《数学专业英语》常用英文表达 PPT
数学专业英语第一讲.ppt
1、了解文献查阅是做科研必不可少的能力； 2、掌握关键词索引查阅办法、学科分类查阅等办法。
学习本课程的基本要求：
1、认真自学好教材，并勾画出学习重点。 /中国知网翻译助手 2、积极参与本课程的讨论，做好听课笔记。 3、按时独立完成平时作业。
f (x) M For all x D ，where M is a constant.
3、能用英语书写文章摘要、学术会议通知、 学术交流信件等。同时培养简单的英语会 话能力。 4、为部分优秀学生攻读研究生奠定数学专 业英语的基础，同时让大部分同学了解数 学专业英语与生活英语的区别，为今后走 上工作岗位，特别是服务于IT业或外资企 业有独当一面的能力。
课程学习安排
❖ 课程类别：专业任选课 ❖ 课程学时：总学时32 ❖ 学 分：1
数学专业英语 第一讲
为什么要学习数学专业英语？
❖ 数学学科发展需要：20世纪90年代计算机科学技术 的迅速发展宣告了人类信息时代的到来。数学，这 个古老而又优雅的学科获得了新的发展动力和发挥 作用的舞台。
❖ 现在国际数学教育与研究交流日益频繁，很多最新 的研究成果是以英文形式呈现的。专业人员需要有 阅读翻译英语，甚至用英文写作论文的能力。对于 学习数学的学生和准备从事数学研究的人员，在掌 握了公共英语的基本
Eg1:Given 0 ，there exists a number N>0 such that an a for all n N .
Eg2: Since h(x) is harmonic on neighborhood of
B(a,r), we have h(x)d (x) h(a) . B
本课程分四部分讲解：
精选课文：1、理解数学专业文章和一般英语文章写作的不同；
数学专业英语(13)
3
Mathematical English 13: Computers and Mathematics
functions to be performed easily. And somewhat later, both Pascal and Leibniz constructed machines to aid in computation. As Leibniz wrote, “it is unworthy of excellent men to lose hours like slaves in the labor of calculation, which could be safely relegated to anyone else if the machine were used.” Unfortunately, neither Leibniz’s machine nor the various improved models built by others during the following century and a half were actually used to any extent in the way Leibniz envisaged. The mathematical practitioners themselves continued to do calculations by hand, probably because the machines, operated manually, provided little advantage in speed. For complicated calculations, naturally, tables were used, particularly tables of logarithms and trigonometric functions, even though these tables, originally calculated by hand, frequently contained errors. It was not until around 1821, when the Industrial Revolution was in full
数学专业英语常用词汇-14页精选文档
数学专业英语词汇代数部分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. 5?x?+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｜=32?round off四舍五入 ?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??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?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Chapter onefunction notation方程符号函数符号quadratic functions 二次函数quadratic equations 二次方程式二次等式chapter twoEquivalent algebraic expressions 等价代数表达式rational expression 有理式有理表达式horizontal and vertical translation of functions 函数的水平和垂直的平移reflections of functions 函数的倒映映射chapter threeExponential functions 指数函数exponential decay 指数式衰减exponent 指数properties of exponential functions 指数函数的特性chapter fourTrigonometry 三角学Reciprocal trigonometric ratios 倒数三角函数比Trigonometric functions 三角函数Discrete functions 离散函数数学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 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 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曲线统计图 curve diagram扇形统计图 pie diagram希望以上资料对你有所帮助，附励志名言3条：：1、世事忙忙如水流，休将名利挂心头。
数学专业英语2-6
For a given real number x>0, it is possible to count the number of primes less than or equal to x. This number is said to be a function of x even though no simple algebraic formula is known for computing it (without counting) when x is known. 对于一个给定的实数x>0，数出小于或者等于x的素数 的个数是有可能的。这个数称为x的函数，尽管还没 有一个简单代数式可以由已知的x计算(不通过计数求) 出它的值。
These are merely devices for describing special relations in a quantitative fashion. Mathematicians refer to certain types of these relations as functions. 这些只是以定量的方式描述特定关系的方法。数学家 将这些关系中的某些类型视作函数。 In this section, we give an informal description of the function concept. A formal definition is given in Section 3. 在本节中，我们给出一个非正式的描述函数的概念。 在第3节给出一个正式的定义 。
EXAMPLE 1. The force F necessary to stretch a steel spring a distance x beyond its natural length is proportional to x. That is, F=cx, where c is a number independent of x called the spring constant. 把一个钢制的弹簧拉伸到超过其自然长度的距离为x 时所需要的力F与x成正比。即，F=cx,这里c是不依赖 与x的数，叫做弹性系数。 This formula, discovered by Robert Hooke in the mid17th century, is called Hooke’s law, and it is said to express the force as a function of the displacement.
数学专业英语
几何的学习使学生在思考问题时更周密、审慎，他们 将不会盲目接受任何结论.
2－B Some geometrical terms
A solid is a three-dimensional figure. Common exaБайду номын сангаасples of solids are cube, sphere, cylinder, cone and pyramid. A cube has six faces which are smooth and flat. These faces are called plane surfaces or simply planes. 立体是一个三维图形，立体常见的例子是立方体，球
This is evident from the fact that they require study of geometry as a prerequisite to matriculation in those schools. 许多居于领导地位的学术机构承认，所有学习这个数 学分支的人都将得到确实的受益。
It is hoped that … 希望…… It is reported that … 据报道…… It is said that … 据说…… It is supposed that … 据推测…… It may be said without fear of exaggeration that … 可以毫不夸张地说… It must be admitted that … 必须承认…… It must be pointed out that … 必须指出…… It will be seen from this that … 由此可见……
平面上的闭曲线当其中每点到一个固定点的距离均相 当时叫做圆。固定点称为圆心。
数学专业英语阅读和翻译初阶PPT课件
算出(v)；compute计算(v)；
例 Given 0 ，there exists a number N 0 such that | an a | for all n N .
( 译文： 任取 0 ，存在数 N 0 ，使得 | an a | 对 所有的 n N 都成立。)
表示“存在”的句型显然不表示主语 a number N
• Now we investigate whether the functions are integrable and why they are integrable or not.（译文：现在，我们来研究这些函数是否可 积及它们可积或不可积的原因。） 若把形容词integrable改为名词integrability（可 积性），句子可写成： Now we investigate the integrability of the functions.
时 • 数学资料通常以叙述方式介绍概念和成果，以论证方法推导有 关结论，包括定理、引理和推论的证明。内容的正确性与时间 无关。结果在以前出现，但资料中仍用现在时态表述。
• 数学史以及专题报告和研究新闻中，为了强调某个历史时间发 生的时间，也常根据需要采用过去时或一般完成时。
2. 被动语态出现频率高，应用广 泛 • 被动语态适合强调客 观 事 实 和 行 为 效 果 本身，不强调行为主体，与科学文献
这里“we have”并不强调“我们有”
什么，而是说明“可以得出”什么结
论，可以换为“one has”或者省略而
不影响原意。
• 数学的结论的成立都是有条件的，推导都有充分根据。叙述 数学命题时必须把条件和结论不遗漏、不重复地表达出来； 推导的过程要把每个论点的来龙去脉有条理地表述清楚。表 述必须精炼、明确和规范。
数学 英语知识点总结ppt
数学英语知识点总结pptArithmeticArithmetic is the most basic and fundamental branch of mathematics. It deals with the operations of numbers, including addition, subtraction, multiplication, and division. In this section, we will review the basic operations of arithmetic, as well as the properties of numbers, such as commutativity, associativity, and distributivity. We will also cover topics such as fractions, decimals, percentages, and ratios, and demonstrate how these concepts are used in everyday life, such as in budgeting, cooking, and shopping.AlgebraAlgebra is a branch of mathematics that uses symbols and letters to represent numbers and quantities. In this section, we will explore the basic principles of algebra, including equations, inequalities, and functions. We will also discuss the various techniques for solving algebraic problems, such as factoring, completing the square, and using the quadratic formula. Additionally, we will demonstrate how algebra is used in various fields, such as science, engineering, and economics, through practical examples and applications.GeometryGeometry is the study of shapes, sizes, and spatial relationships. In this section, we will cover the fundamental concepts of geometry, including points, lines, angles, and polygons. We will also discuss the properties of geometric figures, such as congruence, similarity, and symmetry, as well as the principles of measurement, such as area, perimeter, volume, and surface area. Furthermore, we will explore the applications of geometry in architecture, design, and art, and highlight its importance in everyday life.TrigonometryTrigonometry is a branch of mathematics that deals with the relationships between angles and sides in right-angled triangles. In this section, we will review the basic trigonometric functions, such as sine, cosine, and tangent, as well as their inverses. We will also discuss the applications of trigonometry in various fields, such as navigation, astronomy, and engineering. Additionally, we will demonstrate how trigonometric principles are used to solve problems involving angles and distances.CalculusCalculus is a branch of mathematics that deals with the study of change and motion. In this section, we will explore the basic concepts of calculus, including derivatives, integrals, and limits. We will also discuss the applications of calculus in physics, engineering, and economics, and demonstrate how it is used to solve real-world problems, such as finding the maximum and minimum values of functions, determining rates of change, and calculating areas and volumes.StatisticsStatistics is the branch of mathematics that deals with the collection, analysis, interpretation, and presentation of data. In this section, we will cover the basic principles of statistics, including data types, measures of central tendency, measures of dispersion, and probability. We will also discuss various statistical methods, such as hypothesis testing, regression analysis, and correlation, and demonstrate their applications in fields such as business, healthcare, and social sciences.In conclusion, mathematics is a diverse and essential field of study that plays a crucial role in many aspects of our lives. This PowerPoint presentation aims to provide a comprehensive overview of various mathematical knowledge points in the English language, from basic arithmetic to advanced calculus and statistics. By understanding these concepts and their applications, we can gain a deeper appreciation for the beauty and utility of mathematics in the world around us. Thank you for your attention, and we hope you find this presentation informative and inspiring.。
数学专业英语第八讲附数学课程英文表达ppt
• 代数几何: 1、Harris,Algebraic Geometry: a first course:代数几何得入门教材; 2、Algebraic Geometry Robin Hartshorne :经典得代数几何教材,难度很高; 3、Basic Algebraic Geometry 1&2 2nd ed、 I、R、Shafarevich、:非常好得代数几 何入门教材; 4、Principles of Algebraic Geometry by giffiths/harris:全面、经典得代数几何参考 书,偏复代数几何; 5、mutative Algebra with a view toward Algebraic Geometry by Eisenbud:高级得 代数几何、交换代数得参考书,最新得交换代数全面参考; 6、The Geometry of Schemes by Eisenbud:很好得研究生代数几何入门教材; 7、The Red Book of Varieties and Schemes by Mumford:标准得研究生代数几何入 门教材; 8、Algebraic Geometry I : plex Projective Varieties by David Mumford:复代数几 何得经典。
数学专业英语第八讲附数学课程英文表达
• 数学类
• 第一学年 几何与拓扑: 1、James R、 Munkres, Topology
• 2、Basic Topology by Armstrong 3、Kelley, General Topology:
• 4、Willard, General Topology:一般拓扑学 5、Topology and geometry:
• 代数拓扑: 1、Algebraic Topology, A、 Hatcher:最新得研究生代数拓扑标准教材; 2、Spaniers “Algebraic Topology”:经典得代数拓扑参考书; 3、Differential forms in algebraic topology, by Raoul Bott and Loring W、 Tu:研究生代数拓扑标准教材; 4、Massey, A basic course in Algebraic topology:经典得研究生代数拓扑教材
《数学专业英语》课件
2 三角恒等式和方程 4 三角学在几何和物理中的应用
IV. Calculus
1 极限和连续性 4 定积分及其性质
2 导数及其性质
3 导数在优化和相关速
率中的应用
5 定积分在面积和体积计算中的应用
V. Linear Algebra
1 向量和向量运算 3 线性方程组
《数学专业英语》PPT课 件
探索数学专业英语的精髓，为您呈现一场精彩的数学之旅。
I. Introduction
- 数学的定义 - 数学在现代社会中的重要性 - 课程目标
II. Algebra
1 基础代数表达式和方程 3 多项式和因式分解
2 根式和指数 4 二次方程和函数
III. Trigonom etry
2 矩阵及其运算 4 特征值和特征向量
VI. Probability and Statistics
1 概率的基本概念 3 数据的统计度量
2 离散和连续概率分布 4 假设检验和置信区间
VII. Conclusion
1 课程内容回顾
2 数学在不同领域的未 3 继
数学专业英语
专业英语1/2 ：a half 或one half1/4：a quarter(fourth)或one quarter(fourth) 1/1234：one over a thousand two hundred and thirty-four4/5：four fifths 或four over five113/300：one hundred and thirteen over three Hundred872：two and seven over eight 或two andseven eighths20o ：wenty degrees 6’ ：six minutes; six feet 10” ：ten seconds; ten inches 2% ：two percent 5‰：five per millea ＋b a plus b; (positive)a －b a minus b; (negative) a±b a plus or minus b a×b a multiplied by b; (times) a÷b a divided by b;a:b the ratio of a to ba=b a is equal to b; a equals to b a ≠b a is not equal to b; a is not b a ＞b a is greater than ba ＜b a is less than ba ≣b a is greater than or equal to b a ≢b a is less than or equal to ba ≡b a is identically equal to b; a is of identity to ba ba is approximately equal to bsquare root of an th root of aa the absolute value of aalgebra 代数学 geometrical 几何的algebraic 代数的 identity 恒等式arithmetic 算术, 算术的 measure 测量，测度axiom 公理numerical 数值的, 数字的conception 概念，观点 operation 运算 constant 常数 postulate 公设logical deduction 逻辑推理 proposition 命题division 除，除法 subtraction 减，减法 formula 公式term 项，术语trigonometry 三角学 variable 变化的，变量angle 角 cube 立方体arc 弧 curved line 曲线major arc 优弧 cylinder 柱体minor arc 劣弧 diameter 直径architect 建筑师 dimention 维数，大小breadth 宽度 endpoint 端点chord 弦 equidistant 等距离的circumference 周长 line segment 直线段cone 圆锥 radius 半径critical 临界的 pyramid 棱锥 ray 射线 sphere 球，球面semicircle 半圆 surface 面，曲面solid 立体的，立体 thickness 厚度brace 大括号 roster 名册consequence 结论，推论roster notation 枚举法designate 标记，指定rule out 排除，否决diagram 图形，图解subset 子集distinct 互不相同的the underlying set 基础集distinguish 区别，辨别universal set 全集divisible 可被除尽的validity 有效性dummy 哑的，哑变量visual 可视的even integer 偶数visualize 可视化irrelevant 无关紧要的void set(empty set) 空集conversely 反之geometric interpretation 几何意义correspond 对应induction 归纳法deducible 可推导的proof by induction 归纳证明difference 差inductive set 归纳集distinguished 著名的inequality 不等式entirely complete 完整的integer 整数Euclid 欧几里得interchangeably 可互相交换的Euclidean 欧式的intuitive直观的the field axiom 域公理irrational 无理的irrational number 无理数rational 有理的the order axiom 序公理rational number 有理数ordered 有序的reasoning 推理product 积scale 尺度，刻度quotient 商sum 和abscissa 横坐标horizontal 水平的analytic geometry 解析几何hypotenuse 斜边arbitrary 任意的integral 整数的,积分的,积分Cartesian 笛卡儿的intersect 相交Rene Descartes 笛卡儿intertwine 融合，结合circular 圆的，圆周的leg 侧边，直角边coordinate 坐标ordinate 纵坐标the origin 坐标原点segment 线段parabolic 抛物线的three-dimensional 三维的perpendicular 垂直的triangle 三角形polygonal 多边形的the unit distance 单位长度quadrant 象限vector 向量, 矢量reduce 归结，化简vertical 竖直的课后答案2-1（1）数学来源于人类的社会实践，包括工农业的劳动，商业、军事和科学技术研究等活动。
《数学专业英语》课件
Introduction to Mathematics Professional EnglishMathematics Professional English VocabularyGrammar and Expression in Mathematical English
01
Definition and Importance
Course content: covering basic mathematical vocabulary, mathematical formulas and symbols, academic paper reading and writing, academic speeches and communication, mathematical literature translation, and other aspects.
Course objectives and content
Course objective: To cultivate students' mastery of basic vocabulary, grammar, and expression in mathematics related English, and to improve their English reading, writing, communication, and translation abilities in the field of mathematics.
English interface of software and tools
Learn how to read and understand English documentation for mathematical software and tools, master the professional terms and expressions in the documentation, and lay a foundation for in-depth learning and application.
数学专业英语2-4
Let P denote the set of all positive integers. Then P is itself an inductive set because (a) it contains 1, and (b) it contains x+1 whenever it contains x. Since the members of P belong to every inductive set, we refer to P as the smallest inductive set. 用P表示所有正整数的集合。那么P本身是一个归纳 集，因为其中含1，满足(a)；只要包含x就包含x+1, 满足(b)。由于P中的元素属于每一个归纳集，因此P 是最小的归纳集。
Quotients of integers a/b (where b≠0) are called rational numbers. The set of rational numbers, denoted by Q, contains Z as a subset. The reader should realize that all the field axioms and the order axioms are satisfied by Q. For this reason, we say that the set of rational numbers is an ordered field. Real numbers that are not in Q are called irrational. 整数a与b的商被叫做有理数，有理数集用Q表示，Z 是Q的子集。读者应该认识到Q满足所有的域公理和 序公理。因此说有理数集是一个有序的域。不是有 理数的实数被称为无理数。
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Example:3x8x is greater than or equal to minus 3
and less than or equal to 8
, Be far less than, be far greater than
Example: c 6 c is far greater than minus 6
1. General signs of operation
+ Plus, positive Example: 2+3 read as two plus three
- Minus, negative Example: 6-2 read as six minus two
± Plus or minus, Positive or negative
c is equivalent to 5
5
Be not equal to
Example: cda0c plus d times a is not equals to 0
Be approximately equal to
Example: 3 0 .4 2 9 3 divided by 7 is approximately
A B A cup B or A join B or A union B A \ B A minus B or
the difference between A and B 6
大家应该也有点累了，稍作休息
大家有疑问的，可以询问和交流
Signs of elementary algebra
Absolute value
2
Some English expressions of numbers:
The set of numbers consists of real numbers and pure imaginary numbers shown as follows
Complex numbers(C)
Pure imaginary numbers(I)
‰ Permille, per mille
Example: 5 ‰ read as 5 per mille
2. Basic signs of relationships
Be equal to, equals
Be identical with/to, be equivalent to
Example: c 5 read as c is identical with (to) 5,
《数学专业英语》常用英文表达 PPT
Aim of the Course:
Expected progress in the following aspects:
. Reading skills of the original mathematical articles and books
. Writing skills of mathematical and other scientific articles
Real numbers(R)
Rational numbers(Q) Irrational numbers(Q´)
Integers(Z)
Fractions(F)
Natural numbers(N), Zero, Negatives of Natural Numof Integers
6
x A x belongs to A
x is an element (or a member) of A
x A x does not belong to A
x is not an element (or a member) of A
AB A is contained in B or A is a subset of B AB A contains B or B is a subset of A A B A cap B or A meet B or A intersection B
. Translating skills of mathematical articles:both translation from Chinese to English and English to Chinese
* Reading, writing and translation of mathematical materials should be brife, simple, exact and easy to be understood
one, ten, hundred, thousand,
ten thousand, hundred thousand, million.
3
Ten million, hundred million, billion···
Expressions of some basic mathematical signs:
7
Equal to zero point four two nine
, Be less than, be greater than
Example: ab,cd a is less than b, c is greater than d
, Be less than or equal to, be greater than or equal to
Example: x 3, read as x equals plus or minus 3
Multiplied by, times
Example: 5 6 read as 5 times 6 or 5 multiplied by 6
, Over or is to or divided by
Example: 2x 1 7 The absolute value of 2 times x plus 1 equals 7
Example: 3 read as 3 over 4, three quarters,
4
4 3 divided by 4
: Proportion
Example: 1 : 2 read as the ratio of 1 to 2
0 0
Percent, Per cent
Example: 2 0 0 read as 2 Percent