数学与应用数学外文+翻译

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【教育资料】各种数学语言名称的英语翻译学习专用

各种数学语言名称的英语翻译数学 mathematics, maths(BrE), math(AmE)公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n.) 被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.) 被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数（reciprocal） x的倒数为1/x有理数 rational number无理数 irrational number实数 real number虚数 imaginary number数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil 十进制 decimal system二进制 binary system十六进制 hexadecimal system 权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit 无效数字 insignificant digit 代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor 等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root sqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量 constant变量 variable坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle 等腰三角形 isosceles triangle 等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram 矩形 rectangle长 length宽 width周长 perimeter面积 area相似 similar全等 congruent三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant集合aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.) 无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral 复数 complex number矩阵 matrix行列式 determinant圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference轨迹 locus, loca(pl.)平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron旋转 rotation轴 axis球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space双曲线 hyperbola抛物线 parabola四面体 tetrahedron五面体 pentahedron六面体 hexahedron菱形 rhomb, rhombus, rhombi(pl.), diamond 正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE) 重心 barycentre(BrE), barycenter(AmE) 内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph 曲线统计图 curve diagram扇形统计图 pie diagram。

数学与应用数学英文文献及翻译

（外文翻译从原文第一段开始翻译，翻译了约2000字）勾股定理是已知最早的古代文明定理之一。

这个著名的定理被命名为希腊的数学家和哲学家毕达哥拉斯。

毕达哥拉斯在意大利南部的科托纳创立了毕达哥拉斯学派。

他在数学上有许多贡献，虽然其中一些可能实际上一直是他学生的工作。

毕达哥拉斯定理是毕达哥拉斯最著名的数学贡献。

据传说，毕达哥拉斯在得出此定理很高兴，曾宰杀了牛来祭神，以酬谢神灵的启示。

后来又发现2的平方根是不合理的，因为它不能表示为两个整数比，极大地困扰毕达哥拉斯和他的追随者。

他们在自己的认知中，二是一些单位长度整数倍的长度。

因此2的平方根被认为是不合理的，他们就尝试了知识压制。

它甚至说，谁泄露了这个秘密在海上被淹死。

毕达哥拉斯定理是关于包含一个直角三角形的发言。

毕达哥拉斯定理指出，对一个直角三角形斜边为边长的正方形面积，等于剩余两直角为边长正方形面积的总和图1根据勾股定理，在两个红色正方形的面积之和A和B，等于蓝色的正方形面积，正方形三区因此，毕达哥拉斯定理指出的代数式是：对于一个直角三角形的边长a，b和c，其中c是斜边长度。

虽然记入史册的是著名的毕达哥拉斯定理，但是巴比伦人知道某些特定三角形的结果比毕达哥拉斯早一千年。

现在还不知道希腊人最初如何体现了勾股定理的证明。

如果用欧几里德的算法使用，很可能这是一个证明解剖类型类似于以下内容：六^维-论~文.网“一个大广场边a+ b是分成两个较小的正方形的边a和b分别与两个矩形A和B，这两个矩形各可分为两个相等的直角三角形，有相同的矩形对角线c。

四个三角形可安排在另一侧广场a+b中的数字显示。

在广场的地方就可以表现在两个不同的方式：1。

由于两个长方形和正方形面积的总和：2。

作为一个正方形的面积之和四个三角形：现在，建立上面2个方程，求解得因此，对c的平方等于a和b的平方和（伯顿1991）有许多的勾股定理其他证明方法。

一位来自当代中国人在中国现存最古老的含正式数学理论能找到对Gnoman和天坛圆路径算法的经典文本。

数学术语中英文对照

数学术语中英文对照数学mathematics, maths(bre), math(ame)公理axiom定理theorem计算calculation运算operation证明prove假设hypothesis, hypotheses(pl.)命题proposition算术arithmetic加plus(prep.), add(v.), addition(n.)被加数augend, summand加数addend和sum减minus(prep.), subtract(v.), subtraction(n.) 被减数minuend减数subtrahend差remainder乘times(prep.), multiply(v.), multiplication(n.) 被乘数multiplicand, faciend乘数multiplicator积product除divided by(prep.), divide(v.), division(n.) 被除数dividend除数divisor商quotient等于equals, is equal to, is equivalent to 大于is greater than小于is lesser than大于等于is equal or greater than小于等于is equal or lesser than运算符operator数字digit数number自然数natural number整数integer小数decimal小数点decimal point分数fraction分子numerator分母denominator比ratio正positive负negative零null, zero, nought, nil十进制decimal system二进制binary system十六进制hexadecimal system权weight, significance进位carry截尾truncation四舍五入round下舍入round down上舍入round up有效数字significant digit无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial多项式polynomial, multinomial系数coefficient未知数unknown, x-factor, y-factor, z-factor 等式，方程式equation一次方程simple equation二次方程quadratic equation三次方程cubic equation四次方程quartic equation不等式inequation阶乘factorial 对数logarithm指数，幂exponent乘方power二次方，平方square三次方，立方cube四次方the power of four, the fourth power n次方the power of n, the nth power开方evolution, extraction二次方根，平方根square root三次方根，立方根cube root四次方根the root of four, the fourth root n次方根the root of n, the nth root集合aggregate元素element空集void子集subset交集intersection并集union补集complement映射mapping函数function定义域domain, field of definition值域range常量constant变量variable单调性monotonicity奇偶性parity周期性periodicity图象image数列，级数series微积分calculus微分differential导数derivative极限limit无穷大infinite(a.) infinity(n.) 无穷小infinitesimal积分integral定积分definite integral不定积分indefinite integral 有理数rational number无理数irrational number实数real number虚数imaginary number复数complex number矩阵matrix行列式determinant几何geometry 点point线line面plane体solid线段segment射线radial平行parallel相交intersect角angle角度degree弧度radian锐角acute angle直角right angle钝角obtuse angle平角straight angle周角perigon底base边side高height三角形triangle锐角三角形acute triangle 直角三角形right triangle 直角边leg斜边hypotenuse勾股定理pythagorean theorem钝角三角形obtuse triangle不等边三角形scalene triangle等腰三角形isosceles triangle等边三角形equilateral triangle四边形quadrilateral平行四边形parallelogram矩形rectangle长length宽width菱形rhomb, rhombus, rhombi(pl.), diamond 正方形square梯形trapezoid直角梯形right trapezoid等腰梯形isosceles trapezoid五边形pentagon六边形hexagon七边形heptagon八边形octagon九边形enneagon十边形decagon十一边形hendecagon十二边形dodecagon 多边形polygon正多边形equilateral polygon 圆circle圆心centre(bre), center(ame) 半径radius直径diameter圆周率pi弧arc半圆semicircle扇形sector环ring椭圆ellipse圆周circumference周长perimeter面积area轨迹locus, loca(pl.)相似similar全等congruent四面体tetrahedron五面体pentahedron六面体hexahedron平行六面体parallelepiped 立方体cube七面体heptahedron八面体octahedron九面体enneahedron十面体decahedron十一面体hendecahedron十二面体dodecahedron二十面体icosahedron多面体polyhedron棱锥pyramid棱柱prism棱台frustum of a prism旋转rotation轴axis圆锥cone圆柱cylinder圆台frustum of a cone球sphere半球hemisphere底面undersurface表面积surface area体积volume空间space坐标系coordinates坐标轴x-axis, y-axis, z-axis 横坐标x-coordinate纵坐标y-coordinate原点origin双曲线hyperbola抛物线parabola三角trigonometry正弦sine余弦cosine正切tangent余切cotangent正割secant余割cosecant反正弦arc sine反余弦arc cosine反正切arc tangent反余切arc cotangent反正割arc secant反余割arc cosecant相位phase周期period振幅amplitude内心incentre(bre), incenter(ame) 外心excentre(bre), excenter(ame)旁心escentre(bre), escenter(ame)垂心orthocentre(bre), orthocenter(ame)重心barycentre(bre), barycenter(ame)内切圆inscribed circle外切圆circumcircle统计statistics平均数average加权平均数weighted average方差variance标准差root-mean-square deviation, standard deviation比例propotion百分比percent 百分点percentage百分位数percentile排列permutation组合combination概率，或然率probability分布distribution正态分布normal distribution非正态分布abnormal distribution 图表graph条形统计图bar graph柱形统计图histogram折线统计图broken line graph。

高中数学常用术语中英对照mathematics

高中数学常用术语中英对照m a t h e m a t i c s -CAL-FENGHAI-(2020YEAR-YICAI)_JINGBIAN数学 mathematics, maths(BrE), math(AmE)公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.) 被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n.) 被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.)被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator平均数mean算术平均数arithmatic mean几何平均数geometric meann个数之积的n次方根倒数（reciprocal）x的倒数为1/x 有理数 rational number无理数 irrational number实数 real number虚数 imaginary number数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil十进制 decimal system二进制 binary system十六进制 hexadecimal system权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit无效数字 insignificant digit代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor 等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth power n次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root sqrt(2)=1.414 sqrt(3)=1.732 sqrt(5)=2.236常量 constant变量 variable坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem 钝角三角形 obtuse triangle不等边三角形 scalene triangle 等腰三角形 isosceles triangle 等边三角形 equilateral triangle 四边形 quadrilateral平行四边形 parallelogram矩形 rectangle长 length宽 width周长 perimeter面积 area相似 similar全等 congruent三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant补充：集合aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.)无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral 复数 complex number矩阵 matrix行列式 determinant圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference轨迹 locus, loca(pl.)平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron旋转 rotation轴 axis球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space双曲线 hyperbola抛物线 parabola四面体 tetrahedron五面体 pentahedron六面体 hexahedron菱形 rhomb, rhombus, rhombi(pl.), diamond 正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE)重心 barycentre(BrE), barycenter(AmE)内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation 比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagram。

Applied Mathematics应用数学

Applied Mathematics （应用数学）和其他学长一样，先自我介绍一下，曹晓萌，Year 2, Applied Mathematics major (本来也是想要进QF的，后来因为政策改变，因为FDDP放弃了QF,我后面会介绍到吧)，USP(University Scholars Programme), FDDP (French Double Degree Programme).应剑溥的邀请，我这篇文章主要介绍一下FDDP和Applied Mathematics的课程要求吧，还有就是CAP的问题。

FDDP，就是French Double Degree Program,这是国大与五所法国Grandes Ecoles（中文叫大学校）的联合办学项目，大一大二由国大从FOS（只限math major 和physics major,我们这届有招st的，但具体规定就不知道了），FOE，SOC里选拔20人左右，进行培训，主要是每学期60小时的数学课，物理课，数学难度自我感觉跨度很大，在MA2108(mathematical analysis I),MA3110( Mathematical Analysis II)和一些lebesgue integration 的知识，可以说是非常的专，物理，难度大致相当于物理系大二的水平，我们这届是有一个从法国很牛的GRANDE ECOLE过来的教授和一个ECOLE CENTRALE DES PARIS的博士交我们。

然后，就是两个Cultural Immersion,自我感觉这就是拿着NUS 的钱去公费旅游，也是这个项目中唯一轻松的部分，而且一般是home stay,所以可以帮我们尽快地融入到法国当地社会中，自我感受着文化冲击，是非常有趣以及终身难忘的经验。

五所Grandes Ecoles 介绍：这五所学校是法国排名前五的授予研究生文凭的学校，每年招的人数极少，以Ecole des Mines为例，每年只在法国招收100名学生，并招收5名International students，竞争是极为激烈的。

数学与应用数学专业英语翻译

3-c (P38/P33)集合论在讨论任何数学的分支，如分析、代数、几何，最好使用符号和集合理论的专业术语。

在19世纪后期被布勒和康托尔发展的这个学科，已对20世纪数学发展有了深远的影响。

它具有统一的许多看似已断开连接的想法，并有助用优雅有系统的方式减少许多逻辑基础上的数学概念。

集合论彻底处理需要漫长的讨论，我们认为超出了这本书的范围。

幸运的是，基础的概念很少涉及数字，通过非正式的讨论他可能已经发展成为集合论的方法和想法的可操作的知识。

实际上，我们将讨论不是像一个有关精确术语的协议一样的一个新的理论，我们将或多或少的应用到熟悉的想法。

在数学中，'"集'"一词用于表示作为单个实体的对象的聚集，集合也被称为'"群'"部落，'一伙人'"'"，团队'，和‘选举团’这是所有集合的示例。

集合中的单个对象称为元素或集合的成员，他们都称为属于或包含于集合中。

反过来，集合包含或由其元素构成。

我们应该主要对数学对象的集合感兴趣：数集、曲线集、几何图形集等等。

在许多应用程序，通过对集合中的各个对象的性质进行没什么特别性质的假定去处理集合是方便快捷的。

这些称为抽象集。

抽象集理论已经发展到处理任意对象的集合，这种集合，并从这种普遍性理论派生其权力。

9-c（P80/P66）积分的基本属性由积分的定义，它可以推导出以下属性，证明有在第1.27 部分中。

定理1，线性性质对被积函数，如果f 和g 都在[a、b] 上可积，那么对于每一对常量c1 和c2有---。

而且有----------（积分等式成立）注解：利用数学归纳法，线性属性可推广，如下所示：如果--在【a，b】上可积那么对于所有实数-----有-----且---------（积分等式成立）定理2.区间可加性，如果以下三个积分的两个存在，那么第三个也存在，并且我们有...注意：在特别是，如果 f 是在[a、c]上是单调的和在[c、b]上也是单调的，且这两个积分存在，则【a，b】区间上的积分也存在且与其他两个积分的和相等定理3.平移不变性，如果f 在区间[a、b]上可积，那么对于任意实数c，都有… …。

数学专业英语词汇大全

数学专业英语词汇大全Aa priori bound 先验界限a priori distribution 先验分布a priori probability 先验概率a summable a可和的abacus 算盘abbreviate 略abbreviation 简化abel equation 阿贝耳方程abel identity 阿贝耳恒等式abel inequality 阿贝耳不等式abel summation method 阿贝耳求和法abelian algebra 阿贝耳代数abelian differential 阿贝耳微分abelian equation 阿贝耳方程abelian extension 阿贝耳扩张abelian function 阿贝耳函数abelian function field 阿贝耳函数域abelian functor 阿贝耳函子abelian group 交换群abelian groupoid 阿贝耳广群abelian integral 阿贝耳积分abelian summation 阿贝耳求和法abelian theorem 阿贝耳定理abelian variety 阿贝耳簇abridge 略abridged notation 简算记号abscissa 横坐标abscissa of absolute convergence 绝对收敛坐标abscissa of summability 可和性坐标abscissa of uniform convergence 一致收敛横坐标absolute 绝对形absolute address 绝对地址absolute class field 绝对类域absolute coding 绝对编码absolute cohomology 绝对上同调absolute conic 绝对二次曲线absolute convergence 绝对收敛absolute curvature vector 绝对曲率向量absolute deviation 绝对偏差absolute differential calculus 绝对微分学absolute error 绝对误差absolute extremes 绝对极值absolute extremum 绝对极值absolute frequency 绝对频率absolute geometry 绝对几何absolute homology group 绝对同岛absolute homotopy group 绝对同伦群absolute inequality 绝对不等式absolute instability 绝对不稳定性absolute maximum 绝对极大值absolute minimum 绝对极小值absolute moment 绝对矩absolute neighborhood 绝对邻域absolute neighborhood retract 绝对邻域收缩核absolute norm 绝对范数absolute number 不名数absolute parallelism 绝对平行性absolute quadric 绝对二次曲面absolute ramification index 绝对分歧指数absolute rotation 绝对旋转absolute singular homology group 绝对奇异同岛absolute space 绝对空间absolute space time 绝对时空absolute stability 绝对稳定性absolute term 常数项absolute unit 绝对单位absolute value 绝对值absolute value sign 绝对值符号absolute velocity 绝对速度absolutely additive measure 完全加性测度absolutely compact set 绝对紧集absolutely complete system 绝对完备系absolutely continuous 绝对连续的absolutely continuous distribution 绝对连续分布absolutely continuous function 绝对连续函数absolutely continuous measure 绝对连续测度absolutely continuous part 绝对连续部分absolutely continuous transformation 绝对连续变换absolutely convergent 绝对收敛的absolutely convergent integral 绝对收敛积分absolutely convergent series 绝对收敛级数absolutely convex hull 绝对凸包absolutely discontinuous function 绝对不连续函数absolutely integrable 绝对可积的absolutely irreducible character 绝对不可约特征absolutely irreducible representation 绝对不可约表示absolutely irreducible variety 绝对不可约簇absolutely normal number 绝对范数absolutely prime ideal 绝对素理想absolutely semisimple algebra 绝对半单代数absolutely simple group 绝对单群absolutely summable sequence 绝对可和序列absolutely unbiased estimator 绝对无偏估计量absolutely unramified extension 绝对非分歧扩张absorbing barrier 吸收障碍absorbing medium 吸收媒体absorbing set 吸收集absorbing state 吸收态absorption 吸收absorption coefficient 吸收系数absorption curve 吸收曲线absorption factor 吸收因数absorption index 吸收指数absorption law 吸收律absorption probability 吸收概率abstract 抽象的abstract algebra 抽象代数abstract algebraic geometry 抽象代数几何abstract automaton 抽象自动机abstract category 抽象范畴abstract code 理想码abstract complex 抽象复形abstract group 抽象群abstract interval function 抽象区间函数abstract mathematics 抽象数学abstract number 不名数abstract ordered simplicial complex 抽象有序单纯复形abstract simplex 抽象单形abstract simplicial subcomplex 抽象单子复形abstract space 抽象空间abstraction 抽象abstraction operator 抽象算子absurd 谬论的absurdity 谬论abundance ratio 丰度比abundant number 过剩数accelerated motion 加速运动acceleration 加速度acceleration of convergence 收敛性的加速acceleration of gravity 重力加速度acceptable quality level 合格质量水平acceptance 肯定acceptance inspection 接受检查acceptance limit 接受界限acceptance line 接受线acceptance number 接受数acceptance probability 接受概率acceptance region 接受区域acceptance zone 接受带access 存取access speed 存取速度access time 存取时间accessibility 可达性accessible boundary point 可达边界点accessible ordinal number 可达序数accessible point 可达点accessible set 可达集accessible vertex 可达顶点accessory extremal 配连极值accidental 偶然的accidental coincidence 偶然符合accidental error 随机误差accommodation 第accumulated error 累积误差accumulating point 聚点accumulation 累积accumulation point 聚点accumulator 累加器存储器accuracy 准确性accuracy grade 准确度accuracy of measurement 测量精确度accuracy rating 准确度acnod 孤点acount 计算action integral 酌积分action variable 酌变量active restriction 有效限制actual 真实的actual infinity 实无穷acute 尖锐的acute angle 锐角acute angled triangle 锐角三角形acute triangle 锐角三角形acuteness 锐度acyclic 非循环的acyclic complex 非循环复形acyclic graph 环道自由图acyclic model theorem 非循环模型定理ad infinitum 无穷地adams circle 阿达姆斯圆adams extrapolation method 阿达姆斯外插法adaptability 适应性adaptation 适应adapted basis 适应基add 加added circuit 加法电路addend 加数adder 加法器addition 加法addition formulas 加法公式addition sign 加号addition system 加法系addition table 加法表addition theorem 加法定理addition theorem of probability 概率的加法定理additional 加法的additional code 附加代码additional condition 附加条件additional error 附加误差additive 加法的additive category 加性范畴additive class 加性类additive functional 加性泛函数additive functional transformation 加性泛函变换additive group 加法群additive interval function 加性区间函数additive inverse element 加性逆元素additive number theory 堆垒数论additive operator 加性算子additive process 加性过程additive relation 加性关系additive separable 加法可分的additive theory of numbers 堆垒数论additive valuation 加法赋值additively commutative ordinal numbers 加性交换序数additivity 加法性address 地址address part 地址部分address register 地址寄存器addressing 指定箱位adele 阿代尔adele group 阿代尔群adequate 适合的adherent point 触点adhesion 附着adjacency 邻接adjacency matrix 邻接矩阵adjacent angles 邻角adjacent edge 邻棱adjacent side 邻边adjacent supplementary angles 邻角adjacent vertex 邻顶adjoint boundary value problem 伴随边值问题adjoint determinant 伴随行列式adjoint difference equation 伴随差分方程adjoint differential equation 伴随微分方程adjoint differential expression 伴随微分式adjoint form 伴随形式adjoint function 伴随函数adjoint functor 伴随函子adjoint graph 导出图adjoint group 伴随群adjoint hilbert problem 伴随希耳伯特问题adjoint integral equation 伴随积分方程adjoint kernel 伴随核adjoint linear map 伴随线性映射adjoint matrix 伴随阵adjoint operator 伴随算子adjoint process 伴随过程adjoint representation 伴随表示adjoint space 伴随空间adjoint surface 伴随曲面adjoint system 伴随系adjoint system of differential equations 微分方程的伴随系adjoint transformation 伴随算子adjoint vector 伴随向量adjunct 代数余子式adjunction 附加adjunction of an identity element 单位元的附加adjustable point 可胆点adjustment 蝶admissibility limit 容许界限admissible 容许的admissible category 容许范畴admissible chart 容许图admissible control 可行控制admissible decision function 容许判决函数admissible decision rule 容许判决函数admissible deformation 容许形变admissible domain 容许区域admissible function 容许函数admissible homomorphism 容许同态admissible hypothesis 容许假设admissible lifting 容许提升admissible map 容许映射admissible sequence 容许序列admissible space 容许空间admissible strategy 容许策略admissible subgroup 容许子群admissible test 容许检定admissible value 容许值affine algebraic set 仿射代数集affine collineation 仿射直射变换affine connection 仿射联络affine coordinates 平行坐标affine curvature 仿射曲率affine differential geometry 仿射微分几何学affine distance 仿射距离affine figure 仿射图形affine function 仿射函数affine geometry 仿射几何学affine group 仿射群affine group scheme 仿射群概型affine isothermal net 仿射等温网affine length 仿射长度affine line 仿射直线affine normal 仿射法线affine parameter 仿射参数affine principal curvature 仿射助率affine rational transformation 仿射有理变换affine space 仿射空间affine sphere 仿射球面affine surface 仿射曲面affine transformation 仿射变换affine variety 仿射簇affinely connected manifold 仿射连通廖affinely connected space 仿射连通空间affinity 仿射变换affirmation 肯定affirmative proposition 肯定命题affix 附标after effect 后效酌aggregate 集aggregation 聚合agreement 一致air coordinates 空间坐标airy function 亚里函数airy integral 亚里积分aitken interpolation 艾特肯插值aitken interpolation formula 艾特肯插值公式albanese variety 阿尔巴内斯簇aleph 阿列夫aleph zero 阿列夫零alexander cohomology module 亚历山大上同担alexander cohomology theory 亚历山大上同帝alexander matrix 亚历山大阵alexander polynomial 亚历山大多项式algebra 代数学algebra of events 事件场algebra of logic 逻辑代数algebra of tensors 张量代数algebra over k 环k上的代数algebraic 代数的algebraic adjunction 代数的附加algebraic affine variety 仿射代数集algebraic algebra 代数的代数algebraic branch point 代数分歧点algebraic calculus 代数计算algebraic closure 代数闭包algebraic closure operator 代数闭包算子algebraic complement 代数余子式algebraic cone 代数锥algebraic correspondence 代数对应algebraic curve 代数曲线algebraic equation 代数方程algebraic expression 代数式algebraic extension 代数扩张algebraic form 代数形式algebraic fraction 代数分式algebraic function 代数函数algebraic function field 代数函数域algebraic geometry 代数几何学algebraic group 代数群algebraic hull 代数包algebraic hypersurface of the seconed order 二阶代数超曲面algebraic integer 代数整数algebraic irrational number 代数无理数algebraic lie algebra 代数的李代数algebraic logic of pocket calculator 袖珍计算机的代数逻辑algebraic multiplicity 代数重度algebraic number 代数数algebraic number field 代数数域algebraic number theory 代数数论algebraic operation 代数运算algebraic polynomial 代数多项式algebraic singularity 代数奇点algebraic space 代数空间algebraic spiral 代数螺线algebraic structure 代数结构algebraic sum 代数和algebraic surface 代数曲面algebraic system 代数系algebraic variety 代数簇algebraically closed field 代数闭域algebraically dependent elements 代数相关元algebraically equivalent 代数等价的algebraically independent elements 代数无关元algebraization 代数化algebro geometric 代数几何的algebroid function 代数体函数algebroidal function 代数体函数algorithm 算法algorithm of division 辗转相除法algorithm of euclid 欧几里得算法algorithm theory 算法论algorithmic language 算法语言algorithmization 算法化aligned systematic sampling 列系统抽样alignment chart 列线图aliquot part 整除部分alligation 混合法allocation problem 配置问题allowable 容许的allowable defects 容许靠allowable error 容许误差allowance 允许almost all 几乎处处almost bounded function 殆有界函数almost certain convergence 几乎必然收敛almost complex manifold 殆复廖almost convergent sequence 殆收敛序列almost equivalent 殆等价almost everywhere 几乎处处almost impossible event 殆不可能事件almost invariant set 殆不变集almost periodic function 殆周期函数almost periodicity 殆周期性almost significant 殆显著的alpha capacity 容量alpha limit set 极限集alphabetical 字母的alphanumeric 字母数字式alphanumeric representation of information 信息的字母数字表示alternate angles 错角alternating chain 交错链alternating differential form 外微分形式alternating differential of differential form 微分形式的交错微分alternating direction method 交替方向法alternating form 交错形式alternating function 反对称函数alternating group 交错群alternating harmonic series 莱布尼兹级数alternating knot 交错纽结alternating matrix 交错矩阵alternating method 交错法alternating product 外积alternating sequence 交错序列alternating series 交错级数alternating series test 交错级数检验alternating sum 交错和alternating tensor 交错张量alternating tensor density 交错张量密度alternating tree 交错树alternation 交错alternative 交错;择一alternative algebra 交错代数alternative field 交错域alternative hypothesis 择一假设alternative normal form 析取范式alternative proposition 选言命题altitude 高度altitude theorem 高度定理amalgamated product 融合积amalgamated subcategory 融和子范畴amalgamation 合并ambient space 环绕空间ambiguous point 歧点amicable numbers 亲和数amount 量amphicheiral knot 双向纽结ample divisor 丰富除子amplitude 振幅;角amplitude of a complex number 复数角analog computer 模拟计算机analogous 类似的analogue display 相似表示analogue method 相似法analogy 类似analysis 数学分析analysis of time series 时间序列分析analysis of variance 方差分析analytic 分析的analytic arc 解析弧analytic completion 解析开拓analytic continuation 解析开拓analytic curve 解析曲线analytic dynamics 分析动力学analytic expression 解析式analytic function 分析函数analytic function of several variables 多元解析函数analytic geometry 分析几何学analytic index 解析指数analytic manifold 解析廖analytic method 解析法analytic prime number theory 解析素数论analytic proof 解析证明analytic proposition 解析命题analytic set 解析集analytic space 解析空间analytic transformation 解析变换analytical differential 解析微分analytical geometry 分析几何学analytical hierarchy 解析分层analytical mapping 全纯映射analytical transformation 全纯映射analytically continuable 可解析开拓的analytically independent 解析无关的analytically irreducible variety 解析不可约簇analytically representable function 解析可表示的函数anastigmatic 去象散的anchor ring 环面ancillary statistic 辅助统计量and circuit 与电路andre permutation 安得列置换andre polynomial 安得列多项式anger function 安格尔函数angle 角angle at center 圆心角angle between chord and tangent 弦和切线的角angle function 角函数angle of 落后角angle of advance 超前角angle of attack 迎角angle of contact 接触角angle of contingence 切线角angle of declination 俯角angle of diffraction 衍射角angle of incidence 入射角angle of inclination 斜角angle of intersection 相交角angle of lead 超前角angle of reflection 反射角angle of refraction 折射角angle of rotation 旋转角angle of torsion 挠率角angle preserving 保角的angle preserving map 保角映象angular 角的angular acceleration 角加速度angular coefficient 角系数angular coordinates 角坐标angular correlation 角相关angular derivative 角微商angular dispersion 角色散angular displacement 角位移angular distance 角距angular distribution 角分布angular domain 角域angular excess 角盈angular frequency 角频率angular magnification 角放大率angular measure 角测度angular metric 角度量angular momentum 角动量angular momentum conservation law 角动量守恒律angular motion 角运动angular neighborhood 角邻域angular transformation 角变换angular unit 角的单位angular velocity 角速度anharmonic oscillation 非低振动anharmonic ratio 交比anisotropic 蛤异性的anisotropic body 蛤异性体anisotropy 蛤异性annihilator 零化子annular 环annulator 零化子annulus 圆环anomalous magnetic moment 反常磁矩anomalous propagation 反常传播anomalous scattering 反常散射anomaly 近点角antecedent 前项anti automorphism 反自同构anti hermitian form 反埃尔米特形式anti isomorphic lattice 反同构格anti isomorphism 反同构anti position 反位置anti reflexiveness 反自反性anti semiinvariant 反半不变量antianalytic function 反解析函数antichain 反链anticlockwise 逆时针的anticlockwise revolution 逆时针回转anticlockwise rotation 逆时针回转anticoincidence 反重合anticoincidence method 反重法anticommutation 反交换anticommutative 反交换的anticommutativity 反交换性anticommutator 反换位子antiderivative 不定积分的antiholomorphic 反全纯的antihomomorphism 反同态antiisomorphy 反同构antilinear 反线性的antilinear mapping 反线性映射antilinear transformation 反线性变换antilogarithm 反对数antimode 反方式antimodule 反模antinode 反结点antinomy 二律背反antiorder homomorphism operator 反序同态算子antiordered set 反有序集合antiparallel 逆平行的antiplane 反平面antipodal map 对映映射antipodal point 对映点antipodal set 对映集antipode 对映点antipoints 反点antiradical 反根式antiresonance 反共振antisymmetric 反对称的antisymmetric function 反对称函数antisymmetric matrix 反对称矩阵antisymmetric relation 反对称关系antisymmetric tensor 反对称张量antisymmetrical state 反对称态antithesis 反题antitone mapping 反序映射antitone sequence 反序列antitonic function 反序函数antitonicity 反序性antitony 反序性antitrigonometric function 反三角函数antiunitary 反酉的aperiodic damping 非周期衰减aperiodic motion 非周期运动aperiodicity 非周期性aperture ratio 口径比apex 顶点apex angle 顶角apical angle 顶角apolar 非极性的apolarity 从配极性apothem 边心距apparent error 貌似误差apparent force 表观力apparent motion 表观运动apparent orbit 表观轨迹apparent singularity 貌似奇性application 应用applied mathematics 应用数学applied mechanics 应用力学approach 接近approach infinity 接近无穷大approximability 可逼近性approximable 可逼近的approximate 近似的;使近似approximate calculation 近似计算approximate construction 近似准approximate continuity 近似连续性approximate derivative 近似导数approximate differentiability 近似可微性approximate differential 近似微分approximate formula 近似公式approximate integration 近似积分approximate limit 近似极限approximate lower semi continuity 近似下半连续性approximate method 近似法approximate number 近似数approximate partial derivative 近似偏导函数approximate partial derived function 近似偏导函数approximate partial differential 近似偏微分approximate solution 近似解approximate total differentiability 近似全可微性approximate total differential 近似全微分approximate upper semi continuity 近似上半连续性approximate value 近似值approximate value in excess 过剩近似值approximately equal 近似等于approximately semicontinuous 近似半连续的approximation 逼近approximation by excess 过剩逼近approximation calculus 近似计算approximation error 近似误差approximation function 逼近函数approximation in excess 过剩逼近approximation method 近似法approximation methods in physics 物理学中的逼近法approximation theorem 逼近定理approximation theory 逼近理论arbitrarily small 任意小arbitrary 任意的arbitrary constant 任意常数arbitrary element 任意元素arbitrary parameter 任意参数arbitrary small number 任意小数arc 弧arc component 弧分量arc cosecant 反余割arc cosine 逆余弦arc cotangent 逆余切arc hyperbolic function 反双曲函数arc length 弧长arc of a circle 圆弧arc secant 反正割arc set 弧集arc sine 逆正弦arc sine distribution 反正弦分布arc sine law 反正弦定律arc sine transformation 反正弦变换arc tangent 反正切arch 拱形archaeometry 考古测量学archimedean 阿基米德性的archimedean group 阿基米德群archimedean semigroup 阿基米德半群archimedean space 阿基米德空间archimedean total order 阿基米德全序archimedean valuation 阿基米德赋值archimedes axiom 阿基米德公理archimedes spiral 阿基米德螺线archimedically ordered field 阿基米德有序域archimedically ordered number field 阿基米德有序数域arcwise connected set 弧连通集arcwise connected space 弧连通空间arcwise connectedness 弧连通性are 公亩area 面积area function 面积函数area of a circle 圆面积area preserving mapping 保面积映射areal coordinates 重心坐标areal derivative 面积导数areal element 面积元素areal integral 面积分areal velocity 面积速度argand plane 复数平面argument 自变数;辐角argument function 辐角函数argument of a function 函数的自变数argument principle 辐角原理argumentation 论证aristotelian logic 亚里斯多德逻辑学arithmetic 算术arithmetic al function 数论函数arithmetic difference 算术差arithmetic division 算术除法arithmetic element 运算元素arithmetic expression 算术表达式arithmetic function 数论函数arithmetic genus 算术狂arithmetic geometric mean 算术几何平均arithmetic geometric series 算术几何级数arithmetic logic of pocket calculator 袖珍计算机的算术逻辑arithmetic mean 算术平均arithmetic number 正实数arithmetic of algebraic number fields 代数数域的数论arithmetic of algebras 代数的数论arithmetic of local fields 局部域的数沦arithmetic operation 算术操作算术运算arithmetic progression 算术级数arithmetic subgroup 算术子群arithmetic unit 运算元素arithmetical hierarchy 算术谱系arithmetical predicate 算术谓词arithmetical triangle 帕斯卡三角形arithmetics 算术arithmetization 算术化arithmometer 四则计算机arrangement 排列array 排列arrow 射artificial variable 人工变量artificial variable method 人工变量法artin conductor 阿廷前导子artin conjecture 阿廷猜想artin reciprocity law 阿廷互反禄artinian module 阿丁模artinian ring 阿丁环ascending 上升的ascending chain condition 升链条件ascending difference 后向差分ascending power series 升幂级数ascending powers 升幂ascending sequence 递升序列aspherical space 非球面空间asphericity 非球面牲assemblage 集assembler 汇编assertion sign 断定号assignable cause 可指定的原因assignment problem 配置问题associate equation 相伴方程associated equation 相伴方程associated fiber bundle 相伴的纤维丛associated form 连带形式associated function 连带函数associated graded module 相伴分次模associated graded ring 形式环associated homogeneous equation 相伴齐次方程associated homogeneous system 相伴齐次组associated laguerre polynomial 连带的拉盖尔多项式associated legendre function 相伴勒让德函数associated legendre polynomial 连带的勒让德多项式associated minimal surface 相伴极小曲面associated power series 相伴幂级数associated prime ideal 相伴素理想associated radius of convergence 相伴收敛半径associated space 相伴空间associated spherical harmonic 相伴球面低associated surface 连带曲面associated system 相伴系associated undirected graph 相伴无向图association 结合associative algebra 结合代数associative law 结合律associative law for series 级数的结合律associativity 结合性assume 假定assumption 假定assumption formula 假定公式asterisk 星号asteroid 星形线asymmetric 非对称的asymmetric relation 非对称关系asymmetric variety 非对称簇asymmetrical 非对称的asymmetrical graph 恒等图asymmetry 非对称性asymptote 渐近线asymptote of curve 曲线的渐近线asymptotic 浙近的asymptotic behavior 渐近状态asymptotic circle 渐近圆asymptotic cone 渐近锥面asymptotic convergence 渐近收敛asymptotic curvature 渐近曲率asymptotic curve 渐近曲线asymptotic density 渐近密度asymptotic direction 渐近方向asymptotic efficiency 渐近效率asymptotic expansion 渐近展开asymptotic formula 渐近公式asymptotic line 渐近线asymptotic mean value 渐近平均值asymptotic minimal basis 渐近极小基asymptotic order 渐近阶asymptotic path 渐近路线asymptotic plane 渐近平面asymptotic point 渐近点asymptotic rate of convergence 渐近收敛速度asymptotic series 渐近级数asymptotic solution 渐近解asymptotic stability 渐近稳定性asymptotic surface 渐近曲面asymptotic unbiased estimator 渐近无偏估计量asymptotic value 渐近值asymptotically efficient estimator 渐近有效估计量asymptotically equal 渐近相等asymptotically equal sequence 渐近相等序列asymptotically equivalent function 渐近等价函数asymptotically normal distribution 渐近正态分布asymptotically normally distributed 渐近正规分布的asymptotically stable 渐近稳定的asymptotically stable solution 渐近稳定解asynchronous computer 异步计算机atiyah singer index theorem 阿蒂亚辛格指数定理atlas 坐标邻域系atom 原子atomic element 原子元素atomic formula 原子公式atomic lattice 原子格atomic proposition 原子命题atomicity 原子性attaching map 接着映射attenuation 衰减attenuation constant 衰减常数attenuation factor 衰减因数attenuator 衰减器attraction 引力attractive force 引力attractor 吸引区attribute 属性augend 被加数augmentation 扩张augmentation preserving map 增广保存映射augmented complex 扩张复形augmented matrix 增广矩阵austausch 交换autocorrelation 自相关autocorrelation coefficient 自相关系数autocorrelation function 自相关函数autocorrelogram 自相关图autocovariance 自协方差autocovariance function 自协方差函数autodistributivity 自分配性automata 自动机automatic check 自动检验automatic coding 自动编码automatic computation 自动计算automatic computer 自动计算机automatic control 自动控制automatic control system 自动控制系统automatic control theory 自动控制理论automatic programming 自动程序设计automatic testing 自动检验automation 自动化automaton 自动机automaton graph 自动机图automorphic form 自守形式automorphic function 自守函数automorphism 自同构automorphism group 自同构群autonomous system 自治系统autoparallel curve 自平行曲线autoregression 自回归autoregression equation 自回归方程autoregressive process 自回归过程autoregressive transformation 自回归变换auxiliary 辅助的auxiliary angle 辅助角auxiliary circle 辅助圆auxiliary equation 相伴齐次方程auxiliary function 辅助函数auxiliary line 辅助线auxiliary variable 辅助变数average 平均值average deviation 平均偏差average error 平均误差average life 平均寿命average outgoing quality 平均出厂质量average outgoing quality limit 平均出厂质量极限average quality protection 平均品质保护average sample number 平均样本数average speed 平均速度average term 普通项average time 平均时间average value 平均值averaging 取平均数averaging method 平均法averaging operator 平均算子axes of coordinates 座标轴axial 轴的axial symmetry 轴对称axial vector 轴向量axially symmetric flow 轴对称流axialsymmetric vector field 轴对称向量场axiom 公理axiom of accessibility 可达性公理axiom of addition 加法公理axiom of choice 选择公理axiom of completeness 完备性公理axiom of comprehension 概括公理axiom of constructibility 可构成性公理axiom of constructivity 可构成性公理axiom of continuity 连续公理axiom of extensionality 外延性公理axiom of infinity 无穷性公理axiom of power set 幂集公理axiom of reducibility 可化归性公理axiom of regularity 正则性公理axiom of subsets 子集公理axiom of substitution 替换公理axiom of sum set 并集公理axiom of the empty set 空集公理axiom of union 并集公理axiom scheme 公理格式axiomatic 公理的axiomatic method 公理法axiomatic set theory 公理论的集论;公理集合论axiomatic system 公理系统axiomatics 公理学axiomatization 公理化axiomatize 公理化axioms of congruence 叠合公理axioms of continuity 连续公理axioms of denumerability 可数公理axioms of incidence 关联公理axioms of order 次序公理axis 轴axis of a cone 锥轴axis of abscissas 横坐标轴axis of absolute convergence 绝对收敛轴axis of affinity 仿射轴axis of convergence 收敛轴axis of coordinate 坐标轴axis of curvature 曲率轴axis of ordinates 纵坐标轴axis of projection 射影轴axis of reals 实轴axis of revolution 回转轴axis of rotation 回转轴axis of symmetry 对称轴axisymmetric 轴对称的axonometric perspective 轴测投影法axonometric projection 轴测投影法axonometry 轴测法azimuth 方位角azimuthal 方位角的Bb measurability b可测性b measurable function 波莱尔可测函数babylonian numerals 巴比伦数字back substitution 逆计算backward difference 后向差分backward difference operator 后向差分算子backward difference quotient 后向差商backward solution 后向解法baire function 贝利函数baire measure 贝利测度baire set 贝利集baire space 贝利空间baire theorem 贝利定理balance 平衡balanced category 平衡范畴balanced functor 平衡函子balanced hypergraph 平衡超图balanced neighborhood 平衡邻域balanced sample 平衡样本balanced set 平衡集balancing method 平衡法balayage 扫除ball 球ballistic curve 弹道banach algebra 巴拿赫代数banach lie group 巴拿赫李群banach space 巴拿赫空间band 带band chart 带状图band matrix 带状矩阵bar construction 棒构成bar diagram 条线图bar graph 条线图barrel 桶集barrel shape 桶型barrelled space 桶型空间barrier 闸barycenter 重心barycenter of a simplex 单形的重心barycentric 重心的barycentric complex 重心复形barycentric coordinates 重心坐标barycentric mapping 重心映射barycentric subdivision 重心重分base 底base angle 底角base line 底线base number 底数base of logarithms 对数的底base point 基点base register 基址寄存器变址寄存器base space 底空间base vector 基向量basic 基础的basic block 基本块basic field 基域basic form 基本形式basic point 基础点basic representation 基本表示basic ring 基环basic solution 基本解basic symbol 基本符号basic variable 基本变量basis 基basis for cohomology 上同爹basis for homology 同爹basis of linear space 线性空间的基basis of vector space 向量空间的基basis replacement procedure 基替换过程basis theorem of hilbert 希耳伯特基定理basis vector 基本向量batch processing 成批处理bayes decision function 贝叶斯判定函数bayes formula 贝叶斯公式bayes postulate 贝叶斯公设bayes solution 贝叶斯解behavior 行为behavior strategy 行为策略bellman principle 贝尔曼原理beltrami equation 贝尔特拉米方程bending point 转向点bergman metric 伯格曼度量bernoulli equation 伯努利方程bernoulli inequality 伯努利不等式bernoulli method 伯努利法bernoulli number 伯努利数bernoulli polynomial 伯努利多项式bernoulli trials 伯努利试验bernoullian polynomial 伯努利多项式bernstein inequality 伯思斯坦不等式bernstein polynomial 伯思斯坦多项式bertrand curves 柏特龙曲线bertrand paradox 柏特龙悖论bessel equation 贝塞耳方程bessel function 贝塞耳函数bessel function of the second kind 第二类贝塞耳函数bessel function of the third kind 第三类贝塞耳函数bessel inequality 贝塞耳不等式bessel integral 贝塞耳积分best approximation 最佳逼近best estimator 最佳估计量best test 最佳检验best uniform approximation 最佳一致逼近beta distribution 分布beta function 函数betti group 贝蒂群betti number 贝蒂数between group variance 群间方差biadditive 双加法的biangular 双角的bias 偏倚biased estimator 有偏估计量biased sample 有偏样本biased statistics 有偏统计量biased test 有偏检验biaxial 双轴的biaxial spherical harmonic function 双轴球面低函数bicartesian square 双笛卡儿方bicharacteristic 双特征bicompact 紧bicompact set 紧集bicompact space 列紧空间bicompact transformation group 列紧变换群。

各种数学语言名称的英语翻译

各种数学语言名称的英语翻译各种数学语言名称的英语翻译数学 mathematics, maths(BrE), math(AmE)公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加数 addend加 plus(prep.), add(v.), addition(n.)和 sum被加数 augend, summand减 minus(prep.), subtract(v.), subtraction(n.)被减数minuend 差remainder减数subtrahend等于equals, is equal to, is equivalent to乘times(prep.), multiply(v.), multiplication(n.)大于is greater than被乘数multiplicand, faciend小于is lesser than乘数multiplicator小于等于is equal or lesser than积product大于等于is equal or greater than商quotient运算符operator除divided by(prep.), divide(v.), division(n.)平均数mean几何平均数geometric mean n个数之积的n次方根算术平均数arithmatic mean被除数dividend除数divisor有理数rational number倒数（reciprocal）x的倒数为1/x无理数irrational number整数integer实数real number小数decimal虚数imaginary number小数点decimal point数字digit分数fraction数number分子numerator自然数natural number分母denominator正positive比ratio负negative权weight, significance零null, zero, nought, nil进位carry十进制decimal system截尾truncation二进制binary system四舍五入round十六进制hexadecimal system下舍入round down有效数字significant digit上舍入round up无效数字insignificant digit代数algebra公式formula, formulae(pl.)单项式monomial系数coefficient多项式polynomial, multinomial 未知数unknown, x-factor, y-factor, z-factor不等式inequation等式，方程式equation阶乘factorial一次方程simple equation对数logarithm二次方程quadratic equation指数，幂exponent三次方程cubic equation乘方power四次方程quartic equation二次方，平方square三次方，立方cube sqrt(2)=1.414四次方the power of four, the fourth power sqrt(3)=1.732n次方the power of n, the nth power sqrt(5)=2.236开方evolution, extraction常量constant二次方根，平方根square root变量variable三次方根，立方根cube root坐标系coordinates四次方根the root of four, the fourth root坐标轴x-axis, y-axis, z-axisn次方根the root of n, the nth root横坐标x-coordinate截距(有正负之分)intercede纵坐标y-coordinate（方程的）解solution原点origin几何geometry象限quadrant点point角angle线line角度degree面plane弧度radian体solid锐角acute angle线段segment直角right angle射线radial钝角obtuse angle平行parallel平角straight angle相交intersect周角perigon底base勾股定理Pythagorean theorem 边side钝角三角形obtuse triangle高height不等边三角形scalene triangle 三角形triangle等腰三角形isosceles triangle 锐角三角形acute triangle等边三角形equilateral triangle 直角三角形right triangle四边形quadrilateral直角边leg平行四边形parallelogram斜边hypotenuse矩形rectangle长length相似similar宽width全等congruent周长perimeter三角trigonometry面积area正弦sine集合aggregate余弦cosine元素element正切tangent空集void余切cotangent子集subset正割secant交集intersection余割cosecant并集union反正弦arc sine补集complement反余弦arc cosine映射mapping反正切arc tangent函数function反余切arc cotangent定义域domain, field of definition反正割arc secant值域range反余割arc cosecant单调性monotonicity数列，级数series奇偶性parity微积分calculus周期性periodicity微分differential图象image导数derivative复数complex number极限limit矩阵matrix无穷大infinite(a.) infinity(n.)行列式determinant无穷小infinitesimal圆circle积分integral圆心centre(BrE), center(AmE)定积分definite integral半径radius不定积分indefinite integral 直径diameter椭圆ellipse圆周率pi圆周circumference弧arc轨迹locus, loca(pl.)半圆semicircle平行六面体parallelepiped 扇形sector 立方体cube环ring七面体heptahedron双曲线hyperbola八面体octahedron抛物线parabola九面体enneahedron四面体tetrahedron十面体decahedron五面体pentahedron十一面体hendecahedron六面体hexahedron十二面体dodecahedron菱形rhomb, rhombus, rhombi(pl.), diamond二十面体icosahedron正方形square多面体polyhedron梯形trapezoid旋转rotation直角梯形right trapezoid轴axis等腰梯形isosceles trapezoid球sphere五边形pentagon半球hemisphere六边形hexagon底面undersurface七边形heptagon表面积surface area八边形octagon体积volume九边形enneagon空间space十边形decagon相位phase十一边形hendecagon周期period十二边形dodecagon振幅amplitude多边形polygon内心incentre(BrE), incenter(AmE)正多边形equilateral polygon外心excentre(BrE), excenter(AmE)统计statistics旁心escentre(BrE), escenter(AmE)平均数average垂心orthocentre(BrE), orthocenter(AmE)加权平均数weighted average重心barycentre(BrE), barycenter(AmE)方差variance内切圆inscribed circle标准差root-mean-square deviation, standard deviation外切圆circumcircle比例propotion排列permutation百分比percent组合combination百分点percentage概率，或然率probability百分位数percentile分布distribution图表graph正态分布normal distribution条形统计图bar graph非正态分布abnormal distribution柱形统计图histogram折线统计图broken line graph曲线统计图curve diagram扇形统计图pie diagram。

数学与应用数学论文中英文资料外文翻译文献

数学与应用数学论文中英文资料外文翻译文献UNITS OF M EASUR EM ENT AND FUNC TIONAL FOR M ( V o t i n g O u t c o m e s a n d C a m p a i g n E x p e n d i t u r e s )In the voting outcome equation in (2.28), R = 0.505. Thus, the share of campaign expenditures explains just over 50 percent of the variation in the election outcomes for this sample. This is a fairly sizable portionTwo important issues in applied economics are (1) understanding how changing theunits of measurement of the dependent and/or independent variables affects OLS estimates and (2) knowing how to incorporate popular functional forms used in e conomi c s i nt o regres s i o n analysis. The mathemati c s ne e ded for a ful l un de rs t anding of functional form issues is reviewed in Appendix A.The Effects of Changing Units of Measurement on OLSStatisticsIn Example 2.3, we chose to measure annual salary in thousands of dollars, and t he return on e quit y was mea s ured as a perc e n t (ra t her than a s a dec i ma l). I t is c ruci a l to know how salary and roe are measured in this example in order to make sense of the estimates in equation (2.39). We must also know that OLS estimates change in entirely expected ways when the units of measurement of the dependent and independent variables change. In Example2.3, suppose that, rather than measuring s a l ary in thousands of do l la rs, we m ea s u re it i n doll a rs. Let sal a rdol be sal a ry i n dollars (salardol =845,761 would be interpreted as $845,761.). Of course, salardol has a simple relationship to the salary measured in thousands of dollars: salardol ? 1,000? salary. We do not need to actually run the regression of salardol on roe to know that the estimated equation is: salaˆrdol = 963,191 +18,501 roe.We obtain the intercept and slope in (2.40) simply by multiplying the intercept and theslope in (2.39) by 1,000. This gives equations (2.39) and (2.40) the same interpretation.Looking at (2.40), if roe = 0, then salaˆrdol = 963,191, so the predicted salary is $963,191 [the same value we obtained from equation (2.39)]. Furthermore, if roe increases by one, then the predicted salary increases by $18,501; again, this isw hat w econcluded from our earlier analysis of equation (2.39).Generally, it is easy to figure out what happens to the intercept and slope estimates when the dependent variable changes units of measurement. If the dependent variable is multiplied by the constant c—which means each value in the s a m ple is multi pl i ed b yc—t h en t he OLS in t ercept a nd s lope esti m at es are als o multiplied by c. (This assumes nothing has changed about the independent variable.) In the CEO salary example, c ?1,000 in moving from salary to salardol.Chapter 2T he Sim pl e Re g re s sion ModelWe can also use the CEO salary example to see what happens when we change the units of measurement of the independent variable. Define roedec =roe/100 to be t he d e cimal equiva l ent of ro e; t hus, roedec =0.23 means a return o n equi ty of23 percent. To focus on changing the unitsof measurement of the independent variable, we return to our original dependent variable, salary, which is measured in thousands of dollars. When we regress salary onroedec, we obtain salˆary =963.191 + 1850.1 roedec.T he coef fi ci e nt on roedec is 100 times t he coe ffi cient on roe i n (2.39). This i s as it should be. Changing roe by one percentage point is equivalent to Δroedec = 0.01. From (2.41), if Δ roedec = 0.01, then Δ salˆary = 1850.1(0.01) = 18.501, which is what is obtained by using (2.39). Note that, in moving from (2.39) to (2.41), the independentv ariable was divided b y 100, and so t h e OLS slope estim a te was multiplied by 100, preserving the interpretation of the equation. Generally, if the independent variable is divided or multiplied by some nonzero constant, c, then the OLS slope coefficient is also multiplied or divided by c respectively.The intercept has not changed in (2.41) because roedec =0 still corresponds to a z ero retur n on equity. In ge n eral, changin g t he uni t s of m easurem e nt of only the independent variable does not affect the intercept.In the previous section, we defined R-squared as a goodness-of-fit measure for OLS regression. We can also ask what happens to R2 when the unit of measurement of either the independent or the dependent variable changes. Without doing any algebra, we should know the result: the goodness-of-fit of the model should not depend on the units of measurement of our variables. For example, the amount of variation in salary, explained by the return on equity, should not depend on whether salary is measured in dollars or in thousands of dollars or on whether return on equity is a percent or a decimal. This intuition can be verified mathematically: using the definition of R2, it can be shown that R2 is, in fact, invariant to changes in the units of y or x.Incor por a ting Nonlinear ities in Simple R egressionSo far we have focused on linear relationships between the dependent and independent variables. As we mentioned in Chapter 1, linear relationships are notn early gen er a l enou g h for a ll e co nomi c a pplications. F ortuna t ely, it is rathe r e a s y to incorporate many nonlinearities into simple regression analysis by appropriately defining the dependent and independent variables. Here we will cover two possibilities that often appear in applied work.In reading applied work in the social sciences, you will often encounter re gr es sion equati o ns w he re the de pende nt varia bl e a pp ears in l og arit hm i c f orm. W h y is this done? Recall the wage-education example, where we regressed hourly wage on years of education. We obtained a slope estimate of 0.54 [ see equation (2.27)], which means that each additional year of education is predicted to increase hourly wage by54 cents.B ecaus e of t he l i near n at ur e of (2.27), 54 c ents is the i ncrea s e f or e i ther the fi rst year of education or the twentieth year; this may not be reasonable.Suppose, instead, that the percentage increase in wage is the same given one m ore yea r of e ducation. Model (2.27) does no t im ply a c onst a nt per c entag e i nc re ase: the percentage increases depends on the initial wage. A model that gives (approximately) a constant percentage effect is log(wage) =β 0 +β 1educ + u,(2.42) where log(.) denotes the natural logarithm. (See Appendix A for a review of logarithms.) In particular, if Δu =0, then % Δwage = (100* β 1) Δ educ.(2.43) N otice ho w we mult i ply β 1 b y 100 t o g et the perc e ntage change in w a ge give n one additional year of education. Since the percentage change in wage is the same for each additional year of education, the change in wage for an extra year of education increases aseducation increases; in other words, (2.42) implies an increasing return to education.B y e x ponenttiat i ng (2.42), we c an w ri t e wage =ex p(β 0+β 1educ + u). T his equationis graphed in Figure 2.6, with u = 0.Estimating a model such as (2.42) is straightforward when using simple regression. Just define the dependent variable, y, to be y = log(wage). The i ndependent v ar i able is represented b y x = e duc. The mechanics of O L S are the sa m e as before: the intercept and slope estimates are given by the formulas (2.17) and (2.19). In other words, we obtain β ˆ0 andβ ˆ1 from the OLS regression of log(wage) on educ.E X A M P L E 2 . 1 0( A L o g W a g e E q u a t i o n )Using the same data as in Example 2.4, but using log(wage) as the dependent variable, we obtain the following relationship: log(ˆwage) =0.584 +0.083 educ(2.44) n = 526, R =0.186.The coefficient on educ has a percentage interpretation when it is multiplied by 100: wage increases by 8.3 percent for every additional year of education. This is what economists mean when they refer to the “return to another year of education.”It is important to remember that the main reason for using the log of wage in (2.42) is to impose a constant percentage effect of education on wage. Once equation (2.42) is obtained, the natural log of wage is rarely mentioned. In particular, it is not correct to say that another year of education increases log(wage) by 8.3%.The intercept in (2.42) is not very meaningful, as it gives the predicted log(wage), when educ =0. The R-squared shows that educ explains about 18.6 percent of the variation in log(wage) (not wage). Finally, equation (2.44) might not capture all of the non-linearity in the relationship between wage and schooling.If there are“diplomae ffects,”t hen t he twelft h ye a r of e ducat i on—gradu a ti on from hi gh s c hool—c ould be worth much more than the eleventh year. We will learn how to allow for this kind of nonlinearity in Chapter 7. Another important use of the natural log is in obtaining a constant elasticity model.E X A M P L E 2 . 1 1( C E O S a l a r y a n d F i r m S a l e s )We can estimate a constant elasticity model relating CEO salary to firm sales. The data set is the same one used in Example 2.3, except we now relate salary to sales. Let sales be annual firm sales, measured in millions of dollars. A constant elasticity model is log(salary =β 0 +β 1log(sales) +u, (2.45) where β 1 is the elasticity of s a l ary w ith respe c t to sal es. T h is model fa ll s under t he simple regressio n model by defining the dependent variable to be y = log(salary) and the independent variable to be x = log(sales). Estimating this equation by OLS givesPart 1Regression Analysis with Cross-Sectional Data l og(salˆary)= 4.822 ?+0.257 log(sa le s)(2.46)n =209, R = 0.211.The coefficient of log(sales) is the estimated elasticity of salary with respect to sales. It implies that a 1 percent increase in firm sales increases CEO salary by about 0.257 pe r cent—t he usual int e rp re tation of an e la s ti c ity.The two functional forms covered in this section will often arise in the remainder of this text. We have covered models containing natural logarithms here because they a ppear so freque nt ly in a ppl ied wo r k. The i nterpr e tat i on of such m odel s w i l l n ot be much different in the multiple regression case.It is also useful to note what happens to the intercept and slope estimates if we change the units of measurement of the dependent variable when it appears in logarithmic form.B ecaus e t he ch a nge t o log ar i thm i c form approx i mates a proportionate change, i t makes sense that nothing happens to the slope. We can see this by writing the rescaled variable as c1yi for each observation i. The original equation is log(yi) =β 0 +β 1xi +ui. If we add log(c1) to both sides, we get log(c1) + log(yi) + [log(c1) β 0] +β 1xi + ui, orlog(c1yi) ? [log(c1) +β 0] +β 1xi +ui.(Remember that the sum of the logs is equal to the log of their product as shown in Appendix A.) Therefore, the slope is still ? 1, but the intercept is now log(c1) ? ? 0. Similarly, if the independent variable is log(x), and we change the units of measurement of x before taking the log, the slope remains the same but the intercept does not change. You will be asked to verify these claims in Problem 2.9.We end this subsection by summarizing four combinations of functional forms available from using either the original variable or its natural log. In Table 2.3, x and y stand for the variables in their original form. The model with y as the dependent variable and x as the independent variable is called the level-level model, because each variable appears in its level form. The model with log(y) as the dependentv ariable a nd x as t he independent va r i able i s called t he l og-level m od el. We w i ll no t explicitly discuss the level-log model here, because it arises less often in practice. In any case, we will see examples of this model in later chapters.Chapter 2Th e Simpl e R e gr e s s i on M od e lTable 2.3The last column in Table 2.3 gives the interpretation of β 1. In the log-level model, 100* β 1 i s so m e t imes called the s emi-elasti c ity of y wit h re s pe ct to x. As we mentioned in Example 2.11, in the log-log model, β1 is the elasticity of y with respect to x. Table 2.3 warrants careful study, as we will refer to it often in the r em aind er of the text.The Meaning of“Linear”RegressionThe simple regression model that we have studied in this chapter is also called the simple linear regression model. Yet, as we have just seen, the general model also allows for certain nonlinear relationships. So what does “linear”mean here? You can se e b y looking a t equ a ti o n (2.1) tha t y =β 0 +β 1x + u. The key i s t hat t his equati on i s linear in the parameters, β 0 and β 1. There are no restrictions on how y and x relate to the original explained and explanatory variables of interest. As we saw in Examples 2.7 and 2.8, y and x can be natural logs of variables, and this is quite common in applications. But we need not stop there. For example, nothing prevents us from using simple regression to estimate a model such as cons =β 0 +β 1√inc+u, where cons is annual consumption and inc is annual income.While the mechanics of simple regression do not depend on how y and x are defined, the interpretation of the coefficients does depend on their definitions. For successful empirical work, it is much more important to become proficient at interpreting coefficients than to become efficient at computing formulas such as (2.19). We will get much more practice with interpreting the estimates in OLS regression lines when we study multiple regression.There are plenty of models that cannot be cast as a linear regression model because they are not linear in their parameters; an example is cons = 1/(β 0 +β 1inc) + u.E s t im a ti on of such mode l s ta ke s us into t he real m of t he nonli ne ar regressi on model, which is beyond the scope of this text. For most applications, choosing a model that can be put into the linear regression framework is sufficient.EXPECTED VAL UES AND VAR IANCES OF THE OLSESTIM ATOR SI n Sec t ion 2.1, we defined the popula t ion m ode l y =β 0 +β 1x +u, a nd w e claimed that the key assumption for simple regression analysis to be useful is that the expected value of u given any value of x is zero. In Sections 2.2, 2.3, and 2.4, we discussed the algebraic properties of OLS estimation. We now return to the population model and study the statistical properties of OLS. In other words, we now view β ˆ0 a nd β ˆ1 as e s timat ors for th e pa rameters ? 0 and ? 1 t ha t appear in t he popula t ion model. This means that we will study properties of the distributions of ? ˆ0 and ? ˆ1 over different random samples from the population. (Appendix C contains definitions of estimators and reviews some of their important properties.)Unbiasedness of OLSW e be g i n by establishing the unbi a s e dne s s of OLS unde r a simple set of assumptions.For future reference, it is useful to number these assumptions using the prefix“S LR”for simple linear regression. The first assumption defines the population model.测量单位和函数形式在投票结果方程（2.28）中，R²=0.505。

国外数学期刊英汉对照

国外数学期刊英汉对照作者:admin 日期:2009-06-17字体大小: 小中大Advances in Applied Mathematics 应用数学Advances in Applied Probability 应用概率论进展Advances in Computational Mathematics 计算数学进展Advances in Mathematics 数学进展Algebra Colloquium 代数学讨论会Algebras and Representation Theory 代数和表示理论American Mathem atical Monthly 美国数学月刊American Statistician 美国统计员Annals of Applied Probability 应用概率论年报Annals of Global Analysis and Geometry 整体分析与几何学年报Annals of Mathematics and Artificial Intelligence 人工智能论题年报Annals of Operations Research 运筹学研究年报Annals of Probability 概率论年报Annals of Pure and Applied Logic 抽象和应用逻辑年报Annals of Statistics 统计学年报Annals of The Institute of Statistical Mathematics 统计数学学会年报Applicable Algebra in Engineering Communication and Computing 代数在工程通信与计算中的应用Applied and Computational Harmonic Analysis 调和分析应用和计算Applied Categorical Structures 应用范畴结构Applied Mathematics and Computation 应用数学与计算Applied Mathematics and Optimization 应用数学与最优化Applied Mathematics Letters 应用数学快报Archive for History of Exact Sciences 科学史档案Archive for Mathem atical Logic 数理逻辑档案Archive for Rational Mechanics and Analysis 理性力学和分析档案Archives of Computational Methods in Engineering 工程计算方法档案Asymptotic Analysis 渐近线分析Autonomous Robots 机器人British Journal of Mathematical & Statistical Psychology 英国数学与统计心理学杂志Bulletin of The American Mathematical Society 美国数学会快报Bulletin of the London Mathematical Society 伦敦数学会快报Calculus of Variations and Partial Differential Equations 变分法与偏微分方程Combinatorics Probability & Computing 组合概率与计算Combustion Theory and Modeling 燃烧理论建模Communications in Algebra 代数通讯Communications in Contemporary Mathematics 当代数学通讯Communications in Mathematical Physics 数学物理学通讯Communications in Partial Differential Equations 偏微分方程通讯Communications in Statistics-Simulation and Computation 统计通讯–模拟与计算Communications on Pure and Applied Mathematics 纯数学与应用数学通讯Computational Geometry-Theory and Applications 计算几何- 理论与应用Computational Optimization and Applications 优化计算与应用Computational Statistics & Data Analysis 统计计算与数据分析Computer Aided Geometric Design 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Computational Mathematics 计算数学基础Fuzzy Sets and Systems 模糊集与模糊系统Glasgow Mathematical Journal 英国格拉斯哥数学杂志Graphs and Combinatorics 图论与组合数学IEEE Robotics & Automation Magazine IEEE机器人与自动化杂志IEEE Transactions on Robotics and Automation IEEE机器人与自动化学报IMA Journal of Applied Mathem atics IMA应用数学学报IMA Journal of Mathem atics Applied in Medicine and Biology IMA数学在医药与生物中的应用杂志IMA Journal of Numerical Analysis IMA数值分析学报Information and Computation 信息与计算Insurance Mathematics & Economics 保险数学和经济学International Journal for Numerical Methods in Engineering 国际工程数值方法杂志International Journal of Algebra and Computation 国际代数和计算杂志International Journal of Computational Geometry & Applications 国际计算几何应用杂志International Journal of Computer Integrated Manufacturing 国际计算机集成制造业国际杂志International Journal of Game Theory 国际对策论国际杂志International Journal of Mathematics 国际数学杂志International Journal of Production Research 国际研究成果杂志International Journal of Robotics Research 国际机器人研究杂志International Journal of Systems Science 国际系统科学杂志International Statistical Review 国际统计评论Inverse Problems 反比问题Journal of Algebra 代数学报Journal of Algebraic Combinatorics 代数组合数学学报Journal of Algebraic Geometry 代数几何学报Journal of Algorithm s 算法学报Journal of Applied Mathematics and Mechanics 数学应用与力学学报Journal of Applied Probability 应用概率杂志Journal of Approximation Theory 近似值理论杂志Journal of Combinatorial Optimization 组合最优化学报Journal of Combinatorial Theory Series B 组合理论学报B辑Journal of Combinatorial Theory Series A 组合理论学报A辑Journal of Computational Acoustics 声学计算杂志Journal of Computational Analysis and Applications 计算分析与应用学报Journal of Computational and Applied Mathematics 计算与应用数学杂志Journal of Computational Biology 生物计算杂志Journal of Computational Mathematics 计算数学学报Journal of Computational Neuroscience 神经系统计算杂志Journal of Computational Neuroscience 神经系统计算杂志Journal of Differential Equations 微分方程组学报Journal of Econom etrics 计量经济学会会刊Journal of Engineering Mathematics 工程数学学报Journal of Functional Analysis 泛函分析学报Journal of Geometry and Physics 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Theoretical Probability 概率理论杂志K-Theory K-理论Lecture Notes in Economics and Mathematical Systems 经济学和数学体系讲座Lecture Notes on Mathematics 数学讲座Letters in Mathematical Physics 数学物理学通讯Linear Algebra and Its Applications 线性代数及其应用Mathematical Biosciences 数理生物学Mathematical Finance 数理财金学Mathematical Geology 数理地质学Mathematical Intelligencer 数学情报Mathematical Logic Quarterly 数理逻辑学报Mathematical Methods in the Applied Sciences 数学应用学科Mathematical Methods of Operations Research 运筹学研究Mathematical Models & Methods in Applied Sciences 数学模拟与应用方法Mathematical Physics Electronic J 数学物理电子杂志Mathematical Proceedings of the Society 数学学会学报Mathematical Programming 数学规划Mathematical Social Sciences 数学社会科学Mathematics and Computers in Simulation 数学与电脑模拟Mathematics and Mechanics of Solids 数学与固体力学Mathematics Archives 数学档案库Mathematics Magazine 数学杂志Mathematics of Computation 计算数学Mathematics of Control Signals and Systems 控制信号系统数学Memoirs of the American Mathematical Society 美国数学会备忘录Modem Logic 现代逻辑学Nonlinear Analysis-Theory Methods & Applications 非线性分析- 理论与应用Nonlinearity 非线性特性Notices 短评Numerical Algorithms 数字算法Numerical Methods for Partial Differential Equations 偏微分方程式数值方法Oxford Bulletin of Economics and Statistics 牛津大学经济与统计快报Potential Analysis 位势分析Proceedings of the American Mathem atical Society 美国数学会会议录Proceedings of the London Mathematical Society 伦敦数学会会议录Proceedings of the Royal Society of Edinburgh Section A-Mathem atics 英国爱丁堡皇家学会会议录A分册数学Quarterly Journal of Mathematics 数学季刊Quarterly Journal of Mechanics and Applied Mathematics 数学与应用数学季刊Quarterly of Applied Mathematics 应用数学季刊Queueing Systems 排列系统Random Structures and Algorithms 随机结构与算法Reports on Mathematical Physics 数学物理学报告Representation Theory 表示法理论Robotics and Autonomous Systems 机器人技术和自动系统Rocky Mountain Journal of Mathematics 数学难题学报Set-Valued Analysis 精点分析Statistical Papers 统计学论文Statistics & Probability Letters 统计和概率通讯Statistics and Computing 统计和计算Stochastic Analysis and Applications 随机分析和应用Stochastic Environm ental Research and Risk Assessm ent 随机环境论研究和风险评估Stochastic Processes and Their Applications 随机过程及其应用Studies in Applied Mathematics 应用数学研究The College Mathematics Journal 大学数学杂志The Electronic Journal of Combinatorics 组合数学电子期刊Theory of Computing Systems 计算方法理论Theory of Probability and Its Applications 概率理论及其应用程序理论Topology 拓扑学Topology and Its Applications 拓扑学及其应用Transactions of the American Mathematical Society 美国数学会学报Applied Numerical Mathematics《应用数值数学》荷兰Annales Scientifiques de l'École Normale Supérieure《高等师范学校科学纪事》法国Applied and Computational Harmonic Analysis《应用和计算谐波分析》美国Applied Stochastic Models in Business and Industry《商业与工业应用随机模型》英国Acta Applicandae Mathematicae 《应用数学学报》荷兰Advances in Computational Mathematics《计算数学进展》荷兰Annals of Mathematics and Artificial Intelligence《数学与人工智能纪事》荷兰Annals of Operations Research《运筹学纪事》荷兰Annals of the Institute of Statistical Mathematics《统计数理研究所纪事》日本。

学术词汇大全四级中常见学科词汇一览

学术词汇大全四级中常见学科词汇一览学术领域中的各个学科都有其独特的词汇，这些词汇是理解和交流学术知识的基础。

对于准备考取四级英语的学生来说，掌握常见的学科词汇是非常重要的。

本文将为大家提供学术词汇大全四级中常见学科词汇一览，希望能帮助大家在考试中取得好成绩。

1. 数学（Mathematics）- algebra 代数- calculus 微积分- geometry 几何学- trigonometry 三角学- statistics 统计学- probability 概率论- equation 方程- derivative 导数- integral 积分- matrix 矩阵2. 物理学（Physics）- mechanics 力学- thermodynamics 热力学- electromagnetism 电磁学- optics 光学- quantum mechanics 量子力学- relativity 相对论- nuclear physics 核物理学- particle physics 粒子物理学- astrophysics 天体物理学- acoustics 声学3. 化学（Chemistry）- organic chemistry 有机化学- inorganic chemistry 无机化学- physical chemistry 物理化学- analytical chemistry 分析化学- biochemistry 生物化学- polymer chemistry 高分子化学- environmental chemistry 环境化学- pharmaceutical chemistry 制药化学 - theoretical chemistry 理论化学- industrial chemistry 工业化学4. 生物学（Biology）- molecular biology 分子生物学- cell biology 细胞生物学- genetics 遗传学- ecology 生态学- evolution 进化论- microbiology 微生物学- zoology 动物学- botany 植物学- anatomy 解剖学- physiology 生理学5. 地球科学（Earth Science）- geology 地质学- meteorology 气象学- oceanography 海洋学- climatology 气候学- seismology 地震学- hydrology 水文学- geomorphology 地貌学- paleontology 古生物学- geophysics 地球物理学- planetary science 行星科学6. 计算机科学（Computer Science） - programming 编程- algorithm 算法- data structure 数据结构- artificial intelligence 人工智能- computer network 计算机网络- operating system 操作系统- database 数据库- software engineering 软件工程- computer graphics 计算机图形学- computer security 计算机安全7. 经济学（Economics）- microeconomics 微观经济学- macroeconomics 宏观经济学- econometrics 计量经济学- international economics 国际经济学 - finance 金融学- labor economics 劳动经济学- economic development 经济发展学- game theory 博弈论- econometric models 计量经济模型- economic policy 经济政策8. 心理学（Psychology）- cognitive psychology 认知心理学- developmental psychology 发展心理学 - social psychology 社会心理学- personality psychology 人格心理学- abnormal psychology 异常心理学- educational psychology 教育心理学- industrial-organizational psychology 工业组织心理学- clinical psychology 临床心理学- counseling psychology 咨询心理学- positive psychology 积极心理学通过掌握以上学科词汇，同学们可以在英语四级考试中更好地理解并回答与学术知识相关的问题。

数学各种专业的英语词汇翻译

1. 有关数*算add，plus 加subtract 减difference 差multiply, times 乘product 积divide 除divisible 可被整除的divided evenly 被整除dividend 被除数，红利divisor 因子，除数quotient 商remainder 余数factorial 阶乘power 乘方radical sign, root sign 根号round to 四舍五入to the nearest 四舍五入2. 有关集合union 并集proper subset 真子集solution set 解集3.有关代数式、方程和不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient 数字系数literal coefficient 字母系数inequality 不等式triangle inequality 三角不等式range 值域original equation 原方程equivalent equation 同解方程，等价方程linear equation 线性方程(e.g. 5x +6=22)4.有关分数和小数proper fraction 真分数improper fraction 假分数mixed number 带分数vulgar fraction，common fraction 普通分数simple fraction 简分数complex fraction 繁分数numerator 分子denominator 分母(least) common denominator （最小）公分母quarter 四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数tenths unit 十分位5. 基本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数exponent 指数，幂base 乘幂的底数,底边cube 立方数，立方体square root 平方根cube root 立方根common logarithm 常用对数digit 数字constant 常数variable 变量inverse function 反函数complementary function 余函数linear 一次的，线性的factorization 因式分解absolute value 绝对值，e.g.｜-32｜=32round off 四舍五入主题：数学专业英语词汇6.有关数论natural number 自然数positive number 正数negative number 负数odd integer, odd number 奇数even integer, even number 偶数integer, whole number 整数positive whole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrational（number）无理数inverse 倒数composite number 合数 e.g. 4,6,8,9,10,12,14,15……prime number 质数 e.g. 2,3,5,7,11,13,15……注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal 倒数common divisor 公约数multiple 倍数(least)common multiple (最小)公倍数(prime) factor (质)因子common factor 公因子ordinary scale, decimal scale 十进制nonnegative 非负的tens 十位units 个位mode 众数median 中数common ratio 公比7.数列arithmetic progression(sequence) 等差数列geometric progression(sequence) 等比数列8.其它approximate 近似(anti)clockwise (逆) 顺时针方向cardinal 基数ordinal 序数direct proportion 正比distinct 不同的estimation 估计，近似parentheses 括号proportion 比例permutation 排列combination 组合table 表格trigonometric function 三角函数unit 单位,位几何部分1. 所有的角alternate angle 内错角corresponding angle 同位角vertical angle 对顶角central angle 圆心角interior angle 内角exterior angle 外角supplementary angles 补角complementary angle 余角adjacent angle 邻角acute angle 锐角obtuse angle 钝角right angle 直角round angle 周角straight angle 平角included angle 夹角2.所有的三角形equilateral triangle 等边三角形scalene triangle 不等边三角形isosceles triangle 等腰三角形right triangle 直角三角形oblique 斜三角形inscribed triangle 内接三角形3.有关收敛的平面图形，除三角形外semicircle 半圆concentric circles 同心圆quadrilateral 四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon 多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方rectangle 长方形regular polygon 正多边形rhombus 菱形trapezoid 梯形4.其它平面图形arc 弧line, straight line 直线line segment 线段parallel lines 平行线segment of a circle 弧形5.有关立体图形cube 立方体，立方数rectangular solid 长方体regular solid/regular polyhedron 正多面体circular cylinder 圆柱体cone 圆锥sphere 球体solid 立体的6.有关图形上的附属物altitude 高depth 深度side 边长circumference, perimeter 周长radian 弧度surface area 表面积volume 体积arm 直角三角形的股cross section 横截面center of a circle 圆心chord 弦radius 半径angle bisector 角平分线diagonal 对角线diameter 直径edge 棱face of a solid 立体的面hypotenuse 斜边included side 夹边leg 三角形的直角边median of a triangle 三角形的中线base 底边，底数（e.g. 2的5次方，2就是底数）opposite 直角三角形中的对边midpoint 中点endpoint 端点vertex (复数形式vertices)顶点tangent 切线的transversal 截线intercept 截距7.有关坐标coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点abscissa 横坐标ordinate 纵坐标number line 数轴quadrant 象限slope 斜率complex plane 复平面8.其它plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 外切inscribe 内切intersect 相交perpendicular 垂直pythagorean theorem 勾股定理congruent 全等的multilateral 多边的其它1.单位类cent 美分penny 一美分硬币nickel 5美分硬币dime 一角硬币dozen 打（12个）score 廿(20个)Centigrade 摄氏Fahrenheit 华氏quart 夸脱gallon 加仑(1 gallon = 4 quart) yard 码meter 米micron 微米inch 英寸foot 英尺minute 分(角度的度量单位，60分=1度)square measure 平方单位制cubic meter 立方米pint 品脱(干量或液量的单位)2.有关文字叙述题，主要是有关商业intercalary year(leap year) 闰年(366天)common year 平年(365天) depreciation 折旧down payment 直接付款discount 打折margin 利润profit 利润interest 利息simple interest 单利compounded interest 复利dividend 红利decrease to 减少到decrease by 减少了increase to 增加到increase by 增加了denote 表示list price 标价markup 涨价per capita 每人ratio 比率retail price 零售价tie 打。

数学与应用数学培养方案(070101) (Mathematics and Applied

数学与应用数学培养方案（070101）（Mathematics and Applied Mathematics 070101）一、专业简介（Ⅰ、Major Introduction）数学与应用数学专业的专业方向有：基础数学和应用数学。

本专业十分重视学生数学基础知识和专业基础知识的学习，注重对他们的创造性和创新能力的培养，为培养高级数学专业人才打好基础。

经过四年学习，使学生初步具备在基础数学或应用数学某个方向从事当代学术前沿问题研究的能力。

毕业后能从事数学及相关学科的教学和科学研究工作，并可继续深造，到高等学校或科研机构的基础数学、应用数学及其他交叉学科做研究生。

The major (Mathematics and Applied Mathematics) have two branches: Pure Mathematics and Applied Mathematics. The major focus teaching on both basic and professional theory of mathematics, and is committed to cultivating the high-level mathematical talents with the innovative and creative ability. After four-years-study, the students should have researching ability for academic open problems in some directions of pure or applied mathematics. When the students in the major graduate, they can teach or study mathematics and related subjects, or they can be postgraduate students of universities or institutes in Pure Mathematics or Applied Mathematics or some other related branches.二、培养目标（Ⅱ、Cultivation Objective）培养掌握数学科学的基本理论与基本方法,具有运用数学知识或使用计算机解决实际问题的能力，受到科学研究训练的高级专门人才，能在科技、教育、经济和企事业等部门从事研究、教学工作或在生产经营及管理部门从事实际应用、开发研究和管理工作，或能继续攻读研究生学位。

数学各种专业的英语词汇翻译

1. 有关数*算add，plus 加subtract 减difference 差multiply, times 乘product 积divide 除divisible 可被整除的divided evenly 被整除dividend 被除数，红利divisor 因子，除数quotient 商remainder 余数factorial 阶乘power 乘方radical sign, root sign 根号round to 四舍五入to the nearest 四舍五入2. 有关集合union 并集proper subset 真子集solution set 解集3.有关代数式、方程和不等式algebraic term 代数项like terms, similar terms 同类项numerical coefficient 数字系数literal coefficient 字母系数inequality 不等式triangle inequality 三角不等式range 值域original equation 原方程equivalent equation 同解方程，等价方程linear equation 线性方程(e.g. 5x +6=22)4.有关分数和小数proper fraction 真分数improper fraction 假分数mixed number 带分数vulgar fraction，common fraction 普通分数simple fraction 简分数complex fraction 繁分数numerator 分子denominator 分母(least) common denominator （最小）公分母quarter 四分之一decimal fraction 纯小数infinite decimal 无穷小数recurring decimal 循环小数tenths unit 十分位5. 基本数学概念arithmetic mean 算术平均值weighted average 加权平均值geometric mean 几何平均数exponent 指数，幂base 乘幂的底数,底边cube 立方数，立方体square root 平方根cube root 立方根common logarithm 常用对数digit 数字constant 常数variable 变量inverse function 反函数complementary function 余函数linear 一次的，线性的factorization 因式分解absolute value 绝对值，e.g.｜-32｜=32round off 四舍五入主题：数学专业英语词汇6.有关数论natural number 自然数positive number 正数negative number 负数odd integer, odd number 奇数even integer, even number 偶数integer, whole number 整数positive whole number 正整数negative whole number 负整数consecutive number 连续整数real number, rational number 实数,有理数irrational （number）无理数inverse 倒数composite number 合数 e.g. 4,6,8,9,10,12,14,15……prime number 质数 e.g. 2,3,5,7,11,13,15……注意：所有的质数(2除外)都是奇数，但奇数不一定是质数reciprocal 倒数common divisor 公约数multiple 倍数(least)common multiple (最小)公倍数(prime) factor (质)因子common factor 公因子ordinary scale, decimal scale 十进制nonnegative 非负的tens 十位units 个位mode 众数median 中数common ratio 公比7.数列arithmetic progression(sequence) 等差数列geometric progression(sequence) 等比数列8.其它approximate 近似(anti)clockwise (逆) 顺时针方向cardinal 基数ordinal 序数direct proportion 正比distinct 不同的estimation 估计，近似parentheses 括号proportion 比例permutation 排列combination 组合table 表格trigonometric function 三角函数unit 单位,位几何部分1. 所有的角alternate angle 内错角corresponding angle 同位角vertical angle 对顶角central angle 圆心角interior angle 内角exterior angle 外角supplementary angles 补角complementary angle 余角adjacent angle 邻角acute angle 锐角obtuse angle 钝角right angle 直角round angle 周角straight angle 平角included angle 夹角2.所有的三角形equilateral triangle 等边三角形scalene triangle 不等边三角形isosceles triangle 等腰三角形right triangle 直角三角形oblique 斜三角形inscribed triangle 内接三角形3.有关收敛的平面图形，除三角形外semicircle 半圆concentric circles 同心圆quadrilateral 四边形pentagon 五边形hexagon 六边形heptagon 七边形octagon 八边形nonagon 九边形decagon 十边形polygon 多边形parallelogram 平行四边形equilateral 等边形plane 平面square 正方形，平方rectangle 长方形regular polygon 正多边形rhombus 菱形trapezoid 梯形4.其它平面图形arc 弧line, straight line 直线line segment 线段parallel lines 平行线segment of a circle 弧形5.有关立体图形cube 立方体，立方数rectangular solid 长方体regular solid/regular polyhedron 正多面体circular cylinder 圆柱体cone 圆锥sphere 球体solid 立体的6.有关图形上的附属物altitude 高depth 深度side 边长circumference, perimeter 周长radian 弧度surface area 表面积volume 体积arm 直角三角形的股cross section 横截面center of a circle 圆心chord 弦radius 半径angle bisector 角平分线diagonal 对角线diameter 直径edge 棱face of a solid 立体的面hypotenuse 斜边included side 夹边leg 三角形的直角边median of a triangle 三角形的中线base 底边，底数（e.g. 2的5次方，2就是底数）opposite 直角三角形中的对边midpoint 中点endpoint 端点vertex (复数形式vertices)顶点tangent 切线的transversal 截线intercept 截距7.有关坐标coordinate system 坐标系rectangular coordinate 直角坐标系origin 原点abscissa 横坐标ordinate 纵坐标number line 数轴quadrant 象限slope 斜率complex plane 复平面8.其它plane geometry 平面几何trigonometry 三角学bisect 平分circumscribe 外切inscribe 内切intersect 相交perpendicular 垂直pythagorean theorem 勾股定理congruent 全等的multilateral 多边的其它1.单位类cent 美分penny 一美分硬币nickel 5美分硬币dime 一角硬币dozen 打（12个）score 廿(20个)Centigrade 摄氏Fahrenheit 华氏quart 夸脱gallon 加仑(1 gallon = 4 quart) yard 码meter 米micron 微米inch 英寸foot 英尺minute 分(角度的度量单位，60分=1度)square measure 平方单位制cubic meter 立方米pint 品脱(干量或液量的单位)2.有关文字叙述题，主要是有关商业intercalary year(leap year) 闰年(366天)common year 平年(365天) depreciation 折旧down payment 直接付款discount 打折margin 利润profit 利润interest 利息simple interest 单利compounded interest 复利dividend 红利decrease to 减少到decrease by 减少了increase to 增加到increase by 增加了denote 表示list price 标价markup 涨价per capita 每人ratio 比率retail price 零售价tie 打。

数学学与应用数学

数学学与应用数学Mathematics is a subject that many students find challenging, whether it's in basic arithmetic or advanced calculus. The importance of mathematics in education cannot be overstated, as it provides the foundational knowledge and skills needed for success in various fields. From science and engineering to finance and computer programming, mathematics plays a crucial role in helping individuals solve complex problems and make informed decisions.数学是许多学生认为具有挑战性的学科，无论是在基本算术还是高级微积分。

数学在教育中的重要性无法被夸大，因为它提供了成功所需的基础知识和技能，无论是在科学和工程领域，还是在金融和计算机编程领域，数学都在帮助个人解决复杂问题和做出明智决策方面发挥着至关重要的作用。

For students pursuing a career in STEM fields, a strong foundation in mathematics is essential. Understanding mathematical concepts and techniques is crucial for conducting research, analyzing data, and developing new technologies. Moreover, mathematics provides a common language that enables scientists and engineers from different backgrounds to communicate effectively and collaborate oninnovative projects. Without a solid understanding of mathematics, it would be challenging to excel in fields such as physics, chemistry, and biology.对于追求STEM领域职业的学生来说，数学基础至关重要。

数学专业英语翻译3.4.5

3.4数学的应用与应用数学3.4.5Construction of mathematical model（建立数学模型）In the preceding discussion we viewed modeling as a process and considered briefly the form of the model.Now let's focus attention on the construction of mathematical models.（在前面的讨论中，我们将建模视为一个过程，并简要地仔细思考了模型的形式。

现在让我们把注意力集中在数学模型的构建上。

）We begin by presenting an outline of a peocedure that is helpful in constructing models.In the next section,we illustrate the various steps in the procedure by discussing several real-world examples.（我们首先介绍一种有助于构建模型的概述。

在下一节中，我们通过讨论几个实际示例来说明过程中的各个步骤。

）STEP1Identify the problem（确定问题）What is the problem you would like to explore?Typically this is a difficult step because in real-life situations no one simply hands you a mathematical problem to solve.（你想探索的问题是什么？通常这是一个困难的步骤，因为在现实生活中，没有人只是给你一个数学问题来解决。

）Usually you have to sort through large amounts of data and identify some particular aspect of the situation to study.Moreover,it is imperative to be sufficiently precise(ultimately)in the formulation of the problem to allow for translation of the verbal statements describing the problem into mathematical symbology.（通常你必须对大量数据进行排序，并确定要研究的某些特定情况。

各种数学语言名称的英语翻译-最新教育文档

各种数学语言名称的英语翻译数学 mathematics, maths(BrE), math(AmE)公理 axiom定理 theorem计算 calculation运算 operation证明 prove假设 hypothesis, hypotheses(pl.)命题 proposition算术 arithmetic加 plus(prep.), add(v.), addition(n.)被加数 augend, summand加数 addend和 sum减 minus(prep.), subtract(v.), subtraction(n.)被减数 minuend减数 subtrahend差 remainder乘 times(prep.), multiply(v.), multiplication(n.) 被乘数 multiplicand, faciend乘数 multiplicator积 product除 divided by(prep.), divide(v.), division(n.) 被除数 dividend除数 divisor商 quotient等于 equals, is equal to, is equivalent to大于 is greater than小于 is lesser than大于等于 is equal or greater than小于等于 is equal or lesser than运算符 operator平均数mean算术平均数arithmatic mean几何平均数geometric mean n个数之积的n次方根倒数（reciprocal） x的倒数为1/x有理数 rational number无理数 irrational number实数 real number虚数 imaginary number数字 digit数 number自然数 natural number整数 integer小数 decimal小数点 decimal point分数 fraction分子 numerator分母 denominator比 ratio正 positive负 negative零 null, zero, nought, nil 十进制 decimal system二进制 binary system十六进制 hexadecimal system 权 weight, significance进位 carry截尾 truncation四舍五入 round下舍入 round down上舍入 round up有效数字 significant digit 无效数字 insignificant digit 代数 algebra公式 formula, formulae(pl.)单项式 monomial多项式 polynomial, multinomial系数 coefficient未知数 unknown, x-factor, y-factor, z-factor 等式，方程式 equation一次方程 simple equation二次方程 quadratic equation三次方程 cubic equation四次方程 quartic equation不等式 inequation阶乘 factorial对数 logarithm指数，幂 exponent乘方 power二次方，平方 square三次方，立方 cube四次方 the power of four, the fourth powern次方 the power of n, the nth power开方 evolution, extraction二次方根，平方根 square root三次方根，立方根 cube root四次方根 the root of four, the fourth rootn次方根 the root of n, the nth root sqrt(2)=1.414sqrt(3)=1.732sqrt(5)=2.236常量 constant变量 variable坐标系 coordinates坐标轴 x-axis, y-axis, z-axis横坐标 x-coordinate纵坐标 y-coordinate原点 origin象限quadrant截距(有正负之分)intercede（方程的）解solution几何geometry点 point线 line面 plane体 solid线段 segment射线 radial平行 parallel相交 intersect角 angle角度 degree弧度 radian锐角 acute angle直角 right angle钝角 obtuse angle平角 straight angle周角 perigon底 base边 side高 height三角形 triangle锐角三角形 acute triangle直角三角形 right triangle直角边 leg斜边 hypotenuse勾股定理 Pythagorean theorem钝角三角形 obtuse triangle不等边三角形 scalene triangle 等腰三角形 isosceles triangle 等边三角形 equilateral triangle四边形 quadrilateral平行四边形 parallelogram 矩形 rectangle长 length宽 width周长 perimeter面积 area相似 similar全等 congruent三角 trigonometry正弦 sine余弦 cosine正切 tangent余切 cotangent正割 secant余割 cosecant反正弦 arc sine反余弦 arc cosine反正切 arc tangent反余切 arc cotangent反正割 arc secant反余割 arc cosecant集合aggregate元素 element空集 void子集 subset交集 intersection并集 union补集 complement映射 mapping函数 function定义域 domain, field of definition 值域 range单调性 monotonicity奇偶性 parity周期性 periodicity图象 image数列，级数 series微积分 calculus微分 differential导数 derivative极限 limit无穷大 infinite(a.) infinity(n.) 无穷小 infinitesimal积分 integral定积分 definite integral不定积分 indefinite integral 复数 complex number矩阵 matrix行列式 determinant圆 circle圆心 centre(BrE), center(AmE) 半径 radius直径 diameter圆周率 pi弧 arc半圆 semicircle扇形 sector环 ring椭圆 ellipse圆周 circumference轨迹 locus, loca(pl.)平行六面体 parallelepiped立方体 cube七面体 heptahedron八面体 octahedron九面体 enneahedron十面体 decahedron十一面体 hendecahedron十二面体 dodecahedron二十面体 icosahedron多面体 polyhedron旋转 rotation轴 axis球 sphere半球 hemisphere底面 undersurface表面积 surface area体积 volume空间 space双曲线 hyperbola抛物线 parabola四面体 tetrahedron五面体 pentahedron六面体 hexahedron菱形 rhomb, rhombus, rhombi(pl.), diamond 正方形 square梯形 trapezoid直角梯形 right trapezoid等腰梯形 isosceles trapezoid五边形 pentagon六边形 hexagon七边形 heptagon八边形 octagon九边形 enneagon十边形 decagon十一边形 hendecagon十二边形 dodecagon多边形 polygon正多边形 equilateral polygon相位 phase周期 period振幅 amplitude内心 incentre(BrE), incenter(AmE)外心 excentre(BrE), excenter(AmE)旁心 escentre(BrE), escenter(AmE)垂心 orthocentre(BrE), orthocenter(AmE) 重心 barycentre(BrE), barycenter(AmE) 内切圆 inscribed circle外切圆 circumcircle统计 statistics平均数 average加权平均数 weighted average方差 variance标准差 root-mean-square deviation, standard deviation 比例 propotion百分比 percent百分点 percentage百分位数 percentile排列 permutation组合 combination概率，或然率 probability分布 distribution正态分布 normal distribution非正态分布 abnormal distribution图表 graph条形统计图 bar graph柱形统计图 histogram折线统计图 broken line graph曲线统计图 curve diagram扇形统计图 pie diagram。

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幂级数的展开及其应用
梁慧
(杭州师范大学理学院数学与应用数学数学053，浙江杭州310000)
【摘要】通过学习幂级数的一些基本知识，得出常用初等函数幂级数的展开式．并且探讨函数幂级数在初等函数的应用。

【关键词】幂级数；马克劳林公式；泰勒公式；初等函数
幂级数是数学分析中的—个非常重要的内容，而且幂级数的应用也非常广泛，可以借助幂级数的展开形式，很容易的解决一些较为复杂的问题，本文旨在研究幂级数的展开形式及其在初等函数的应用。

一、马克劳林(Maclaurin)公式
幂级数实际上可以视为多项式的延伸，因此在考虑函数()f x 能否展开成幂级数时，可以从函数()f x 与多项式的关系入手来解决这个问题．为此，这里不加证明地给出如下的公式．
泰勒(Taylor)公式如果函数()f x 在0x x =的某一邻域内，有直到1n +阶的导数，则在这个邻域内有如下公式：
()2
0000000()()()()()()()()()2!!
n n n f x f x f x f x f x x x x x x x r x n '''=+-+-++-+…,(9
51)
其中
(1)10()
()()(1)!
n n n f r x x x n ξ++=-+．
称()n r x 为拉格朗日型余项．称(951)式为泰勒公式．
如果令00x =，就得到
2()(0)()n n f x f x x x r x =+++++…， (952)
此时，
(1)(1)11
1()()()(1)!(1)!
n n n n n f f x r x x x n n ξθ+++++==++, (01θ<<)．
称(952)式为马克劳林公式．
公式说明，任一函数()f x 只要有直到1n +阶导数，就可等于某个n 次多项式与一个余项的和．
我们称下列幂级数
()2(0)(0)()(0)(0)2!!
n n
f f f x f f x x x n '''=+++++ (953)
为马克劳林级数．那么，它是否以()f x 为和函数呢?若令马克劳林级数(953)的前1
n +项和为1()n S x +，即
()21(0)(0)()(0)(0)2!!
n n
n f f S x f f x x x n +'''=++++…，
那么，级数(953)收敛于函数()f x 的条件为
1lim ()()n n s x f x +→∞
=．
注意到马克劳林公式(952)与马克劳林级数(953)的关系，可知
1()()()n n f x S x r x +=+．
于是，当
()0n r x =
时，有
1()()n f x S x +=．
反之亦然．即若
1lim ()()n n s x f x +→∞
=
则必有
()0n r x =．
这表明，马克劳林级数(953)以()f x 为和函数⇔马克劳林公式(952)中
的余项()0n r x → (当n →∞时)．
这样，我们就得到了函数()f x 的幂级数展开式：
()()20
(0)(0)(0)()(0)(0)!2!!
n n n n
n f f f f x x f f x x x n n ∞
='''==+++++∑
(954)
它就是函数()f x 的幂级数表达式，也就是说，函数的幂级数展开式是唯一的．事实上，假设函数()f x 可以表示为幂级数
20120()n n n n n f x a x a a x a x a x ∞
===+++++∑……，
(955)
那么，根据幂级数在收敛域内可逐项求导的性质，再令0x =(幂级数显然在0x =点收
敛)，就容易得到
()2012(0)(0)(0),(0),,,,,2!!
n n
n f f a f a f x a x a x n '''====……．
将它们代入(955)式，所得与()f x 的马克劳林展开式(954)完全相同．
综上所述，如果函数()f x 在包含零的某区间内有任意阶导数，且在此区间内的马克劳林公式中的余项以零为极限(当n →∞时)，那么，函数()f x 就可展开成形如(954)
式的幂级数．
幂级数
()00000()()
()()()()1!!
n n f x f x f x f x x x x x n '=+-++-……,
称为泰勒级数．
二、初等函数的幂级数展开式
利用马克劳林公式将函数()f x 展开成幂级数的方法，称为直接展开法．例1 试将函数()x
f x e =展开成x 的幂级数．解因为
()()n x f x e =, (1,2,3,)n =…
所以
()(0)(0)(0)(0)1n f f f f '''====…，
于是我们得到幂级数
211
12!!
n x x x n ++
+++……，
(956)
显然，(956)式的收敛区间为(,)-∞+∞，至于(956)式是否以()x
f x e =为
和函数，即它是否收敛于()x
f x e =，还要考察余项()n r x ．
因为
1e ()(1)!
x
n n r x x n θ+=+ (01θ<<)，且x x x θθ≤≤，
所以
11
e e ()(1)!(1)!
x
x n n n r x x x n n θ++=<++．
注意到对任一确定的x 值，x
e 是一个确定的常数，而级数(956)是绝对收敛的，
因此其一般项当n →∞时，
1
0(1)!
n x
n +→+，所以当n →∞时，有
1
0(1)!
n x
x
e
n +→+，
由此可知
lim ()0n n r x →∞
=．
这表明级数(956)确实收敛于()x
f x e =，因此有
211
12!!
x n e x x x n =++
+++…… (x -∞<<+∞)．这种运用马克劳林公式将函数展开成幂级数的方法，虽然程序明确，但是运算往往过于
繁琐，因此人们普遍采用下面的比较简便的幂级数展开法．
在此之前，我们已经得到了函数
x
-11，x
e 及sin x 的幂级数展开式，运用这几个已知的展开式，通过幂级数的运算，可以求得许多函数的幂级数展开式．这种求函数的幂级数展开式的方法称为间接展开法．
例2 试求函数()cos f x x =在0x =处的幂级数展开式．解因为
(sin )cos x x '=，
而
3521111sin (1)3!5!(21)!
n n x x x x x n +=-
+-+-++……,
（x -∞<<+∞），
所以根据幂级数可逐项求导的法则，可得
342111cos 1(1)2!4!(2)!
n n x x x x n =-
+-+-+……,（x -∞<<+∞）．
三、函数幂级数展开的应用举例
幂级数展开式的应用很广泛，例如可利用它来对某些数值或定积分值等进行近似计算．例3 利用arctan x 的展开式估计π的值．解由于πarctan14
=，又因
357
arctan 357
x x x x x =-+-+…， (11x -≤≤)，
所以有
1114arctan14(1)357
π==-+-+…．
可用右端级数的前n 项之和作为π的近似值．但由于级数收敛的速度非常慢，要取足够多的项才能得到π的较精确的估计值．
参考文献
[1] 陈传璋，欧阳光中．数学分析(下册)[M]．北京：高等教育出版税社，1983：18O-192 [2] 史济怀．母函数[M]．上海：上海教育出版社，1980
[3] 钟玉泉．复变函数论[M]．北京：高等教育出版社，1988:14l 一162。

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