%8A%A0" title="加">加</a><a href="/wiki/%E6%B8%9B" title="減">減</a>數噉<sup id="cite_ref-turingmachineadd_12-0" class="reference"><a href="#cite_note-turingmachineadd-12"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>，而有咗加減數，就可以計到好多嘢。好似圖靈機等嘅概念性機械就係運算模型，運算理論家會思考唔同種類嘅運算模型，以及剖析呢啲運算模型喺解難能力上有乜分別，加深人對運算同電腦嘅理論性了解<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading2"><h2 id="概率論"><span id=".E6.A6.82.E7.8E.87.E8.AB.96"></span>概率論</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=3" title="編輯小節: 概率論"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1488945/mw-parser-output/.tmulti">.mw-parser-output .tmulti .thumbinner{display:flex;flex-direction:column}.mw-parser-output .tmulti .trow{display:flex;flex-direction:row;clear:left;flex-wrap:wrap;width:100%;box-sizing:border-box}.mw-parser-output .tmulti .tsingle{margin:1px;float:left}.mw-parser-output .tmulti .theader{clear:both;font-weight:bold;text-align:center;align-self:center;background-color:transparent;width:100%}.mw-parser-output .tmulti .thumbcaption{background-color:transparent}.mw-parser-output .tmulti .text-align-left{text-align:left}.mw-parser-output .tmulti .text-align-right{text-align:right}.mw-parser-output .tmulti .text-align-center{text-align:center}@media all and (max-width:720px){.mw-parser-output .tmulti .thumbinner{width:100%!important;box-sizing:border-box;max-width:none!important;align-items:center}.mw-parser-output .tmulti .trow{justify-content:center}.mw-parser-output .tmulti .tsingle{float:none!important;max-width:100%!important;box-sizing:border-box}.mw-parser-output .tmulti .trow>.thumbcaption{text-align:center}}</style><div class="thumb tmulti tright"><div class="thumbinner" style="width:292px;max-width:292px"><div class="trow"><div class="tsingle" style="width:290px;max-width:290px"><div class="thumbimage" style="height:191px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg/288px-13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg" decoding="async" width="288" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a4/13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg/432px-13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a4/13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg/576px-13-02-27-spielbank-wiesbaden-by-RalfR-093.jpg 2x" data-file-width="4288" data-file-height="2848" /></a></span></div></div></div><div class="trow"><div class="tsingle" style="width:136px;max-width:136px"><div class="thumbimage" style="height:179px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Coin_tossing.JPG" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Coin_tossing.JPG/134px-Coin_tossing.JPG" decoding="async" width="134" height="179" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Coin_tossing.JPG/201px-Coin_tossing.JPG 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e8/Coin_tossing.JPG/268px-Coin_tossing.JPG 2x" data-file-width="3240" data-file-height="4320" /></a></span></div></div><div class="tsingle" style="width:152px;max-width:152px"><div class="thumbimage" style="height:179px;overflow:hidden"><span typeof="mw:File"><a href="/wiki/File:Oh_the_games_people_play_now..._(38575282372).jpg" class="mw-file-description"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Oh_the_games_people_play_now..._%2838575282372%29.jpg/150px-Oh_the_games_people_play_now..._%2838575282372%29.jpg" decoding="async" width="150" height="180" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Oh_the_games_people_play_now..._%2838575282372%29.jpg/225px-Oh_the_games_people_play_now..._%2838575282372%29.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Oh_the_games_people_play_now..._%2838575282372%29.jpg/300px-Oh_the_games_people_play_now..._%2838575282372%29.jpg 2x" data-file-width="2818" data-file-height="3373" /></a></span></div></div></div><div class="trow" style="display:flex"><div class="thumbcaption"><a href="/wiki/%E8%BC%AA%E7%9B%A4" title="輪盤">輪盤</a>（上）、<a href="/wiki/%E6%8E%9F%E9%8A%80%E4%BB%94" title="掟銀仔">掟銀仔</a>（左下）同<a href="/wiki/%E6%93%B2%E9%AA%B0%E4%BB%94" class="mw-redirect" title="擲骰仔">擲骰仔</a>（右下）一般都俾人認為係<a href="/wiki/%E9%9A%A8%E6%A9%9F%E4%BA%8B%E4%BB%B6" class="mw-redirect" title="隨機事件">本質上隨機性嘅事件</a>。</div></div></div></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></div> <div role="note" class="hatnote">睇埋：<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a></div> <p><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a>（probability theory）研究<a href="/wiki/%E6%A6%82%E7%8E%87" title="概率">概率</a>。概率係指一件<a href="/wiki/%E9%9A%A8%E6%A9%9F%E4%BA%8B%E4%BB%B6" class="mw-redirect" title="隨機事件">事件</a><a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A%E6%80%A7" class="mw-redirect" title="不確定性">有幾可能</a>係真，1 代表件事實會發生，0 代表件事實唔會發生，而 0.5 就代表件事「有 50% 機會發生」；例如家陣<a href="/wiki/%E6%8E%9F%E9%8A%80%E4%BB%94" title="掟銀仔">掟一個銀仔</a>，假設個銀仔冇出千嘅話，應該會有 50% 機會出公、50% 機會出字，而呢件事嘅結果（公定字）原則上係冇可能預測嘅<sup id="cite_ref-feller1968_14-0" class="reference"><a href="#cite_note-feller1968-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>，反映咗<a href="/wiki/%E4%B8%8D%E7%A2%BA%E5%AE%9A%E6%80%A7" class="mw-redirect" title="不確定性">不確定性</a>（uncertainty）<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>。 </p><p>喺概率論史上，「概率呢個數值<a href="/wiki/%E6%A6%82%E7%8E%87%E5%98%85%E8%A9%AE%E9%87%8B" title="概率嘅詮釋">要點樣理解</a>」係一個有相當爭議性嘅問題：喺最基本上，古典嘅<a href="/wiki/%E6%B1%BA%E5%AE%9A%E8%AB%96" title="決定論">決定論</a>主張，如果一個觀察者喺而家呢一刻完美知道嗮<a href="/wiki/%E5%AE%87%E5%AE%99" title="宇宙">宇宙</a>嘅狀態（例：知道每粒<a href="/wiki/%E5%8E%9F%E5%AD%90" title="原子">原子</a>喺乜位置同以乜嘢<a href="/wiki/%E9%80%9F%E5%BA%A6" title="速度">速度</a>郁緊等等），佢將會有能力靠<a href="/wiki/%E7%89%A9%E7%90%86%E5%AE%9A%E5%BE%8B" title="物理定律">物理定律</a>－假設佢識嗮所需嘅<a href="/wiki/%E7%89%A9%E7%90%86" class="mw-redirect" title="物理">物理</a>知識－完美預測宇宙下一刻嘅狀態<sup id="cite_ref-laplacedemon_16-0" class="reference"><a href="#cite_note-laplacedemon-16"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup>，所以概率淨係反映人類知識唔夠，而主張呢個觀點嘅人會話「人之所以預測唔到掟銀仔嘅結果，係因為人知唔嗮<a href="/wiki/%E9%A2%A8%E5%90%91" title="風向">風向</a>等嘅<a href="/wiki/%E8%B3%87%E8%A8%8A" title="資訊">資訊</a>」<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>。不過廿世紀<a href="/wiki/%E9%87%8F%E5%AD%90%E5%8A%9B%E5%AD%B8" title="量子力學">量子力學</a>研究指出，宇宙裏面有部份嘅事件似乎係本質上就冇可能完全準確噉預測嘅，人頂嗮櫳都淨係有得估呢啲事件發生嘅概率<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>。 </p><p>喺廿一世紀初，概率論經已成為咗一個重要嘅數學理論。例如<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a>就係建基於概率論嘅<sup id="cite_ref-feller1968_14-1" class="reference"><a href="#cite_note-feller1968-14"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>，而概率同相關概念喺<a href="/wiki/%E6%A9%9F%E6%A2%B0%E5%AD%B8%E7%BF%92" title="機械學習">機械學習</a>（教<a href="/wiki/%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD" title="人工智能">人工智能</a><a href="/wiki/%E5%AD%B8%E7%BF%92" title="學習">學習</a>同處理不確定性嘅技術）<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>同埋<a href="/wiki/%E9%81%8A%E6%88%B2%E8%A8%AD%E8%A8%88" title="遊戲設計">遊戲設計</a>（可能會涉及設計<a href="/wiki/%E6%A9%9F%E7%8E%87%E9%81%8A%E6%88%B2" title="機率遊戲">帶有隨機性嘅遊戲</a>）<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>上都有用。 </p> <div class="mw-heading mw-heading2"><h2 id="博弈論"><span id=".E5.8D.9A.E5.BC.88.E8.AB.96"></span>博弈論</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=4" title="編輯小節: 博弈論"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <div role="note" class="hatnote">内文：<a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a></div> <p><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a>（game theory）專門研究<a href="/wiki/%E7%90%86%E6%80%A7" title="理性">理性</a>嘅<a href="/wiki/%E6%B1%BA%E7%AD%96%E8%80%85" class="mw-redirect" title="決策者">決策者</a>之間嘅互動<sup id="cite_ref-myerson1991_22-0" class="reference"><a href="#cite_note-myerson1991-22"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup>：博弈論會將<b>一場博弈</b>（a game）想像成一件<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>上嘅<a href="/wiki/%E6%95%B8%E5%AD%B8%E7%89%A9%E9%AB%94" title="數學物體">物體</a>，一場博弈由某啲規則同若干個參與者組成，每個參與者手上都有一柞可能選擇同埋特定嘅<a href="/wiki/%E8%B3%87%E8%A8%8A" title="資訊">資訊</a>，而對於一個參與者嚟講，佢每一個選擇都會引致某啲得失，呢啲得失由場博弈嘅規則話事；每一個參與者會想令自己嘅利益最多，並且按照呢條原則做<a href="/wiki/%E6%B1%BA%E7%AD%96" title="決策">決策</a>。捉棋、<a href="/wiki/%E6%89%93%E6%A9%9F" class="mw-redirect" title="打機">打機</a>以至<a href="/wiki/%E5%9C%8B%E9%9A%9B%E9%97%9C%E4%BF%82" title="國際關係">國際關係</a>等好多嘅現象都涉及博弈<sup id="cite_ref-what_23-0" class="reference"><a href="#cite_note-what-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>，而原則上，所有人類之間嘅互動都可以想像成博弈，所以博弈論能夠應用落去所有嘅<a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a>－尤其係<a href="/wiki/%E7%B6%93%E6%BF%9F%E5%AD%B8" title="經濟學">經濟學</a>同<a href="/wiki/%E6%94%BF%E6%B2%BB%E5%AD%B8" title="政治學">政治學</a>等－嗰度，解釋各式各樣嘅社會現象。到咗廿一世紀，就連<a href="/wiki/%E9%82%8F%E8%BC%AF%E5%AD%B8" class="mw-redirect" title="邏輯學">邏輯學</a>、<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8" title="生物學">生物學</a>同<a href="/wiki/%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="電腦科學">電腦科學</a>都會用到博弈論<sup id="cite_ref-what_23-1" class="reference"><a href="#cite_note-what-23"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup>。 </p><p>除咗俾人攞嚟做<b>解釋性</b>（explanatory）嘅研究，博弈論仲有俾人用嚟做一啲<b>規範性</b>（normative）嘅研究：有學者運用博弈論嚟分析喺某啲情況（例如係某啲使錢上嘅決擇）之下，一個參與者有邊啲選擇同埋應該要點樣做決策先至可以令到自身利益最多<sup id="cite_ref-24" class="reference"><a href="#cite_note-24"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-25" class="reference"><a href="#cite_note-25"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup>－有好多經濟分析師都興用博弈論分析<a href="/wiki/%E4%BC%81%E6%A5%AD" title="企業">企業</a>彼此之間喺<a href="/wiki/%E5%B8%82%E5%A0%B4" title="市場">市場</a>上嘅鬥爭，並且用呢啲分析嚟向企業提供營運方面嘅建議<sup id="cite_ref-b2u_26-0" class="reference"><a href="#cite_note-b2u-26"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-27" class="reference"><a href="#cite_note-27"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>。 </p><p>博弈論源於廿世紀初：博弈論係喺廿世紀上半橛由<a href="/wiki/%E9%A6%AE%E7%B4%90%E6%9B%BC" title="馮紐曼">馮紐曼</a>（John von Neumann）等嘅<a href="/wiki/%E6%95%B8%E5%AD%B8%E5%AE%B6" title="數學家">數學家</a>諗出嚟嘅，打後呢個理論喺廿世紀中期俾<a href="/wiki/%E7%B6%93%E6%BF%9F%E5%AD%B8%E5%AE%B6" title="經濟學家">經濟學家</a>同<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8%E5%AE%B6" title="生物學家">生物學家</a>用嚟分析佢哋各自嘅領域當中嘅現象，而且仲有多個經濟學家靠住佢哋用博弈論對經濟現象進行嘅分析攞到<a href="/wiki/%E8%AB%BE%E8%B2%9D%E7%88%BE%E7%B6%93%E6%BF%9F%E5%AD%B8%E7%8D%8E" title="諾貝爾經濟學獎">諾貝爾經濟學獎</a>。到咗今日，博弈論上嘅發展令到佢出咗大量嘅專有概念同子理論，成為咗一門獨立於第啲應用數學領域嘅領域<sup id="cite_ref-weintraub1992_28-0" class="reference"><a href="#cite_note-weintraub1992-28"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup>。 </p> <div style="clear: both;"></div> <div class="mw-heading mw-heading2"><h2 id="睇埋"><span id=".E7.9D.87.E5.9F.8B"></span>睇埋</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=5" title="編輯小節: 睇埋"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E7%B4%94%E7%B2%B9%E6%95%B8%E5%AD%B8" title="純粹數學">純粹數學</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="引述"><span id=".E5.BC.95.E8.BF.B0"></span>引述</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit&section=6" title="編輯小節: 引述"><span>編輯</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r2020813">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width reflist-columns-2"> <ol class="references"> <li id="cite_note-weisstein-1"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-weisstein_1-0">1.0</a></sup> <sup><a href="#cite_ref-weisstein_1-1">1.1</a></sup></span> <span class="reference-text">Weisstein, Eric W. "<a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Limit.html">Limit</a>". <i>mathworld.wolfram.com</i>.</span> </li> <li id="cite_note-wolfderiv-2"><span class="mw-cite-backlink"><a href="#cite_ref-wolfderiv_2-0">↑</a></span> <span class="reference-text">"<a rel="nofollow" class="external text" href="https://mathworld.wolfram.com/Derivative.html">Derivative</a>". <i>mathworld.wolfram.com</i>.</span> </li> <li id="cite_note-stewart2008-3"><span class="mw-cite-backlink"><a href="#cite_ref-stewart2008_3-0">↑</a></span> <span class="reference-text">Stewart, James (2008). <i>Calculus: Early Transcendentals</i> (6th ed.). Brooks/Cole.</span> </li> <li id="cite_note-rudin1976-4"><span class="mw-cite-backlink"><a href="#cite_ref-rudin1976_4-0">↑</a></span> <span class="reference-text">W. Rudin, "<i>Principles of mathematical analysis</i>", McGraw-Hill (1976) pp. 75-78</span> </li> <li id="cite_note-jinjin2007-5"><span class="mw-cite-backlink"><a href="#cite_ref-jinjin2007_5-0">↑</a></span> <span class="reference-text">Jin, Z., & Jin, G. (2007). <i>Mathematical analysis</i>. Dalian: Dalian University of Technology Press.</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">Nalimov, V. V. (2014). <i>The application of mathematical statistics to chemical analysis</i>. Elsevier.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Sipser, M. (2006). <i>Introduction to the Theory of Computation</i> (Vol. 2). Boston: Thomson Course Technology.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">Lewis, H. R., & Papadimitriou, C. H. (1997). <i>Elements of the Theory of Computation</i>. Prentice Hall PTR.</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">Michael Sipser (2013). <i>Introduction to the Theory of Computation</i> 3rd. Cengage Learning. <a href="/wiki/Special:%E6%9B%B8%E6%9C%AC%E4%BE%86%E6%BA%90/9781133187790" class="internal mw-magiclink-isbn">ISBN 978-1-133-18779-0</a>. p. 1.</span> </li> <li id="cite_note-hodges2012-10"><span class="mw-cite-backlink"><a href="#cite_ref-hodges2012_10-0">↑</a></span> <span class="reference-text">Hodges, Andrew (2012). <i>Alan Turing: The Enigma (The Centenary Edition)</i>. Princeton University Press.</span> </li> <li id="cite_note-rabin2012-11"><span class="mw-cite-backlink"><a href="#cite_ref-rabin2012_11-0">↑</a></span> <span class="reference-text">Rabin, Michael O. (June 2012). <a rel="nofollow" class="external text" href="http://videolectures.net/turing100_rabin_turing_church_goedel/">Turing, Church, Gödel, Computability, Complexity and Randomization: A Personal View</a> <a href="/wiki/Wayback_Machine" title="Wayback Machine">互聯網檔案館</a>嘅<a rel="nofollow" class="external text" href="https://web.archive.org/web/20190605192515/http://videolectures.net/turing100_rabin_turing_church_goedel/">歸檔</a>，歸檔日期2019年6月5號，..</span> </li> <li id="cite_note-turingmachineadd-12"><span class="mw-cite-backlink"><a href="#cite_ref-turingmachineadd_12-0">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://courses.washington.edu/css502/zander/Notes/14langTuringEx.pdf">Turing Machine example to add two numbers</a>.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">Donald Monk (1976). <i>Mathematical Logic</i>. Springer-Verlag.</span> </li> <li id="cite_note-feller1968-14"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-feller1968_14-0">14.0</a></sup> <sup><a href="#cite_ref-feller1968_14-1">14.1</a></sup></span> <span class="reference-text">William Feller, <i>An Introduction to Probability Theory and Its Applications</i>, (Vol 1), 3rd Ed, (1968), Wiley.</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text">Kallenberg, O. (2006). <i>Foundations of modern probability</i>. Springer Science & Business Media.</span> </li> <li id="cite_note-laplacedemon-16"><span class="mw-cite-backlink"><a href="#cite_ref-laplacedemon_16-0">↑</a></span> <span class="reference-text">Richard Langdon Franklin (1968). <i>Freewill and determinism: a study of rival conceptions of man</i>. Routledge & K. Paul.</span> </li> <li id="cite_note-17"><span class="mw-cite-backlink"><a href="#cite_ref-17">↑</a></span> <span class="reference-text">Laplace, Pierre Simon. <i>A Philosophical Essay on Probabilities</i>, translated into English from the original French 6th ed. by Truscott, F.W. and Emory, F.L., Dover Publications (New York, 1951).</span> </li> <li id="cite_note-18"><span class="mw-cite-backlink"><a href="#cite_ref-18">↑</a></span> <span class="reference-text">Moore, W.J. (1992). <i>Schrödinger: Life and Thought</i>. Cambridge University Press. p. 479.</span> </li> <li id="cite_note-19"><span class="mw-cite-backlink"><a href="#cite_ref-19">↑</a></span> <span class="reference-text">Stephen Hawking's Grand Design (2010), page 32: "the molecular basis of biology shows that biological processes are governed by the laws of physics and chemistry and therefore are as determined as the orbits of the planets...so it seems that we are no more than biological machines and that free will is just an illusion", and page 72: "Quantum physics might seem to undermine the idea that nature is governed by laws, but that is not the case. Instead it leads us to accept a new form of determinism: Given the state of a system at some time, the laws of nature determine the probabilities of various futures and pasts rather than determining the future and past with certainty." (discussing a Many worlds interpretation).</span> </li> <li id="cite_note-20"><span class="mw-cite-backlink"><a href="#cite_ref-20">↑</a></span> <span class="reference-text">Mohri, Mehryar; Rostamizadeh, Afshin; Talwalkar, Ameet (2012). <i>Foundations of Machine Learning</i>. USA, Massachusetts: MIT Press.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><a href="#cite_ref-21">↑</a></span> <span class="reference-text">Dervishi, Kay (2019-06-18). "<a rel="nofollow" class="external text" href="https://www.cityandstateny.com/articles/policy/gambling/new-york-games-chance-and-skill.html">Other games of chance and skill on Albany's agenda</a> <a href="/wiki/Wayback_Machine" title="Wayback Machine">互聯網檔案館</a>嘅<a rel="nofollow" class="external text" href="https://web.archive.org/web/20210518083130/https://www.cityandstateny.com/articles/policy/gambling/new-york-games-chance-and-skill.html">歸檔</a>，歸檔日期2021年5月18號，.". <i>CSNY</i>.</span> </li> <li id="cite_note-myerson1991-22"><span class="mw-cite-backlink"><a href="#cite_ref-myerson1991_22-0">↑</a></span> <span class="reference-text">Myerson, Roger B. (1991). <i>Game Theory: Analysis of Conflict</i>. Harvard University Press, p. 1.</span> </li> <li id="cite_note-what-23"><span class="mw-cite-backlink">↑ <sup><a href="#cite_ref-what_23-0">23.0</a></sup> <sup><a href="#cite_ref-what_23-1">23.1</a></sup></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.dklevine.com/general/whatis.htm">What is Game Theory?</a>.</span> </li> <li id="cite_note-24"><span class="mw-cite-backlink"><a href="#cite_ref-24">↑</a></span> <span class="reference-text">Ross, Don. "<a rel="nofollow" class="external text" href="https://plato.stanford.edu/archives/spr2008/entries/game-theory/">Game Theory</a>". <i>The Stanford Encyclopedia of Philosophy</i> (Spring 2008 Edition). Edward N. Zalta (ed.).</span> </li> <li id="cite_note-25"><span class="mw-cite-backlink"><a href="#cite_ref-25">↑</a></span> <span class="reference-text">Velegol, Darrell; Suhey, Paul; Connolly, John; Morrissey, Natalie; Cook, Laura (14 September 2018). "Chemical Game Theory". <i>Industrial & Engineering Chemistry Research</i>. 57 (41): 13593–13607.</span> </li> <li id="cite_note-b2u-26"><span class="mw-cite-backlink"><a href="#cite_ref-b2u_26-0">↑</a></span> <span class="reference-text"><a rel="nofollow" class="external text" href="https://www.business-to-you.com/introduction-game-theory-the-basics/">An Introduction To Game Theory: The Basics And Key Concepts</a>. <i>B2U</i>.</span> </li> <li id="cite_note-27"><span class="mw-cite-backlink"><a href="#cite_ref-27">↑</a></span> <span class="reference-text">Colin F. Camerer (2003). <i>Behavioral Game Theory: Experiments in Strategic Interaction</i>, pp. 5–7 "What Is Game Theory Good For?".</span> </li> <li id="cite_note-weintraub1992-28"><span class="mw-cite-backlink"><a href="#cite_ref-weintraub1992_28-0">↑</a></span> <span class="reference-text">Weintraub, E. R. (Ed.). (1992). <i>Toward a history of game theory</i> (Vol. 24). Duke University Press.</span> </li> </ol></div> <div role="navigation" class="navbox" aria-labelledby="應用數學" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><div class="plainlinks hlist navbar mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="Template:應用數學"><abbr title="去睇呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">睇</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="Template talk:應用數學"><abbr title="傾呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">傾</abbr></a></li><li class="nv-edit"><a class="external text" href="https://zh-yue.wikipedia.org/w/index.php?title=Template:%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8&action=edit"><abbr title="編輯呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">改</abbr></a></li></ul></div><div id="應用數學" style="font-size:114%;margin:0 4em"><a class="mw-selflink selflink">應用數學</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div id="泛指數學喺科學同工程學上嘅應用">泛指<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>喺<a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>同<a href="/wiki/%E5%B7%A5%E7%A8%8B%E5%AD%B8" title="工程學">工程學</a>上嘅應用</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%95%B8%E5%AD%B8" title="離散數學">離散數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%91%BD%E9%A1%8C%E9%82%8F%E8%BC%AF" title="命題邏輯">命題邏輯</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%86%E5%90%88%E8%AB%96" title="集合論">集合論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學">代數學</a>（<a href="/wiki/%E5%A0%B4_(%E6%95%B8%E5%AD%B8)" class="mw-redirect mw-disambig" title="場 (數學)">場</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學">組合數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%9C%96%E8%AB%96" title="圖論">圖論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%A2%E6%95%A3%E5%B9%BE%E4%BD%95%E5%AD%B8" class="mw-redirect" title="離散幾何學">離散幾何學</a></div></td><td class="navbox-image" rowspan="8" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Aizerman2d.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/150px-Aizerman2d.jpg" decoding="async" width="150" height="144" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/225px-Aizerman2d.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d9/Aizerman2d.jpg/300px-Aizerman2d.jpg 2x" data-file-width="591" data-file-height="569" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數<br />學<br />分<br />析</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">分析基礎</div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%AF%A6%E6%95%B8" title="實數">實數</a>同<a href="/wiki/%E8%99%9B%E6%95%B8" title="虛數">虛數</a>（<a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>同<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%96%93%E8%B7%9D" title="間距">間距</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E7%9B%A1" title="無窮盡">無窮盡</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%84%A1%E7%AA%AE%E5%B0%8F%E9%87%8F" title="無窮小量">無窮小量</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E6%95%B8%E5%88%97" class="mw-redirect" title="數列">數列</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%AD%90%E6%95%B8%E5%88%97" title="子數列">子數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A2%9E%E6%B8%9B%E6%95%B8%E5%88%97" title="增減數列">增減數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%83%9D%E6%B0%8F%E6%95%B8%E5%88%97" title="郝氏數列">郝氏數列</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BF%9D%E8%A5%BF%E5%A5%B4-%E8%8F%AF%E5%AF%A6%E6%96%AF%E5%AE%9A%E7%90%86" title="保西奴-華實斯定理">保西奴-華實斯定理</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%87%BD%E6%95%B8" title="函數">函數</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%80%A3%E7%BA%8C%E5%87%BD%E6%95%B8" title="連續函數">連續函數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A5%B5%E9%99%90_(%E5%87%BD%E6%95%B8)" title="極限 (函數)">極限</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%80%BC%E8%BF%91%E7%90%86%E8%AB%96" title="逼近理論">逼近理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a>（<a href="/wiki/%E8%AE%8A%E5%88%86%E6%B3%95" title="變分法">變分法</a>）</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th id="微分" scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E5%BE%AE%E5%88%86" title="微分">微分</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a>（<a href="/wiki/%E5%B8%B8%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="常微分方程">常</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%81%8F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="偏微分方程">偏</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="隨機微分方程">隨機</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%A4%87%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="複微分方程">複</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a></div></td></tr><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E7%A9%8D%E5%88%86" title="積分">積分</a>（<a href="/wiki/%E9%BB%8E%E6%9B%BC%E7%A9%8D%E5%88%86" title="黎曼積分">黎曼積分</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A9%8D%E5%88%86%E6%96%B9%E7%A8%8B" title="積分方程">積分方程</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E5%85%83%E5%BE%AE%E7%A9%8D%E5%88%86" title="多元微積分">多元微積分</a>（<a href="/wiki/%E5%90%91%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="向量微積分">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F%E5%BE%AE%E7%A9%8D%E5%88%86" title="張量微積分">張量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%9A%E9%87%8D%E7%A9%8D%E5%88%86" title="多重積分">多重積分</a>）</div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">第啲分析</div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%A4%9A%E9%87%8D%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="多重線性代數">多線代數</a>（<a href="/wiki/%E5%90%91%E9%87%8F" title="向量">向量</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%90%91%E9%87%8F%E7%A9%BA%E9%96%93" title="向量空間">向量空間</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%BC%B5%E9%87%8F" title="張量">張量</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8B%95%E6%85%8B%E7%B3%BB%E7%B5%B1" title="動態系統">動態系統</a>（<a href="/wiki/%E6%B7%B7%E6%B2%8C%E7%90%86%E8%AB%96" title="混沌理論">混沌理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AB%96" title="控制理論">控制理論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%80%BC%E5%88%86%E6%9E%90" title="數值分析">數值分析</a></div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E5%AD%B8" title="運算數學">運算數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E9%82%8F%E8%BC%AF" title="運算邏輯">運算邏輯</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%87%AA%E5%8B%95%E6%A9%9F%E7%90%86%E8%AB%96" title="自動機理論">自動機理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95" title="演算法">演算法</a>（<a href="/wiki/%E6%BC%94%E7%AE%97%E6%B3%95%E5%88%86%E6%9E%90" title="演算法分析">分析</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E8%B3%87%E8%A8%8A%E7%90%86%E8%AB%96" title="資訊理論">資訊理論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" title="密碼學">密碼學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E8%AB%96" title="運算數論">運算數論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E9%81%8B%E7%AE%97" title="科學運算">科學運算</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9B%BB%E8%85%A6%E4%BB%A3%E6%95%B8" title="電腦代數">電腦代數</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E9%9A%A8%E6%A9%9F%E8%AE%8A%E6%95%B8" title="隨機變數">隨機變數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E9%81%8E%E7%A8%8B" title="隨機過程">隨機過程</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%A6%AC%E5%8F%AF%E5%A4%AB%E9%8F%88" title="馬可夫鏈">馬可夫鏈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A6%82%E7%8E%87%E5%88%86%E4%BD%88" title="概率分佈">概率分佈</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%9A%A8%E6%A9%9F%E5%BE%AE%E7%A9%8D%E5%88%86" title="隨機微積分">隨機微積分</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%B1%BA%E7%AD%96%E8%AB%96" title="決策論">決策論</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a>（<a href="/wiki/%E6%8F%8F%E8%BF%B0%E7%B5%B1%E8%A8%88%E5%AD%B8" title="描述統計學">描述</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">推論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%9C%80%E4%BD%B3%E5%8C%96" title="最佳化">最佳化</a>（<a href="/wiki/%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="線性規劃">線性</a>同<a href="/wiki/%E9%9D%9E%E7%B7%9A%E6%80%A7%E8%A6%8F%E5%8A%83" title="非線性規劃">非線性</a>規劃）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%B6%93%E6%BF%9F%E5%AD%B8" title="數理經濟學">數理經濟學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E9%87%91%E8%9E%8D%E5%AD%B8" title="數理金融學">數理金融學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學">運籌學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B2%BE%E7%AE%97%E5%AD%B8" title="精算學">精算學</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E7%90%86%E7%89%A9%E7%90%86%E5%AD%B8" title="數理物理學">數理物理</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E5%88%86%E6%9E%90%E5%8A%9B%E5%AD%B8" title="分析力學">分析力學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A0%B4_(%E7%89%A9%E7%90%86)" title="場 (物理)">場</a>（<a href="/wiki/%E8%A6%8F%E7%AF%84%E5%A0%B4%E8%AB%96" title="規範場論">規範場論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%87%8F%E5%AD%90%E5%A0%B4%E8%AB%96" title="量子場論">量子場論</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E9%87%8F%E5%AD%90%E7%BE%A3" title="量子羣">量子羣</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜應用</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%95%B8%E7%90%86%E5%8C%96%E5%AD%B8" title="數理化學">數理化學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">數理生物學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E5%BF%83%E7%90%86%E5%AD%B8" title="數理心理學">數理心理學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E7%90%86%E7%A4%BE%E6%9C%83%E5%AD%B8" title="數理社會學">數理社會學</a>（<a href="/wiki/%E7%A4%BE%E6%9C%83%E9%81%B8%E6%93%87%E7%90%86%E8%AB%96" title="社會選擇理論">社會選擇理論</a>）</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜相關</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"><a href="/wiki/%E6%95%B8%E5%AD%B8%E6%A8%A1%E5%9E%8B" title="數學模型">數學模型</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%B7%A5%E7%A8%8B%E6%95%B8%E5%AD%B8" title="工程數學">工程數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%87%89%E7%94%A8%E7%A7%91%E5%AD%B8" title="應用科學">應用科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%A8%A1%E6%8E%A7%E5%AD%B8" title="模控學">模控學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B3%BB%E7%B5%B1" title="系統">系統</a>（<a href="/wiki/%E8%A4%87%E9%9B%9C%E7%B3%BB%E7%B5%B1" title="複雜系統">複雜系統</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%AD%B8%E5%96%BA%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8%E4%B8%8A%E5%98%85%E8%B6%85%E5%B8%B8%E6%95%88%E7%94%A8" title="數學喺自然科學上嘅超常效用">數學喺自然科學上嘅超常效用</a></div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div><b><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" data-file-height="128" /></a></span> <a href="/wiki/Portal:%E6%95%B8%E5%AD%B8" title="Portal:數學">數學主題</a></b><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/Category:%E6%87%89%E7%94%A8%E6%95%B8%E5%AD%B8" title="Category:應用數學">應用數學類</a></div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="現代數學同數學各領域" style="padding:3px"><table class="nowraplinks mw-collapsible mw-collapsed navbox-inner" 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padding:0;">改</abbr></a></li></ul></div><div id="現代數學同數學各領域" style="font-size:114%;margin:0 4em">現代<a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>同數學各領域</div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div id="純粹同應用數學_·_數學史_·_數學之美"><a href="/wiki/%E7%B4%94%E7%B2%B9%E6%95%B8%E5%AD%B8" title="純粹數學">純粹</a>同<a class="mw-selflink selflink">應用</a>數學<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%AD%B8%E5%8F%B2" title="數學史">數學史</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E6%95%B8%E5%AD%B8%E4%B9%8B%E7%BE%8E" title="數學之美">數學之美</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E8%AD%89%E6%98%8E" title="數學證明">數學證明</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%B4%E6%8E%A5%E8%AD%89%E6%98%8E" title="直接證明">直接證明</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E6%AD%B8%E7%B4%8D%E6%B3%95" title="數學歸納法">數學歸納法</a></li> <li><a href="/wiki/%E5%90%A6%E5%AE%9A%E8%AD%89%E6%98%8E" title="否定證明">否定證明</a></li> <li><a href="/wiki/%E5%8F%8D%E8%AD%89%E6%B3%95" title="反證法">反證法</a></li> <li><a href="/wiki/%E6%A7%8B%E9%80%A0%E6%B3%95" title="構造法">構造法</a></li> <li><a href="/wiki/%E5%88%86%E9%A1%9E%E8%AD%89%E6%98%8E" title="分類證明">分類證明</a></li></ul> </div></td><td class="navbox-image" rowspan="10" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Mathematics.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Mathematics.png/150px-Mathematics.png" decoding="async" width="150" height="150" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/79/Mathematics.png/225px-Mathematics.png 1.5x, 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title="數學符號">數學符號</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8%E7%89%A9%E9%AB%94" title="數學物體">數學物體</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E8%AB%96" title="數論">數論</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B8" title="數">數</a>（<a href="/wiki/%E8%B3%AA%E6%95%B8" title="質數">質數</a>）</li> <li><a href="/wiki/%E7%AE%97%E8%A1%93" title="算術">算術</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8%E8%AB%96" title="代數數論">代數數論</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E6%95%B8%E8%AB%96" title="解析數論">解析數論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%BB%A3%E6%95%B8%E5%AD%B8" title="代數學">代數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9F%BA%E6%9C%AC%E4%BB%A3%E6%95%B8" title="基本代數">基本代數</a></li> <li><a href="/wiki/%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="線性代數">線性代數</a>（<a href="/wiki/%E5%A4%9A%E9%87%8D%E7%B7%9A%E6%80%A7%E4%BB%A3%E6%95%B8" title="多重線性代數">多重</a>）</li> <li><a href="/wiki/%E6%8A%BD%E8%B1%A1%E4%BB%A3%E6%95%B8" title="抽象代數">抽象代數</a>（<a href="/wiki/%E4%BA%A4%E6%8F%9B%E4%BB%A3%E6%95%B8" title="交換代數">交換代數</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%BE%A3%E8%AB%96" title="羣論">羣論</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BC%BD%E8%8F%AF%E7%90%86%E8%AB%96" title="伽華理論">伽華理論</a>）</li> <li><a href="/wiki/%E5%A0%B4%E8%AB%96" title="場論">場論</a></li> <li><a href="/wiki/%E6%B3%9B%E4%BB%A3%E6%95%B8" title="泛代數">泛代數</a></li> <li><a href="/wiki/%E5%90%8C%E8%AA%BF%E4%BB%A3%E6%95%B8" title="同調代數">同調代數</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%B9%BE%E4%BD%95%E5%AD%B8" title="幾何學">幾何學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%AD%90%E5%B9%BE%E9%87%8C%E5%BE%97%E5%B9%BE%E4%BD%95" title="歐幾里得幾何">歐幾里得幾何</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E5%B9%BE%E4%BD%95" title="代數幾何">代數幾何</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%B9%BE%E4%BD%95" title="解析幾何">解析幾何</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E5%B9%BE%E4%BD%95" title="微分幾何">微分幾何</a></li> <li><a href="/wiki/%E9%9B%A2%E6%95%A3%E5%B9%BE%E4%BD%95" title="離散幾何">離散幾何</a></li> <li><a href="/wiki/%E6%8B%93%E6%92%B2%E5%AD%B8" title="拓撲學">拓撲學</a>（<a href="/wiki/%E4%BB%A3%E6%95%B8%E6%8B%93%E6%92%B2" title="代數拓撲">代數拓撲</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B8%E5%AD%B8%E5%88%86%E6%9E%90" title="數學分析">數學分析</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" title="微積分">微積分</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a></li> <li><a href="/wiki/%E5%AF%A6%E5%88%86%E6%9E%90" title="實分析">實分析</a>同<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a></li> <li><a href="/wiki/%E6%B8%AC%E5%BA%A6" title="測度">測度</a></li> <li><a href="/wiki/%E8%AB%A7%E6%B3%A2%E5%88%86%E6%9E%90" title="諧波分析">諧波分析</a></li> <li><a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%9B%A2%E6%95%A3%E6%95%B8%E5%AD%B8" title="離散數學">離散數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B5%84%E5%90%88%E6%95%B8%E5%AD%B8" title="組合數學">組合數學</a></li> <li><a href="/wiki/%E5%9C%96%E8%AB%96" title="圖論">圖論</a></li> <li><a href="/wiki/%E5%BA%8F%E7%90%86%E8%AB%96" title="序理論">序理論</a></li> <li><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AB%96" title="博弈論">博弈論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">應用數學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><td colspan="2" class="navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B8%E7%90%86%E7%89%A9%E7%90%86%E5%AD%B8" title="數理物理學">數理物理學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E5%8C%96%E5%AD%B8" title="數理化學">數理化學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">數理生物學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E5%BF%83%E7%90%86%E5%AD%B8" title="數理心理學">數理心理學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%A4%BE%E6%9C%83%E5%AD%B8" title="數理社會學">數理社會學</a></li> <li><a href="/wiki/%E6%8E%A7%E5%88%B6%E7%90%86%E8%AB%96" title="控制理論">控制理論</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;">　<a href="/wiki/%E6%B1%BA%E7%AD%96%E8%AB%96" title="決策論">決策論</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%A6%82%E7%8E%87%E8%AB%96" title="概率論">概率論</a>同<a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%B6%93%E6%BF%9F%E5%AD%B8" title="數理經濟學">數理經濟學</a></li> <li><a href="/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學">運籌學</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E9%87%91%E8%9E%8D%E5%AD%B8" title="數理金融學">數理金融學</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E9%81%8B%E7%AE%97%E6%95%B8%E5%AD%B8" title="運算數學">運算數學</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="電腦科學">電腦科學</a></li> <li><a href="/wiki/%E9%81%8B%E7%AE%97%E7%90%86%E8%AB%96" title="運算理論">運算理論</a></li> <li><a href="/wiki/%E6%95%B8%E5%80%BC%E5%88%86%E6%9E%90" title="數值分析">數值分析</a></li> <li><a href="/wiki/%E6%9C%80%E4%BD%B3%E5%8C%96" title="最佳化">最佳化</a></li> <li><a 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href="/wiki/%E7%B3%BB%E7%B5%B1%E7%A7%91%E5%AD%B8" title="系統科學">系統</a>）</li> <li><a href="/wiki/%E7%A7%91%E6%8A%80" title="科技">科技</a></li> <li><a href="/wiki/%E8%97%9D%E8%A1%93" title="藝術">藝術</a></li> <li><a href="/wiki/%E6%A8%82%E7%90%86" title="樂理">樂理</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div><b><span class="noviewer" typeof="mw:File"><a href="/wiki/File:Nuvola_apps_edu_mathematics_blue-p.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/28px-Nuvola_apps_edu_mathematics_blue-p.svg.png" decoding="async" width="28" height="28" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/42px-Nuvola_apps_edu_mathematics_blue-p.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/3e/Nuvola_apps_edu_mathematics_blue-p.svg/56px-Nuvola_apps_edu_mathematics_blue-p.svg.png 2x" data-file-width="128" 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href="/w/index.php?title=Template_talk:%E7%A7%91%E5%AD%B8%E5%90%84%E9%A0%98%E5%9F%9F&action=edit&redlink=1" class="new" title="Template talk:科學各領域 (無呢版)"><abbr title="傾呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">傾</abbr></a></li><li class="nv-edit"><a class="external text" href="https://zh-yue.wikipedia.org/w/index.php?title=Template:%E7%A7%91%E5%AD%B8%E5%90%84%E9%A0%98%E5%9F%9F&action=edit"><abbr title="編輯呢個模" style=";;background:none transparent;border:none;-moz-box-shadow:none;-webkit-box-shadow:none;box-shadow:none; padding:0;">改</abbr></a></li></ul></div><div id="科學嘅各領域" style="font-size:114%;margin:0 4em"><a href="/wiki/%E7%A7%91%E5%AD%B8" title="科學">科學</a>嘅<a href="/wiki/%E7%A7%91%E5%AD%B8%E5%88%86%E6%94%AF" title="科學分支">各領域</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div id="科學哲學_·_科學家_·_科學教育_·_科學文獻_·_科學史"><a href="/wiki/%E7%A7%91%E5%AD%B8%E5%93%B2%E5%AD%B8" title="科學哲學">科學哲學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E5%AE%B6" title="科學家">科學家</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E6%95%99%E8%82%B2" title="科學教育">科學教育</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E6%96%87%E7%8D%BB" title="科學文獻">科學文獻</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%A7%91%E5%AD%B8%E5%8F%B2" title="科學史">科學史</a></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%BD%A2%E5%BC%8F%E7%A7%91%E5%AD%B8" title="形式科學">形式科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E9%82%8F%E8%BC%AF" title="邏輯">邏輯</a></li> <li><a href="/wiki/%E6%95%B8%E5%AD%B8" title="數學">數學</a>（<a class="mw-selflink selflink">應用數學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E7%B5%B1%E8%A8%88%E5%AD%B8" title="統計學">統計學</a>）</li> <li><a href="/wiki/%E7%90%86%E8%AB%96%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="理論電腦科學">理論電腦科學</a></li> <li><a href="/wiki/%E7%B3%BB%E7%B5%B1%E7%A7%91%E5%AD%B8" title="系統科學">系統科學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B4%94%E7%A7%91%E5%AD%B8" title="純科學">純科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"></div><table class="nowraplinks navbox-subgroup" style="border-spacing:0"><tbody><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E8%87%AA%E7%84%B6%E7%A7%91%E5%AD%B8" title="自然科學">自然科學</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%89%A9%E7%90%86%E7%A7%91%E5%AD%B8" title="物理科學">物理科學</a>（<a href="/wiki/%E7%89%A9%E7%90%86%E5%AD%B8" title="物理學">物理學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%8C%96%E5%AD%B8" title="化學">化學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%9C%B0%E7%90%83%E7%A7%91%E5%AD%B8" title="地球科學">地球科學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%A4%A9%E6%96%87%E5%AD%B8" title="天文學">天文學</a>）</li> <li><a href="/wiki/%E7%94%9F%E5%91%BD%E7%A7%91%E5%AD%B8" title="生命科學">生命科學</a>（<a href="/wiki/%E7%94%9F%E7%89%A9%E5%AD%B8" title="生物學">生物學</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E8%AA%8D%E7%9F%A5%E7%A7%91%E5%AD%B8" title="認知科學">認知科學</a></div></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AA%9E%E8%A8%80%E5%AD%B8" title="語言學">語言學</a></li> <li><a href="/wiki/%E4%BA%BA%E9%A1%9E%E5%AD%B8" title="人類學">人類學</a></li> <li><a href="/wiki/%E7%A5%9E%E7%B6%93%E7%A7%91%E5%AD%B8" title="神經科學">神經科學</a></li> <li><a href="/wiki/%E5%BF%83%E7%90%86%E5%AD%B8" title="心理學">心理學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%;padding-left:0em;padding-right:0em;"><div style="padding:0em 0.75em;"><a href="/wiki/%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="社會科學">社會科學</a></div></th><td class="navbox-list navbox-even" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%9C%B0%E7%90%86%E5%AD%B8" title="地理學">地理學</a></li> <li><a href="/wiki/%E8%80%83%E5%8F%A4%E5%AD%B8" title="考古學">考古學</a></li> <li><a href="/wiki/%E7%A4%BE%E6%9C%83%E5%AD%B8" title="社會學">社會學</a></li> <li><a href="/wiki/%E7%B6%93%E6%BF%9F%E5%AD%B8" title="經濟學">經濟學</a></li> <li><a href="/wiki/%E8%B3%87%E8%A8%8A%E7%A7%91%E5%AD%B8" title="資訊科學">資訊科學</a></li> <li><a href="/wiki/%E6%94%BF%E6%B2%BB%E5%AD%B8" title="政治學">政治學</a></li></ul> </div></td></tr></tbody></table><div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%87%89%E7%94%A8%E7%A7%91%E5%AD%B8" title="應用科學">應用科學</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%A8%88%E9%87%8F%E5%AD%B8" title="計量學">計量學</a></li> <li><a href="/wiki/%E8%BE%B2%E5%AD%B8" title="農學">農學</a>同<a href="/wiki/%E8%BE%B2%E6%A5%AD%E7%A7%91%E5%AD%B8" title="農業科學">農業科學</a></li> <li><a href="/wiki/%E5%B7%A5%E7%A8%8B%E5%AD%B8" title="工程學">工程學</a></li> <li><a href="/wiki/%E9%86%AB%E5%AD%B8" title="醫學">醫學</a></li> <li><a href="/wiki/%E9%81%8B%E5%8B%95%E7%A7%91%E5%AD%B8" title="運動科學">運動科學</a></li> <li><a href="/wiki/%E6%B3%95%E8%AD%89%E7%A7%91%E5%AD%B8" title="法證科學">法證科學</a></li> <li><a href="/wiki/%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="電腦科學">電腦科學</a>（<a href="/wiki/%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD" title="人工智能">AI</a>）</li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">拉雜相關</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%B2%BE%E5%AF%86%E7%A7%91%E5%AD%B8" title="精密科學">精密科學</a></li> <li><a href="/wiki/%E7%A1%AC%E5%90%8C%E8%BB%9F%E7%A7%91%E5%AD%B8" title="硬同軟科學">硬同軟科學</a></li> <li><a href="/wiki/%E8%B7%A8%E5%AD%B8%E7%A7%91%E7%A0%94%E7%A9%B6" title="跨學科研究">跨學科</a></li> <li><a href="/wiki/%E5%81%87%E7%A7%91%E5%AD%B8" title="假科學">假科學</a></li> <li><a href="/wiki/%E7%A7%91%E6%8A%80" title="科技">科技</a>同<a href="/wiki/%E7%A7%91%E5%B9%BB" title="科幻">科幻</a></li> <li><a href="/wiki/%E7%A7%91%E5%AD%B8%E8%AB%96" title="科學論">科學論</a></li> <li><a href="/wiki/%E9%96%8B%E6%94%BE%E7%A7%91%E5%AD%B8" title="開放科學">開放科學</a></li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div><b>睇埋</b><br /> <a href="/wiki/%E7%9F%A5%E8%AD%98%E8%AB%96" title="知識論">知識論</a>（<a href="/wiki/%E7%B6%93%E9%A9%97%E4%B8%BB%E7%BE%A9" title="經驗主義">經驗主義</a>）<span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%95%86%E5%AD%B8" title="商學">商學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E4%BA%BA%E6%96%87%E5%AD%B8" title="人文學">人文學</a><span style="white-space:nowrap; font-weight:bold;"> ·</span> <a href="/wiki/%E5%AD%B8%E8%A1%93" title="學術">學術</a>同<a href="/wiki/%E5%AD%B8%E8%A1%93%E5%87%BA%E7%89%88" title="學術出版">學術出版</a></div></td></tr></tbody></table></div> <div role="navigation" class="navbox" aria-labelledby="權威控制" style="padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="權威控制" scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%AC%8A%E5%A8%81%E6%8E%A7%E5%88%B6" title="權威控制">權威控制</a></th><td class="navbox-list navbox-odd" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="https://en.wikipedia.org/wiki/Library_of_Congress_Control_Number" class="extiw" title="en:Library of Congress Control Number">LCCN</a>: <span class="uid"><a rel="nofollow" class="external text" href="http://id.loc.gov/authorities/subjects/sh93002523">sh93002523</a></span></li> <li><a href="https://en.wikipedia.org/wiki/Integrated_Authority_File" class="extiw" title="en:Integrated Authority File">GND</a>: <span 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