Difference between revisions of "Language/Multiple-languages/Vocabulary/Algebra"

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Line 2: Line 2:


{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 20: Line 20:
|  ||  
|  ||  
|-
|-
| algebra ||
| 代数 ||
| dàishù ||
| Algebra [f] ||
| algèbre [f] ||
| 代数学 ||
| だ↑いす↓うがく ||
| а́лгебра ||
|-
| elementary algebra ||
| 初等代数 ||  
| 初等代数 ||  
| chūděng dàishù ||  
| chūděng dàishù ||  
| elementare Algebra ||  
| elementare Algebra ||  
| elementary algebra ||
| algèbre [f] élémentaire, algèbre [f] classique ||  
| algèbre [f] élémentaire, algèbre [f] classique ||  
| 初等代数学 ||  
| 初等代数学 ||  
Line 38: Line 29:
| элемента́рная а́лгебра ||  
| элемента́рная а́лгебра ||  
|-
|-
| abstract algebra ||
| 抽象代数 ||  
| 抽象代数 ||  
| chōuxiàng dàishù ||  
| chōuxiàng dàishù ||  
| abstrakte Algebra ||  
| abstrakte Algebra ||  
| abstract algebra ||
| algèbre [f] générale, algèbre [f] abstraite ||  
| algèbre [f] générale, algèbre [f] abstraite ||  
| 抽象代数学 ||  
| 抽象代数学 ||  
Line 47: Line 38:
| общая а́лгебра, абстра́ктная а́лгебра, вы́сшая а́лгебра ||  
| общая а́лгебра, абстра́ктная а́лгебра, вы́сшая а́лгебра ||  
|-
|-
| group theory ||
| 群论 ||  
| 群论 ||  
| qún lùn ||  
| qún lùn ||  
| Gruppentheorie [f] ||  
| Gruppentheorie [f] ||  
| group theory ||
| théorie [f] des groupes ||  
| théorie [f] des groupes ||  
| 群論 ||  
| 群論 ||  
Line 56: Line 47:
| тео́рия групп ||  
| тео́рия групп ||  
|-
|-
| ring theory ||
| 环论 ||  
| 环论 ||  
| huán lùn ||  
| huán lùn ||  
| Ringtheorie [f] ||  
| Ringtheorie [f] ||  
| ring theory ||
| théorie [f] des anneaux ||  
| théorie [f] des anneaux ||  
| 環論 ||  
| 環論 ||  
Line 65: Line 56:
| тео́рия коле́ц ||  
| тео́рия коле́ц ||  
|-
|-
| category theory ||
| 范畴论 ||  
| 范畴论 ||  
| fànchóu lùn ||  
| fànchóu lùn ||  
| Kategorientheorie [f] ||  
| Kategorientheorie [f] ||  
| category theory ||
| théorie [f] des catégories ||  
| théorie [f] des catégories ||  
| 圏論 ||  
| 圏論 ||  
Line 74: Line 65:
| тео́рия катего́рий ||  
| тео́рия катего́рий ||  
|-
|-
| commutative algebra ||
| 交换代数 ||  
| 交换代数 ||  
| jiāohuàn dàishù ||  
| jiāohuàn dàishù ||  
| kommutative Algebra ||  
| kommutative Algebra ||  
| commutative algebra ||
| algèbre [f] commutative ||  
| algèbre [f] commutative ||  
| 可換環論 ||  
| 可換環論 ||  
Line 83: Line 74:
| коммутати́вная а́лгебра ||  
| коммутати́вная а́лгебра ||  
|-
|-
| linear algebra ||
| 线性代数 ||  
| 线性代数 ||  
| xiànxìng dàishù ||  
| xiànxìng dàishù ||  
| lineare Algebra, Vektoralgebra [f] ||  
| lineare Algebra, Vektoralgebra [f] ||  
| linear algebra ||
| algèbre [f] linéaire ||  
| algèbre [f] linéaire ||  
| 線型代数 ||  
| 線型代数 ||  
Line 92: Line 83:
| лине́йная а́лгебра ||  
| лине́йная а́лгебра ||  
|-
|-
| multilinear algebra ||
| 多重线性代数 ||  
| 多重线性代数 ||  
| duōchóng xiànxìng dàishù ||  
| duōchóng xiànxìng dàishù ||  
| multilineare Algebra ||  
| multilineare Algebra ||  
| multilinear algebra ||
| algèbre [f] multilinéaire ||  
| algèbre [f] multilinéaire ||  
| 多重線型代数 ||  
| 多重線型代数 ||  
Line 101: Line 92:
| полилине́йная а́лгебра ||  
| полилине́йная а́лгебра ||  
|-
|-
| universal algebra, common algebra ||
| 泛代数 ||  
| 泛代数 ||  
| fàn dàishù ||  
| fàn dàishù ||  
| universelle Algebra, allgemeine Algebra ||  
| universelle Algebra, allgemeine Algebra ||  
| universal algebra, common algebra ||
| algèbre [f] universelle ||  
| algèbre [f] universelle ||  
| 普遍代数学，一般代数学 ||  
| 普遍代数学，一般代数学 ||  
Line 110: Line 101:
| универса́льная а́лгебра ||  
| универса́льная а́лгебра ||  
|-
|-
| homological algebra ||
| 同调代数 ||  
| 同调代数 ||  
| tóngdiào dàishù ||  
| tóngdiào dàishù ||  
| homologische Algebra ||  
| homologische Algebra ||  
| homological algebra ||
| algèbre [f] homologique ||  
| algèbre [f] homologique ||  
| ホモロジー代数学 ||  
| ホモロジー代数学 ||  
Line 131: Line 122:
== Main ==
== Main ==
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 149: Line 140:
|  ||  
|  ||  
|-
|-
| algebraic equation || coefficient
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| algebraic equation || coefficient
|  ||  
|  ||  
|  ||  
|  ||  
Line 158: Line 149:
|  ||  
|  ||  
|-
|-
| algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| algebraic expression || expression <mathematical logic>; integer; constant; variable; algebraic operation
|  ||  
|  ||  
|  ||  
|  ||  
Line 167: Line 158:
|  ||  
|  ||  
|-
|-
| algebraic fraction || fraction; algebraic expression
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| algebraic fraction || fraction; algebraic expression
|  ||  
|  ||  
|  ||  
|  ||  
Line 176: Line 167:
|  ||  
|  ||  
|-
|-
| algebraic operation || operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| algebraic operation || operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 185: Line 176:
|  ||  
|  ||  
|-
|-
| argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| argument of the maximum || domain <mathematical logic>; maximum <mathematical analysis>
|  ||  
|  ||  
|  ||  
|  ||  
Line 194: Line 185:
|  ||  
|  ||  
|-
|-
| argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| argument of the minimum || domain <mathematical logic>; minimum <mathematical analysis>
|  ||  
|  ||  
|  ||  
|  ||  
Line 203: Line 194:
|  ||  
|  ||  
|-
|-
| coefficient || multiplication <number theory>; expression <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| coefficient || multiplication <number theory>; expression <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 212: Line 203:
|  ||  
|  ||  
|-
|-
| constant function || constant <number theory>; function
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| constant function || constant <number theory>; function
|  ||  
|  ||  
|  ||  
|  ||  
Line 221: Line 212:
|  ||  
|  ||  
|-
|-
| dependent variable || fraction; operand <mathematical logic>
| 因变量 ||  
| 因变量 ||  
| yīn biànliàng ||  
| yīn biànliàng ||  
| abhängige Variable
| abhängige Variable
| dependent variable || fraction; operand <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 230: Line 221:
|  ||  
|  ||  
|-
|-
| equation || equality <mathematical logic>; expression <mathematical logic>
| 等式，方程 ||  
| 等式，方程 ||  
| děng shì, fāngchéng ||  
| děng shì, fāngchéng ||  
| Gleichung [f] ||  
| Gleichung [f] ||  
| equation || equality <mathematical logic>; expression <mathematical logic>
| équation [f]
| équation [f]
|  ||  
|  ||  
Line 240: Line 231:
|  ||  
|  ||  
|-
|-
| even function || function <mathematical logic>; line symmetry <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| even function || function <mathematical logic>; line symmetry <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 250: Line 241:
|  ||  
|  ||  
|-
|-
| identity || equality <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity || equality <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 259: Line 250:
|  ||  
|  ||  
|-
|-
| identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity element, neutral element || set <mathematical logic>; binary operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 268: Line 259:
|  ||  
|  ||  
|-
|-
| independent variable, argument of a function || function <mathematical logic>
| 自变量 ||  
| 自变量 ||  
| zì biànliàng ||  
| zì biànliàng ||  
| unabhängige Variable ||  
| unabhängige Variable ||  
| independent variable, argument of a function || function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 277: Line 268:
|  ||  
|  ||  
|-
|-
| indeterminate || variable
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| indeterminate || variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 286: Line 277:
|  ||  
|  ||  
|-
|-
| inequation || inequality <mathematical logic>
| 不等式 ||  
| 不等式 ||  
| bùděng shì ||  
| bùděng shì ||  
| Ungleichung [f] ||  
| Ungleichung [f] ||  
| inequation || inequality <mathematical logic>
| inéquation [f]
| inéquation [f]
|  ||  
|  ||  
Line 296: Line 287:
|  ||  
|  ||  
|-
|-
| integral expression || algebraic fraction
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| integral expression || algebraic fraction
|  ||  
|  ||  
|  ||  
|  ||  
Line 305: Line 296:
|  ||  
|  ||  
|-
|-
| irrational expression ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| irrational expression ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 314: Line 305:
|  ||  
|  ||  
|-
|-
| irrational fraction || algebraic fraction; polynomial; exponent
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| irrational fraction || algebraic fraction; polynomial; exponent
|  ||  
|  ||  
|  ||  
|  ||  
Line 323: Line 314:
|  ||  
|  ||  
|-
|-
| irreducible polynomial || polynomial; factorization
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| irreducible polynomial || polynomial; factorization
|  ||  
|  ||  
|  ||  
|  ||  
Line 332: Line 323:
|  ||  
|  ||  
|-
|-
| linear equation || equation; coefficient
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear equation || equation; coefficient
|  ||  
|  ||  
|  ||  
|  ||  
Line 341: Line 332:
|  ||  
|  ||  
|-
|-
| left identity || identity element <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| left identity || identity element <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 350: Line 341:
|  ||  
|  ||  
|-
|-
| monomial || variable; natural number
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| monomial || variable; natural number
|  ||  
|  ||  
|  ||  
|  ||  
Line 359: Line 350:
|  ||  
|  ||  
|-
|-
| odd function || function <mathematical logic>; point symmetry <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| odd function || function <mathematical logic>; point symmetry <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 368: Line 359:
|  ||  
|  ||  
|-
|-
| parameter ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| parameter ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 377: Line 368:
|  ||  
|  ||  
|-
|-
| partial fraction decomposition, partial fraction expansion || algebraic fraction; polynomial
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| partial fraction decomposition, partial fraction expansion || algebraic fraction; polynomial
|  ||  
|  ||  
|  ||  
|  ||  
Line 386: Line 377:
|  ||  
|  ||  
|-
|-
| polynomial || expression <mathematical logic>; coefficient; indeterminate
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| polynomial || expression <mathematical logic>; coefficient; indeterminate
|  ||  
|  ||  
|  ||  
|  ||  
Line 395: Line 386:
|  ||  
|  ||  
|-
|-
| polynomial function || polynomial; function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| polynomial function || polynomial; function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 404: Line 395:
|  ||  
|  ||  
|-
|-
| quadratic equation || equation; coefficient
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| quadratic equation || equation; coefficient
|  ||  
|  ||  
|  ||  
|  ||  
Line 413: Line 404:
|  ||  
|  ||  
|-
|-
| rational function || algebraic fraction; polynomial
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| rational function || algebraic fraction; polynomial
|  ||  
|  ||  
|  ||  
|  ||  
Line 422: Line 413:
|  ||  
|  ||  
|-
|-
| right identity || identity element <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| right identity || identity element <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 431: Line 422:
|  ||  
|  ||  
|-
|-
| solution || equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| solution || equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 440: Line 431:
|  ||  
|  ||  
|-
|-
| square || exponentiation <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| square || exponentiation <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 449: Line 440:
|  ||  
|  ||  
|-
|-
| system of equations, simultaneous equations || finite set <mathematical logic>; equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| system of equations, simultaneous equations || finite set <mathematical logic>; equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 458: Line 449:
|  ||  
|  ||  
|-
|-
| unknown || variable
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| unknown || variable
|  ||  
|  ||  
|  ||  
|  ||  
Line 467: Line 458:
|  ||  
|  ||  
|-
|-
| variable || mathematical object <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| variable || mathematical object <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 476: Line 467:
|  ||  
|  ||  
|-
|-
| zero; root || domain; solution
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| zero; root || domain; solution
|  ||  
|  ||  
|  ||  
|  ||  
Line 497: Line 488:
=== Abstract Algebra ===
=== Abstract Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 515: Line 506:
|  ||  
|  ||  
|-
|-
| algebraic structure || underlying set; arity; identity
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| algebraic structure || underlying set; arity; identity
|  ||  
|  ||  
|  ||  
|  ||  
Line 524: Line 515:
|  ||  
|  ||  
|-
|-
| arity || argument <mathematical logic>; operand <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| arity || argument <mathematical logic>; operand <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 533: Line 524:
|  ||  
|  ||  
|-
|-
| Boolean domain || set; tautology <logic>; falsity <logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Boolean domain || set; tautology <logic>; falsity <logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 542: Line 533:
|  ||  
|  ||  
|-
|-
| direct product || Cartesian product <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| direct product || Cartesian product <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 551: Line 542:
|  ||  
|  ||  
|-
|-
| field || set <mathematical logic>; basic operations <number theory>; rational number <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| field || set <mathematical logic>; basic operations <number theory>; rational number <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 560: Line 551:
|  ||  
|  ||  
|-
|-
| inverse element || set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| inverse element || set <mathematical logic>; additive inverse <number theory>; multiplicative inverse <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 569: Line 560:
|  ||  
|  ||  
|-
|-
| underlying set, carrier set || empty set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| underlying set, carrier set || empty set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 590: Line 581:
==== Group Theory ====
==== Group Theory ====
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 608: Line 599:
|  ||  
|  ||  
|-
|-
| Cayley table || finite group
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Cayley table || finite group
|  ||  
|  ||  
|  ||  
|  ||  
Line 617: Line 608:
|  ||  
|  ||  
|-
|-
| group || set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| group || set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 626: Line 617:
|  ||  
|  ||  
|-
|-
| finite group || underlying set; finite set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| finite group || underlying set; finite set <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 635: Line 626:
|  ||  
|  ||  
|-
|-
| normal subgroup, invariant subgroup || subgroup; conjugation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| normal subgroup, invariant subgroup || subgroup; conjugation
|  ||  
|  ||  
|  ||  
|  ||  
Line 644: Line 635:
|  ||  
|  ||  
|-
|-
| open interval || interval
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| open interval || interval
|  ||  
|  ||  
|  ||  
|  ||  
Line 653: Line 644:
|  ||  
|  ||  
|-
|-
| semigroup || algebraic structure; associative property
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| semigroup || algebraic structure; associative property
|  ||  
|  ||  
|  ||  
|  ||  
Line 662: Line 653:
|  ||  
|  ||  
|-
|-
| subgroup || group; binary operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| subgroup || group; binary operation <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 683: Line 674:
==== Ring Theory ====
==== Ring Theory ====
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 701: Line 692:
|  ||  
|  ||  
|-
|-
| ring ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| ring ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 722: Line 713:
=== Commutative Algebra ===
=== Commutative Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 752: Line 743:
=== Linear Algebra ===
=== Linear Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 770: Line 761:
|  ||  
|  ||  
|-
|-
| basis || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| basis || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
Line 779: Line 770:
|  ||  
|  ||  
|-
|-
| characteristic equation || characteristic polynomial
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| characteristic equation || characteristic polynomial
|  ||  
|  ||  
|  ||  
|  ||  
Line 788: Line 779:
|  ||  
|  ||  
|-
|-
| characteristic polynomial || square matrix; eigenvalue; matrix similarity; zero
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| characteristic polynomial || square matrix; eigenvalue; matrix similarity; zero
|  ||  
|  ||  
|  ||  
|  ||  
Line 797: Line 788:
|  ||  
|  ||  
|-
|-
| conjugate matrix, Hermitian matrix || conjugate transpose
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| conjugate matrix, Hermitian matrix || conjugate transpose
|  ||  
|  ||  
|  ||  
|  ||  
Line 806: Line 797:
|  ||  
|  ||  
|-
|-
| conjugate transpose, Hermitian transpose || complex conjugate <mathematical logic>; transpose
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| conjugate transpose, Hermitian transpose || complex conjugate <mathematical logic>; transpose
|  ||  
|  ||  
|  ||  
|  ||  
Line 815: Line 806:
|  ||  
|  ||  
|-
|-
| diagonal matrix || matrix; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| diagonal matrix || matrix; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
Line 824: Line 815:
|  ||  
|  ||  
|-
|-
| identity matrix || square matrix; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| identity matrix || square matrix; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
Line 833: Line 824:
|  ||  
|  ||  
|-
|-
| invertible matrix, nonsingular matrix || identity matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| invertible matrix, nonsingular matrix || identity matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 842: Line 833:
|  ||  
|  ||  
|-
|-
| linear combination || expression <mathematical logic>; coefficient; vector space
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear combination || expression <mathematical logic>; coefficient; vector space
|  ||  
|  ||  
|  ||  
|  ||  
Line 851: Line 842:
|  ||  
|  ||  
|-
|-
| linear dependence || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear dependence || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
Line 860: Line 851:
|  ||  
|  ||  
|-
|-
| linear independence || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear independence || linear combination
|  ||  
|  ||  
|  ||  
|  ||  
Line 869: Line 860:
|  ||  
|  ||  
|-
|-
| linear mapping || vector addition; scalar multiplication
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear mapping || vector addition; scalar multiplication
|  ||  
|  ||  
|  ||  
|  ||  
Line 878: Line 869:
|  ||  
|  ||  
|-
|-
| linear transformation || linear mapping
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| linear transformation || linear mapping
|  ||  
|  ||  
|  ||  
|  ||  
Line 887: Line 878:
|  ||  
|  ||  
|-
|-
| binary matrix, logical matrix, relation matrix, Boolean matrix || matrix; Boolean domain
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| binary matrix, logical matrix, relation matrix, Boolean matrix || matrix; Boolean domain
|  ||  
|  ||  
|  ||  
|  ||  
Line 896: Line 887:
|  ||  
|  ||  
|-
|-
| like terms || term <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| like terms || term <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 905: Line 896:
|  ||  
|  ||  
|-
|-
| lower triangular matrix || triangular matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| lower triangular matrix || triangular matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 914: Line 905:
|  ||  
|  ||  
|-
|-
| main diagonal || matrix; diagonal <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| main diagonal || matrix; diagonal <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 923: Line 914:
|  ||  
|  ||  
|-
|-
| matrix || rectangle <geometry>; expression <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| matrix || rectangle <geometry>; expression <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 932: Line 923:
|  ||  
|  ||  
|-
|-
| matrix addition || matrix; addition <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| matrix addition || matrix; addition <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 941: Line 932:
|  ||  
|  ||  
|-
|-
| matrix of ones || matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| matrix of ones || matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 950: Line 941:
|  ||  
|  ||  
|-
|-
| matrix multiplication || matrix; multiplication <number theory>; addition <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| matrix multiplication || matrix; multiplication <number theory>; addition <number theory>
|  ||  
|  ||  
|  ||  
|  ||  
Line 959: Line 950:
|  ||  
|  ||  
|-
|-
| matrix similarity || invertible matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| matrix similarity || invertible matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 968: Line 959:
|  ||  
|  ||  
|-
|-
| proportional function || proportionality <number theory>; function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| proportional function || proportionality <number theory>; function <mathematical logic>
|  ||  
|  ||  
|  ||  
|  ||  
Line 977: Line 968:
|  ||  
|  ||  
|-
|-
| rotation matrix || linear transformation; rotation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| rotation matrix || linear transformation; rotation <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 986: Line 977:
|  ||  
|  ||  
|-
|-
| skew-Hermitian matrix, anti-Hermitian matrix || Hermitian matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| skew-Hermitian matrix, anti-Hermitian matrix || Hermitian matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 995: Line 986:
|  ||  
|  ||  
|-
|-
| square matrix || matrix; square <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| square matrix || matrix; square <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,004: Line 995:
|  ||  
|  ||  
|-
|-
| system of linear equations; linear system || linear equation
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| system of linear equations; linear system || linear equation
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,013: Line 1,004:
|  ||  
|  ||  
|-
|-
| transformation matrix || linear transformation; matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transformation matrix || linear transformation; matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,022: Line 1,013:
|  ||  
|  ||  
|-
|-
| translation matrix || translation <geometry>; matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| translation matrix || translation <geometry>; matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,031: Line 1,022:
|  ||  
|  ||  
|-
|-
| transpose || reflection <geometry>; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| transpose || reflection <geometry>; main diagonal
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,040: Line 1,031:
|  ||  
|  ||  
|-
|-
| triangular matrix || square matrix; triangle <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| triangular matrix || square matrix; triangle <geometry>
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,049: Line 1,040:
|  ||  
|  ||  
|-
|-
| upper triangular matrix || triangular matrix
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| upper triangular matrix || triangular matrix
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,070: Line 1,061:
{| class="wikitable sortable"
{| class="wikitable sortable"
|+ theorem in linear algebra
|+ theorem in linear algebra
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 1,079: Line 1,070:
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
|-
|-
| theorem in linear algebra ||
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| theorem in linear algebra ||
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,097: Line 1,088:
|  ||  
|  ||  
|-
|-
| Cayley–Hamilton theorem || characteristic polynomial; identity matrix; determinant; scalar; ring
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
|  ||  
| Cayley–Hamilton theorem || characteristic polynomial; identity matrix; determinant; scalar; ring
|  ||  
|  ||  
|  ||  
|  ||  
Line 1,127: Line 1,118:
=== Multilinear Algebra ===
=== Multilinear Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 1,157: Line 1,148:
=== Universal Algebra ===
=== Universal Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
Line 1,187: Line 1,178:
=== Homological Algebra ===
=== Homological Algebra ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! 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]
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
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=== Sentence ===
=== Sentence ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: concept !! eng-Latn-US: prerequisite
! cmn-Hans-CN: 语句 !! cmn-Hans-CN: 前提
! cmn-Hans-CN: 概念 !! cmn-Hans-CN: 前提
! cmn-Latn.Pinyin-CN: yǔjù !! cmn-Latn.Pinyin-CN: qiántí
! cmn-Latn.Pinyin-CN: gàiniàn !! cmn-Latn.Pinyin-CN: qiántí
! deu-Latn-DE: Satz [m] !! deu-Latn-DE: Voraussetzung [f]
! deu-Latn-DE: Begriff [m] !! deu-Latn-DE: Voraussetzung [f]
! eng-Latn-US: sentence !! eng-Latn-US: prerequisite
! fra-Latn-FR: concept [m] !! fra-Latn-FR: préalable [m]
! fra-Latn-FR: phrase [f] !! fra-Latn-FR: préalable [m]
! jpn-Jpan-JP: 概念 !! jpn-Jpan-JP: 前提
! jpn-Jpan-JP: 文章 !! jpn-Jpan-JP: 前提
! jpn-Hrkt-JP: が↓いねん !! jpn-Hrkt-JP: ぜ↑んてい
! jpn-Hrkt-JP: ぶ​↑んしょ↓う !! jpn-Hrkt-JP: ぜ↑んてい
! rus-Cyrl-RU: конце́пция !! rus-Cyrl-RU: предпосы́лка
! rus-Cyrl-RU: фра́за !! rus-Cyrl-RU: предпосы́лка
|-
|-
|  ||  
|  ||  
Line 1,249: Line 1,240:
{| class="wikitable sortable"
{| class="wikitable sortable"
! symbol
! symbol
! eng-Latn-US: concept
! cmn-Hans-CN: 概念
! cmn-Hans-CN: 概念
! cmn-Latn.Pinyin-CN: gàiniàn
! cmn-Latn.Pinyin-CN: gàiniàn
! deu-Latn-DE: Begriff [m]
! deu-Latn-DE: Begriff [m]
! eng-Latn-US: concept
! fra-Latn-FR: concept [m]
! fra-Latn-FR: concept [m]
! jpn-Jpan-JP: 概念
! jpn-Jpan-JP: 概念
Line 1,281: Line 1,272:
=== Process ===
=== Process ===
{| class="wikitable sortable"
{| class="wikitable sortable"
! eng-Latn-US: process !! eng-Latn-US: constituent
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Hans-CN: 过程 !! cmn-Hans-CN: 构件
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! cmn-Latn.Pinyin-CN: guòchéng !! cmn-Latn.Pinyin-CN: gòujiàn
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! deu-Latn-DE: Prozess [m] !! deu-Latn-DE: Bestandteil [m]
! eng-Latn-US: process !! eng-Latn-US: constituent
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! fra-Latn-FR: procès [m] !! fra-Latn-FR: composant [m]
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材
! jpn-Jpan-JP: 過程 !! jpn-Jpan-JP: 構材

Revision as of 08:15, 26 March 2022

Hello polyglots, 😀

On this page you will find a part of the Sci–Tech Index, a project for science and technology learners.

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
初等代数 chūděng dàishù elementare Algebra elementary algebra algèbre [f] élémentaire, algèbre [f] classique 初等代数学 しょ↑とうだいす↓うがく элемента́рная а́лгебра
抽象代数 chōuxiàng dàishù abstrakte Algebra abstract algebra algèbre [f] générale, algèbre [f] abstraite 抽象代数学 ちゅ↑うしょうだいす↓うがく общая а́лгебра, абстра́ктная а́лгебра, вы́сшая а́лгебра
群论 qún lùn Gruppentheorie [f] group theory théorie [f] des groupes 群論 ぐ↓んろん тео́рия групп
环论 huán lùn Ringtheorie [f] ring theory théorie [f] des anneaux 環論 か↑んろん тео́рия коле́ц
范畴论 fànchóu lùn Kategorientheorie [f] category theory théorie [f] des catégories 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

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 equation coefficient
algebraic expression expression <mathematical logic>; integer; constant; variable; algebraic operation
algebraic fraction fraction; algebraic expression
algebraic operation operation <mathematical logic>
argument of the maximum domain <mathematical logic>; maximum <mathematical analysis>
argument of the minimum domain <mathematical logic>; minimum <mathematical analysis>
coefficient multiplication <number theory>; expression <mathematical logic>
constant function constant <number theory>; function
因变量 yīn biànliàng abhängige Variable dependent variable fraction; operand <mathematical logic>
等式，方程 děng shì, fāngchéng Gleichung [f] equation equality <mathematical logic>; expression <mathematical logic> équation [f]
even function function <mathematical logic>; line symmetry <geometry>
identity equality <mathematical logic>
identity element, neutral element set <mathematical logic>; binary operation <mathematical logic>
自变量 zì biànliàng unabhängige Variable independent variable, argument of a function function <mathematical logic>
indeterminate variable
不等式 bùděng shì Ungleichung [f] inequation inequality <mathematical logic> inéquation [f]
integral expression algebraic fraction
irrational expression
irrational fraction algebraic fraction; polynomial; exponent
irreducible polynomial polynomial; factorization
linear equation equation; coefficient
left identity identity element <mathematical logic>
monomial variable; natural number
odd function function <mathematical logic>; point symmetry <geometry>
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
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

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

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

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

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

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
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

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

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

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

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

symbol cmn-Hans-CN: 概念 cmn-Latn.Pinyin-CN: gàiniàn deu-Latn-DE: Begriff [m] eng-Latn-US: concept fra-Latn-FR: concept [m] jpn-Jpan-JP: 概念 jpn-Hrkt-JP: が↓いねん rus-Cyrl-RU: конце́пция

Process

cmn-Hans-CN: 过程 cmn-Hans-CN: 构件 cmn-Latn.Pinyin-CN: guòchéng cmn-Latn.Pinyin-CN: gòujiàn deu-Latn-DE: Prozess [m] deu-Latn-DE: Bestandteil [m] eng-Latn-US: process eng-Latn-US: constituent fra-Latn-FR: procès [m] fra-Latn-FR: composant [m] jpn-Jpan-JP: 過程 jpn-Jpan-JP: 構材 jpn-Hrkt-JP: か↑てい jpn-Hrkt-JP: こ↑うざい rus-Cyrl-RU: проце́сс rus-Cyrl-RU: соста́вная часть

Resource under a Public License

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Sci–Tech Index

40px-3-4.svg.png Introduction

Philosophy

40px-1-4.svg.png Logic

40px-0-4.svg.png Metaphysics

Mathematics

40px-2-4.svg.png Mathematical Logic

40px-0-4.svg.png Category Theory


40px-2-4.svg.png Number Theory


40px-1-4.svg.png Algebra


40px-1-4.svg.png Geometry


40px-1-4.svg.png Probability Theory

40px-1-4.svg.png Statistics

40px-1-4.svg.png Information Theory


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40px-1-4.svg.png Topology

40px-1-4.svg.png Discrete Mathematics


40px-1-4.svg.png Computational Science

Physics

40px-1-4.svg.png Mechanics

└ 40px-1-4.svg.png Structural Analysis

└ 40px-1-4.svg.png Tribology

40px-1-4.svg.png Thermodynamics


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40px-1-4.svg.png Acoustics


40px-1-4.svg.png Electromagnetism

40px-1-4.svg.png Electronic Component


40px-0-4.svg.png Metrology

└ 40px-1-4.svg.png Unit of Measurement


40px-0-4.svg.png Particle Physics

Biology

40px-1-4.svg.png Cell Biology

Chemistry

40px-1-4.svg.png Chemical Element

40px-0-4.svg.png Material Science

└ 40px-0-4.svg.png Metallurgy

40px-0-4.svg.png Computer Science
40px-1-4.svg.png Technical Drawing
Mechanical Engineering

40px-0-4.svg.png Mechanism

40px-1-4.svg.png Machine Element

40px-1-4.svg.png Metalworking


40px-0-4.svg.png Hydraulics and Pneumatics


40px-1-4.svg.png Theory of Inventive Problem Solving

Software Engineering

40px-1-4.svg.png Computer Language

Systems Science

40px-0-4.svg.png Chaos Theory

40px-0-4.svg.png Cybernetics

└ 40px-0-4.svg.png Control Theory

40px-0-4.svg.png Robotics

40px-0-4.svg.png Anthropology

40px-0-4.svg.png Psychology
40px-0-4.svg.png Linguistics

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