数学专业英语.doc

第二章 精读课文-入门必修2.1数学方程与比例（Mathematics，Equation and Ratio）一、词汇及短语：1. change the terms about 变形2. full of ：有许多的 充满的例 The streets are full of people as on a holiday(像假日一样，街上行人川流不息)3. in groups of ten4. match something against sb. “匹配”例 Long ago ,when people had to count many things ,they matched them against their fingers. 古时候，当人们必须数东西时，在那些东西和自己的手指之间配对。5. grow out of 源于 由引起例 Many close friendships grew out of common acquaintance6. arrive at 得出（到达 抵达 达到 达成）例 we both arrived at the same conclusion(我们俩个得出了相同的结论)7. stand for “表示，代表”8. in turn “反过来，依次”9. bring about 发生 导致 造成10. arise out of 引起 起源于11. express by“用表示”12. occur 发生，产生13. come from 来源于， 起源于14. resulting method 推论法15. be equal to 等于的 相等的例 Twice two is equal to four(2乘以2等于4)16. no matter 无论 不管17. mathematical analysis 数学分析18. differential equation 微分方程19. higher mathematics 高等数学 higher algebra 高等代数20. equation of condition 条件等式二 句型及典型翻译1. For a long period of the history of mathematics, the centric place of mathematical methods was occupied by the logical deductions“在数学史的很长的时期内，是逻辑推理一直占据数学方法的中心地位”2. An equation is a statement of the equality between two equal numbers or number symbols. equation ：“方程”“等式” 等式是关于两个数或数的符号相等的一种陈述3. In such an equation either the two members are alike, or become alike on performance of the indicated operation. 这种等式的两端要么一样，要么经过执行指定的运算后变成一样。注 “two members”表等号的两端 alike 相同的 一样的On the performance of 中的“on”引导一个介词短语做状语Eitheror4. is true “成立”5. to more and change the terms移次和变形without making the equation untrue 保持方程同解2.2几何与三角（Geometry and Trigondogy）一、词汇cube 立方体、 cylinder 柱体、 geometrical 几何的、 surface 曲面、plane 平面、 breadth 宽度、 segment 线段 弓形（面积）、abound 大量存在、 prerequisite 先决条件、 sphere 球 cone 圆锥、 triangle 三角形、 solid 立体的 立体、 straight line 直线、 line segment 直线段、 infinitely 无限地、broken line 折线、 diameter 直径、 angle 角、prerequisite 先决条件、 chord 弦、 blind acceptance of 盲目接受二、典型句子翻译1. Many leading institutions of higher learning have recognized that positive benefits can be gained by all who study this branch of mathematics.其中“higher learning”表示“高学识”“博学” Positive “确实的”“肯定的”全句 许多居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收获。2.we find the land surveyors of these people re-establishing vanishing landmarks and boundaries by utilizing the truths of geometry 我们发现这些民族的土地测量者利用几何只是重新确定消失了的土地标志和边界。3.A circle is a closed curve lying in one plane, all point of which are equidistant from a fined point called the center.平面上到定点的距离等于定长的所有点组成的图形叫做圆。2.3 Basic Concepts of the Theory of SetsSection A1. sets are a means by which mathematicians talk of collections of things in an abstract way 注by which 引起一个定语从句 talk of “表达译为 集合是数学家们用抽象的方式来表达一些事物的集体的工具2. belong to “属于”3. even integers 偶数less than 小于more than 大于4. be denoted by 被记作5. be referred to as 被称为6. exactly the same 完全相同7. there fore , the definition requires that we call these sets equal .因此，根据定义我们认为这两个集合相等8. divisible by 被整除Section B1. For example, the set consisting of those positive integers less than 10. which are divisible by 4 is a subset of the set of all even integers less than.由小于10且能被4整除的正整数组成的集合是所有小于10的偶数集的子集2. “AB”读作A is contained in B or B contains A 3. A=BAB and BA A is equal to B if and only if A is contained in B，and B is also contained in A4. reference to 提到 涉及 关于5. 真子集 proper subset6. “” empty set 或 void set7. 单元集 one element set 2.4 整数 有理数与实数(Integers, Rational Numbers and Real Numbers)一、专业词语1 rational number 有理数 irrational number 无理数2. difference 差 quotient 商3 real axis 实轴4. fraction 分数 denominator 分母 numerator 分子5. 数学归纳法：proof by induction 二、Section-A Integers and rational numbers1. 1+1=2The number 1 plus 1 is denoted by 22. Strictly speaking 严格地说3. repeated addition of 1 “反复加1”4. Convenient method 简便方法5. ordered field 有序域6. The sum, difference , or product of two integers is an integer ,but the quotient of two integers need not be an integer. (两个整数的和、差或积是一个整数，但是两个整数的商未必是一个整数)思考 What is an inductive set?A set of real numbers is called an inductive set if it has the following two properties:(a) The number 1 is in the set (b)For every x in the set , the number x+1 is also in the set.三、Section-B Geometric interpretation of real number as points on a line1. be familiar with 熟悉 be familiar to 被某人熟悉2. If xy, the point x lies to the left of the point y“lies to ”位于如果xy, by x点位于y点的左侧3. This device for representing real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers这种用几何来表示实数的办法对于帮助我们更好地发现与理解实数的性质是非常有价值的。2.5笛卡儿几何学的基本概念（Basic Concepts of Cartesian Geometry）一、词组与词汇1. integral 积分的、整数的、积分2. calculation 计算3. the origin 坐标原点4. coordinate system 坐标系5 an ordered pair 一个有序对6. horizontal 水平的Perpendicular 垂直的7. 解析几何：analytic geometry二、Section A-The coordinate system of Cartesian geometry 1. As mentioned earlier, one of the applications of the integral is the calculation of area.译：计算图形的面积是积分的一种重要应用。2 .If we hope to arrive at a treatment of area that will enable us to deal with many different kinds of objects, we must first find an effective way to describe these objects. 译：如果我们希望获得面积的计算方法以便能用它来处理多种不 同类型的图形，我们就必须首先找出描述这些图形的有效办法。3 .On the x-axis a convenient point is chosen to the right of O and its distance from O is called the unit distance. 译：在x-轴上O点右边选定一个适当的点，并把它到O点的距离称为单位长度。4.It is clear that two ordered pairs (a,b) and (c,d) represent the same point if and only if we have a=c and b=d.译：易知当(a,b)与(c,d)表示同一点时当且仅当a=c b=dSection B Geometric figures 1. By translating these conditions into expressions, involving the coordinates x and y ,we obtain one or more equations which characterize the figure in question. 译：“the figure in question”在谈论中的图形，“该图形”通过把这 些条件转化成含有坐标x和y的表达式，我们就得到了一个或多个刻画该图形特征的方程。2. Throughout their historical development, calculus and analytic geometry have been intimately intertwined.译：微积分与解析几何在它们的发展史上已经互相融合在一起了。3. A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and this study will be carried out in later chapters using vector methods as well as the methods of calculus. 译：如果想拓展微积分的范围与应用，需要进一步研究解析几何，而这种研究需要用到向量的方法。2.6函数的概念与函数思想(Function concept and function idea)一、 生词与词组cake 立方体 edge 棱、边 prime 素数（质数） displacement 位移 generalization 推广 domain 区域 定义域 range 值域 范围 function idea 函数思想 real-valued functions 实值函数 the triangle inequality 三角不等式 real variable 实变量 the identity function 恒等函数 absolute-valued function 绝对值函数 schematic representation 图解表示 二、 经典句型Section A Informal description of functions1. Various fields of human have to do with relationships that exist between one collection of objects and another. 译：各行各业的人们都必须处理一类事物与另一类事物之间存在的各种关系2. The force F necessary to stretch a steel spring a distance x beyond its natural length is proportional to x. 译：把一条弹簧伸到超过其自然长度的距离x时所需要的力F与x成正比。3. That is 换句话说4. 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. 译：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。Section-B1. The function idea may be illustrated schematically in many ways.译：可以用许多方式给出函数思想的图解说明。2. The identity function 单位函数3. absolute-value function 绝对值函数作业；P48. 22.7 序列及其极限（ Sequences and Their Limits）一、 生词与词组1.succession 连续 2.sequence 序列 数列 3.series 级数 序列 4.infinite sequence 无穷序列 5.event 事件 6.recursion formula 递推公式 7.complex-valued sequence 复值序列 8.real-valued sequence 实值序列 9.the positive integers=the set of all positive integers 正整数集 10.assume 假定 11.convergence 收敛 12.divergent 发散的 Converge to 收敛于 diverge 发散 Convergent 收敛的 divergence 发散二、句型翻译1. In everyday usage of the English language, the words “sequence” and “series” are synonyms, and they are used to suggest a succession of things or events arranged in some order.译：在日常英语中，单词“sequence”和“series”是同义词，用以表示按某种次序排列的一串东西或事件。 2. The word “sequence” is employed as in the common use of the term to convey the idea of a set of things arranged in order, but the word “series” is used in a somewhat different sense.译：像通常用法一样，术语“sequence”用以表达按次序排列的一串东西的意思，但是“series”一词则用于某种别的意思。3. Another common way to define a sequence is by a set of instructions which explains how to carry on after a given start.译：另一种常用的定义序列的方法是，通过一串指令说明在给定初项后如何给出后面一项。4.It is clear that句型2.8 函数的导数和它的几何意义The Derivative of a function and its Geomtric Interpretation一、 词汇：1、derivate 导数 differentiation 微分法 The first derivate 一阶导数 The second derivate 二阶导数2. numerator 分子3. constant 常数4. interval 区间 线节 open interval close interval5. velocity 速度 Acceleration 加速度 Instantaneous 瞬时速度6. average 平均average value 平均值average rate 平均变化率7. function 函数 position function 位置函数 linear function 线性函数8. approach 趋于 逼近approach zero 09. geometric interpretation 几何解释10.respective coordinates 相应的坐标11. altitude 高度12. slope 坡度 Steepness 陡峭13. tangent 正切 切线14. bound 齐 without bound=boundlessSection A The derivate of a function 1. at least 至少2. whetheror不管还是3. The quotient itself is referred to as the average rate of the change of f in the interval joining x to x+h译：商差表示函数f在连接x与x+h的区别上的平均变化率。4. The derivative of f at x5. formal definition 正式定义6. f prime of x7. provided=providing that8. the rate of change of f at x (f在点的变化率)9. with respect to 关于10. In general, the limit process which produces from gives us a way of obtaining a new function from a given function .11. the nth derivative of Section B: Geometric interpretation of the derivative as a slope.12.When this is interpreted geometrically it tells us that ,as gets nearer to 0, the point P remains fixed ,Q moves along the curve toward P .,and the line though PQ changes its direction in such a way that its slope approaches the number as a limit .译：其几何意义为，当h0时，点p保持不动，而点Q沿曲线趋近P;同时，经过的PQ直线以这样的方式改变方向，即斜率趋近数值，并以它为极限作业：阅读：Section-C Logarithms （对数）2.9微分方程简介Introduction to Differential EquationsSection A Introduction1. A large variety of scientific problems arisein which(修饰problems) one tries to determine something from its of change (变化率)A large variety of(大量的)2.moving particle 运动粒子3.radioactive substance 放射性的物质4.a given time 给定时间5.differential equations 微分方程ordinary and partial 常微与偏微one variablemore variables6.exponential function 指数函数7.Thw study of differential equations is one part of mathematics that, perhaps more than any other, has been directly inspired by mechanics, astronomy ,and mathematical physics译：研究微分方程是数学中重要的一部分，微分方程的研究直接受到力学，天文学和数学物理的推动8.“special tricks ”技巧、诀窍9.in relatively few case 在相对少的情况下Section B Terminology and notation1. By A is meant B “A”的含义为“B”,“A”即“B”By the order of an equation is meant the order of thehighest derivate which appears. 2. differentiable function 微分函数3. f(x,y) is independent(无关)of y f(x,y) is dependent(有关)of y 4. We simply integrate Q and add any constant 我们直接对Q积分并加上任意常数5. polynomials 多项式rational function 有理函数trigonometric and inverse trigonometric functions. 三角函数与反三角函数 6. Automatic high-speed computing machines are often designed with this kind of problem in mind （行为方式状语）7. a first-order differential equation一阶微分方程8. a initial condition 初始条件an initial-value problem 初始问题作业：P65 2 ,32.10 线性相关与线性无关集 Dependent and Independent Sets in a linear Space一.生词与词组1.dependentindependent 相关的无关的2.linear space 线性空间3.The Pythagorean identity 毕达哥拉斯等式4.the induction hypothesis （假设）假设5.coefficient 系数6.linear combination 线性组合7.the subspace spanned by S 由S组成的子空间8.ordered basis 有序基9.finite（infinite）dimensional有（无）限维的10.unite coordinate vector 单位坐标向量11.multiple 倍数multiply 将乘上multiplication 乘法二、句型：1. DEFINTION : A set S of elements in a linear space V is called dependent if there is a finite set of distinct elements in S ,say and corresponding set of scalars not all zero ,such that .译：线性空间V的一组元素S称为相关的，如果在S中存在有限个元素，例如 和相应的一组不全为0的数使得：.Ex1: If a subset T of a set S is dependent ,then S itself is dependent .This is logically equivalent to the statementthat every subset of an independent set is independent. Ex2: The empty set is independent.Ex3: If 0S, then S is dependent 2.the subspace spanned by S 由S张成的子空间3.THEOREM 10.5 Let S be an independent set consisting of k elements in a linear space V and let L(S) be the subspace spanned by S, then every set of k+1 elements in L(S) is dependent. 4 The same argument with S and T interchanged shows that KM 译: 把S与T交换后,做同样的讨论证明KM 5.The space of all polynomials p(t) of degreen has dimension n+1 (维数是n+1)译:阶数小于等于n的所有多次项式组成的空间维数是n+12.11 数理逻辑入门 Elementary Mathematical Logic一、 生词语词组：1. statement语句subject of the statement 语句的主语2. proposition 命题propositional 命题的；propositional function 命题函数3. predicate 谓词4. universe 通集，底集universe of discourse 论域，通集5. quantification 量词quantification 量词化universal quantifier 全称量词 quantification 全称量词化existential 存在量词 存在量词化6. inclusive exclusive 可兼的 不可兼的ambiguousunambiguous不清楚的 清楚的7. propositional connective 命题连词8. artificial intelligence 人工智能9. rule of inference 推演规则10. true 真 truth value 真假值二、 句型与符号表示1. These statements are neither true nor false when the values of the variables are not specified 注：specify values“指定取值”或“确定值”简称“ 赋值”译：若未给语句中的所有赋值，则不能判断语句是真是假2. 详解例题P763. 在逻辑运算中，主要的运算符号 译not(非)否定符号 译or(或)折取符号 译and(与)合取符号 译implies(蕴涵)蕴涵符号三、 详译课文并理解定义（略）作业：P80 2.,32.12 概率论与数理统计Probability theory and mathematical statistics 一，生词与词组 1、probability 概率 probability theory 概率论 probability space 概率空间 2、event 事件 impossible event不可能事件 certain event 必然事件3、universal set 通集 全集4、outcome 结束，结局5、statistics统计学mathematical statistics数理统计6、finitely additive measure 有限可加测度7、destructive nature 破坏性，有害的物质8、sampling unit 样本单位，样本个体9、combinatorial analysis 组合分析10、inference 推测，推断11、trial 试验，试用12、mutually 互斥的13、equally likely 同等可能的14、probability zero 零概率二，句型1、The number