Editing Language/Multiple-languages/Vocabulary/Algebra

{{Sci-Tech-Index-Intro}}

{| class="wikitable sortable"
! cmn-Hans-CN: 科目
! cmn-Latn.Pinyin-CN: kēmù
! deu-Latn-DE: Fach [n]
! eng-Latn-US: subject
! fra-Latn-FR: matière [f]
! jpn-Jpan-JP: 科目
! jpn-Hrkt-JP: か↑もく
! rus-Cyrl-RU: предме́т
|-
| 
| 
| 
| 
| 
| 
| 
| 
|-
| 抽象代数
| chōuxiàng dàishù
| abstrakte Algebra
| abstract algebra
| algèbre générale, algèbre abstraite
| 抽象代数学
| ちゅ↑うしょうだいす↓うがく
| абстра́ктная а́лгебра, общая а́лгебра, вы́сшая а́лгебра
|-
| 群论
| qún lùn
| Gruppentheorie [f]
| group theory
| théorie [f] des groupes [m pl]
| 群論
| ぐ↓んろん
| тео́рия групп
|-
| 环论
| huán lùn
| Ringtheorie [f]
| ring theory
| théorie [f] des anneaux [m pl]
| 環論
| か↑んろん
| тео́рия коле́ц
|-
| 范畴论
| fànchóu lùn
| Kategorientheorie [f]
| category theory
| théorie [f] des catégories [f pl]
| 圏論
| け↑んろん
| тео́рия катего́рий
|-
| 交换代数
| jiāohuàn dàishù
| kommutative Algebra
| commutative algebra
| algèbre [f] commutative
| 可換環論
| か↑かんか↓んろん
| коммутати́вная а́лгебра
|-
| 线性代数
| xiànxìng dàishù
| lineare Algebra, Vektoralgebra [f]
| linear algebra
| algèbre [f] linéaire
| 線型代数
| せ↑んけいだいす↓うがく
| лине́йная а́лгебра
|-
| 多重线性代数
| duōchóng xiànxìng dàishù
| multilineare Algebra
| multilinear algebra
| algèbre [f] multilinéaire
| 多重線型代数
| た↑じゅうせんけいだいす↓う
| полилине́йная а́лгебра
|-
| 泛代数
| fàn dàishù
| universelle Algebra, allgemeine Algebra
| universal algebra, common algebra
| algèbre [f] universelle
| 普遍代数学，一般代数学
| ふ↑へんだいすう↓がく，い↑っぱんだいすう↓がく
| универса́льная а́лгебра
|-
| 同调代数
| tóngdiào dàishù
| homologische Algebra
| homological algebra
| algèbre [f] homologique
| ホモロジー代数学
| ホ↑モロジ↓ーだいす↑うがく
| гомологи́ческая а́лгебра
|-
| 
| 
| 
| 
| 
| 
| 
| 
|}

== Main ==
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
| 代数方程 || 
| dàishù fāngchéng || 
| algebraische Gleichung || 
| algebraic equation || coefficient
| équation polynomiale, équation [f] algébrique || 
| 代数方程式 || 
| だ↑いす↓うほ↑うて↓いしき || 
| алгебраи́ческое уравне́ние || 
|-
| 代数式 || 
| dàishù shì || 
| algebraischer Ausdruck || 
| algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation
| expression [f] algébrique || 
| 代数式 || 
| だ↑いす↓うしき || 
| алгебраи́ческим выраже́нием || 
|-
| 代数分式 || 
| dàishù fēnshì || 
|  || 
| algebraic fraction || fraction; algebraic expression
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| algebraic operation || operation <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
| 最大值自变量点集 || 
| zuìdàzhí zìbiànliàng diǎn jí || 
| Argument [n] des Maximums [n] || 
| argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis>
| argument [m] du maximum [m] || 
| 最大点作用素集合 || 
| さ↑いだいてんさ↓ようそしゅうごう || 
| аргуме́нт максимиза́ции || 
|-
| 最小值自变量点集 || 
| zuìxiǎozhí zìbiànliàng diǎn jí || 
| Argument [n] des Minimums [n] || 
| argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis>
| argument [m] du minimum [m] || 
| 最小点作用素集合 || 
| さ↑いしょうてんさ↓ようそしゅうごう || 
| аргуме́нт минимиза́ции || 
|-
| 二项式 || 
| èrxiàng shì || 
| Binom [n] || 
| binomial || 
| binôme [m] || 
| 二項式 || 
| に↑こうしき || 
| бино́м, двучле́н || 
|-
| 系数 || 
| xì shù || 
| Koeffizient [n], Beizahl [f], Vorzahl [f] || 
| coefficient || multiplication <number theory>; expression <mathematical logic>
| coefficient [f] || 
| 係数 || 
| け↑いす↓う || 
| коэффицие́нт || 
|-
| 常数函数 || 
| chángshù hánshù || 
| konstante Funktion || 
| constant function || constant <number theory>; function
| fonction constante || 
| 定数関数 || 
| て↑いすうか↓んすう || 
| конста́нтная фу́нкция, постоя́нная фу́нкция || 
|-
|  || 
|  || 
|  || 
| constant term || term <logic>; algebraic expression; constant
|  || 
|  || 
|  || 
|  || 
|-
| 因变量 || 
| yīn biànliàng || 
| abhängige Variable || 
| dependent variable || fraction; operand <mathematical logic>
| variable dépendante || 
| 従属変数 || 
| じ↑ゅうぞくへ↓んすう || 
| зави́симая переме́нная || 
|-
| 等式，方程 || 
| děng shì, fāngchéng || 
| Gleichung [f] || 
| equation || equality <mathematical logic>; expression <mathematical logic>
| équation [f] || 
|  || 
|  || 
|  || 
|-
| 偶函数 || 
| ǒu hánshù || 
| gerade Funktion || 
| even function || function <mathematical logic>; line symmetry <geometry>
| fonction paire || 
| 偶関数 || 
| ぐ↑うかんす↓う || 
| чётная фу́нкция || 
|-
|  || 
|  || 
|  || 
| identity || equality <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
| 单位元，中立元 || 
| dānwèi yuán, zhōnglì yuán || 
| neutrales Element || 
| identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic>
| élément [m] neutre, élément [m] identité || 
| 単位元，中立元 || 
| た↑んいげん，ちゅ↑うりつげん || 
| нейтра́льный элеме́нт || 
|-
| 自变量 || 
| zì biànliàng || 
| unabhängige Variable || 
| independent variable || function <mathematical logic>
| variable indépendante || 
| 独立変数 || 
| ど↑くりつへ↓んすう || 
| незави́симая переме́нная || 
|-
| 未定元 || 
| wèidìng yuán || 
| Unbestimmte [f] || 
| indeterminate || variable
| indéterminée [f] || 
| 不定元 || 
| ふ↑ていげん || 
| неопределённый || 
|-
| 不等式 || 
| bùděng shì || 
| Ungleichung [f] || 
| inequation || inequality <mathematical logic>
| inéquation [f] || 
| 不等式 || 
| ふ↑と↓うしき || 
| неуравне́ние || 
|-
| 代数分式  || 
| dàishù fēnshì || 
|  || 
| irrational fraction || algebraic fraction; polynomial; exponent
|  || 
|  || 
|  || 
|  || 
|-
| 不可约多项式 || 
| bùkěyuē duōxiàngshì || 
| irreduzibles Polynom || 
| irreducible polynomial || polynomial; factorization
| polynôme [m] irréductible || 
| 既約多項式 || 
| き↑やくたこ↓うしき || 
| неприводимый многочле́н || 
|-
| 一次方程 || 
| yīcì fāngchéng || 
| lineare Gleichung || 
| linear equation || equation; coefficient
| équation linéaire || 
| 一次方程式 || 
| い↑ち↓じほ↑うて↓いしき || 
| лине́йное уравне́ние || 
|-
|  || 
|  || 
|  || 
| left identity || identity element <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| monomial || variable; natural number
|  || 
|  || 
|  || 
|  || 
|-
| 奇函数 || 
| jī hánshù || 
| ungerade Funktion || 
| odd function || function <mathematical logic>; point symmetry <geometry>
| fonction impaire || 
| 奇関数 || 
| き↑か↓んすう || 
| нечётная фу́нкция || 
|-
|  || 
|  || 
|  || 
| parameter || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| partial fraction decomposition, partial fraction expansion || algebraic fraction; polynomial
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| polynomial || expression <mathematical logic>; coefficient; indeterminate
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| polynomial function || polynomial; function <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| quadratic equation || equation; coefficient
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| rational function || algebraic fraction; polynomial
|  || 
|  || 
|  || 
|  || 
|-
| 可约多项式 || 
| kěyuē duōxiàngshì || 
| reduzibles Polynom || 
| reducible polynomial || polynomial; factorization
| polynôme [m] réductible || 
| 可約多項式 || 
| か↑やくたこ↓うしき || 
| приводимый многочле́н || 
|-
|  || 
|  || 
|  || 
| right identity || identity element <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| solution || equation
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| square || exponentiation <number theory>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| system of equations, simultaneous equations || finite set <mathematical logic>; equation
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| unknown || variable
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| variable || mathematical object <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| zero; root || domain; solution
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Abstract Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| algebraic structure || underlying set; arity; identity
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| arity || argument <mathematical logic>; operand <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| Boolean domain || set; tautology <logic>; falsity <logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| direct product || Cartesian product <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| field || set <mathematical logic>; basic operations <number theory>; rational number <number theory>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| inverse element || set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| underlying set, carrier set || empty set <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

==== Group Theory ====
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| Cayley table || finite group
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| group || set <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| finite group || underlying set; finite set <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| normal subgroup, invariant subgroup || subgroup; conjugation
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| open interval || interval
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| semigroup || algebraic structure; associative property
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| subgroup || group; binary operation <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

==== Ring Theory ====
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| ring || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Commutative Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Linear Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| basis || linear combination
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| characteristic equation || characteristic polynomial
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| characteristic polynomial || square matrix; eigenvalue; matrix similarity; zero
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| conjugate matrix, Hermitian matrix || conjugate transpose
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| conjugate transpose, Hermitian transpose || complex conjugate <mathematical logic>; transpose
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| diagonal matrix || matrix; main diagonal
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| identity matrix || square matrix; main diagonal
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| invertible matrix, nonsingular matrix || identity matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| linear combination || expression <mathematical logic>; coefficient; vector space
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| linear dependence || linear combination
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| linear independence || linear combination
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| linear mapping || vector addition; scalar multiplication
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| linear transformation || linear mapping
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| binary matrix, logical matrix, relation matrix, Boolean matrix || matrix; Boolean domain
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| like terms || term <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| lower triangular matrix || triangular matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| main diagonal || matrix; diagonal <geometry>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| matrix || rectangle <geometry>; expression <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| matrix addition || matrix; addition <number theory>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| matrix of ones || matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| matrix multiplication || matrix; multiplication <number theory>; addition <number theory>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| matrix similarity || invertible matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| proportional function || proportionality <number theory>; function <mathematical logic>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| rotation matrix || linear transformation; rotation <geometry>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| skew-Hermitian matrix, anti-Hermitian matrix || Hermitian matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| square matrix || matrix; square <geometry>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| system of linear equations; linear system || linear equation
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| transformation matrix || linear transformation; matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| translation matrix || translation <geometry>; matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| transpose || reflection <geometry>; main diagonal
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| triangular matrix || square matrix; triangle <geometry>
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| upper triangular matrix || triangular matrix
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

{| class="wikitable sortable"
|+ theorem in linear algebra
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
| theorem in linear algebra || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
| Cayley–Hamilton theorem || characteristic polynomial; identity matrix; determinant; scalar; ring
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Multilinear Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Universal Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Homological Algebra ===
{| class="wikitable sortable"
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

== Appendix ==
=== Sentence ===
{| class="wikitable sortable"
! cmn-Hans-CN: 语句 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: yǔjù !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Satz [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: sentence !! eng-Latn-US: prerequisite
! fra-Latn-FR: phrase [f] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 文章 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: ぶ↑んしょ↓う !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: фра́за !! rus-Cyrl-RU: предпосы́лка
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|-
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|  || 
|}

=== Symbol ===
{| class="wikitable sortable"
! symbol
! cmn-Hans-CN: 含义
! cmn-Latn.Pinyin-CN: hányì
! deu-Latn-DE: Bedeutung [f]
! eng-Latn-US: meaning
! fra-Latn-FR: signification [f]
! jpn-Jpan-JP: 意味
! jpn-Hrkt-JP: い↓み
! rus-Cyrl-RU: значе́ние
|-
| 
| 
| 
| 
| 
| 
| 
| 
| 
|-
| 
| 
| 
| 
| 
| 
| 
| 
| 
|}

=== Resource under a Public License ===
{| class="wikitable sortable"
! name
! language
! link
|-
| 
| 
| 
|-
| 
| 
| 
|}

<center>
https://upload.wikimedia.org/wikipedia/commons/thumb/6/6d/Quadratic_function_graph_key_values.svg/480px-Quadratic_function_graph_key_values.svg.png
</center>

{{Sci-Tech-Index-Menu}}

==Other Lessons==
* [[Language/Multiple-languages/Vocabulary/Category-Theory|Category Theory]]
* [[Language/Multiple-languages/Vocabulary/Mechanics|Mechanics]]
* [[Language/Multiple-languages/Vocabulary/Animal-sounds-in-many-languages|Animal sounds in many languages]]
* [[Language/Multiple-languages/Vocabulary/Common-Han-Characters-with-⾡|Common Han Characters with ⾡]]
* [[Language/Multiple-languages/Vocabulary/Machine-Element|Machine Element]]
* [[Language/Multiple-languages/Vocabulary/Body-in-many-languages|Body in many languages]]
* [[Language/Multiple-languages/Vocabulary/Mathematical-Logic|Mathematical Logic]]
* [[Language/Multiple-languages/Vocabulary/Thermodynamics|Thermodynamics]]
* [[Language/Multiple-languages/Vocabulary/Greetings-in-All-Languages|Greetings in All Languages]]
* [[Language/Multiple-languages/Vocabulary/Greetings-General-greeting|Greetings General greeting]]
<span links></span>