数学专业英语

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 ten…
4. 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 acquaintance
6. 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
Either…or…
4.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 Sets
Section A
1.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 B
1.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.“A⊆B”读作A is contained in B or B contains A
3.A=B⇔A⊆B and B⊆A
A is equal to
B if and only if A is contained in B，and B is also contained in A
4.reference to 提到涉及关于
5.真子集proper subset
6.“φ” empty set 或void set
7.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 numbers
1.1+1=2
The number 1 plus 1 is denoted by 2
2.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 line
1.be familiar with 熟悉…
be familiar to 被某人熟悉
2.If x<y, the point x lies to the left of the point y
“lies to ”位于
如果x<y, 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=d
Section 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 functions
1. 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-B
1. 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. 2
§2.7 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
plex-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 “seri e s” 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 tha t…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 interval
5. 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 →0
9. 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=boundless
Section A The derivate of a function
1. at least 至少
2. whethe r …or …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 x
5. formal definition 正式定义
6. f prime of x →()f x '
7. provided=providing that
8. 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 ()f x ' from ()f x 'gives us a way of obtaining a new function f ' from a given function f .
11. the nth derivative of f ()n f
Section B: Geometric interpretation of the derivative as a slope.
12.When this is interpreted geometrically it tells us that ,as h 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
' as a limit .
slope approaches the number ()
f x
译：其几何意义为，当h→0时，点p保持不动，而点Q沿曲线趋近P;同时，经过
'，并以它为极限
的PQ直线以这样的方式改变方向，即斜率趋近数值()
f x
作业：阅读：Section-C Logarithms （对数）
§2.9微分方程简介
Introduction to Differential Equations
Section A Introduction
1. A large variety of scientific problems arise
in 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 variabl e～more variables
6.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 notation
1.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 the
highest 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 ,3
2.10 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.dependen t ～independent 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 1,
,,k x x and corresponding set of scalars 1,,,k c c not all zero ,such that
10k i i i c x
==∑.
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
1,,,k x x 和相应的一组不全为0的数1,,,k c c 使得：
10k i i i c x
==∑.
Ex1: If a subset T of a set S is dependent ,then S itself is dependent .This is logically equivalent to the statement
that every subset of an independent set is independent.
Ex2: The empty set is independent.
Ex3: If 0 S, 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 K≤M 译: 把S与T交换后,做同样的讨论证明K≤M
5.The space of all polynomials p(t) of degree≤n 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+1
§2.11 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
ambiguous～unambiguous
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P76
3.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.,3
§2.12 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 P(A) is also called the probability that an outcome of the experiment is one of the element of A.
“that”引起一个定语从句，修饰probability .
译：数又称为试验的结果是A的一个元素的概率
2、“Not more than one of A or B occurs .”
译：事件A与B至多只有一个发生
3、For instance , the treatment for an allergy may provide long-lasting relief for some individuals whereas it may bring only transient relief or even none at all to others.
译：例如，对一种过敏的治疗可以使某些人得到长时间的缓解，但对其他人可能只是短时间的缓解或者完全无效。

4、Likewise, it is unrealistic to expect that college freshmen whose high school records were alike would perform equally well in college .Nature does not follow such a rigid law
译：类似地，希望那些在高中时成绩一样的大学一年级新生在大雪中表现也一样好是不现实的，自然界不会遵循一个固定不变的规律运行。

5、In public opinion or consumer expenditure studies , a complete body of information would emerge only if data were gathered from every individual in the nation-undoubtedly a monumental if not an impossible task.
译: 在公众意见或顾客消费的统计研究中,要想得到一个完全的信息体,必须收集到该国家的每一个体的数据.无疑地,这个任务即使可能完成,也是极其庞大的. 6、To collect an exhaustive set of data related to the damage sustained by all cars of a particular model under collision at a specified speed ,every car of that model coming off the production lines would have to be subjected to a collision.
译: 如果要完全地收集某种特殊型号的汽车在一定速度之下碰撞时的耐损能力的有关数据，那么来自该生产线的该型号的每一辆汽车都要接受一场碰撞。

7、A statistical population is the set of measurements ( or record of some qualitative trait ) corresponding to the entire collection of units about which information is sought.
译：统计的总体是与有待于收集信息的个体组成的整体相对应的，有观测数据（或关于某种特性的纪录）组成的.
作业:P88,2,3
小学二（2）班班规
一、安全方面
1、每天课间不能追逐打闹。

2、中午和下午放学要结伴回家。

3、公路上走路要沿右边走，过马路要注意交通安全。

4、不能在上学路上玩耍、逗留。

二、学习方面
1、每天到校后，不允许在走廊玩耍打闹，要进教室读书。

2、每节课铃声一响，要快速坐好，安静地等老师来上课。

3、课堂上不做小动作，不与同桌说悄悄话，认真思考，积极回答问题。

4、养成学前预习、学后复习的好习惯。

每天按时完成作业，保证字迹工整，卷面整洁。

5、考试时做到认真审题，不交头接耳，不抄袭，独立完成答卷。

三、升旗排队和两操方面
1、升旗时，要快速出教室排好队，做到快、静、齐，安静整齐地排队走出课室门，班长负责监督。

2、上午第二节后，快速坐好，按要求做好眼保健操。

3、下午预备铃声一响，在座位上做眼保健操。

四、卫生方面
1、每组值日生早晨7：35到校做值日。

2、要求各负其责，打扫要迅速彻底，打扫完毕劳动工具要摆放整齐。

3、卫生监督员（剑锋，锶妍，炜薪）要按时到岗，除负责自己的值日工作外，还要做好记录。

五、一日常规
1、每天学生到齐后，班长要检查红领巾。

2、劳动委员组织检查卫生。

3、每天负责领读的学生要督促学生学习。

4、上课前需唱一首歌，由文娱委员负责。

5、做好两操。

6、放学后，先做作业，然后帮助家长至少做一件家务事。

7、如果有人违反班规，要到老师处说明原因。

班训：
坐如钟站如松快如风静无声
班规：
课堂听讲坐如钟，精神集中认真听；
排队升旗站如松，做操到位展雄风；
做事迅速快如风，样样事情记得清；
自习课上静无声，踏实学习不放松；
个人努力进步快，团结向上集体荣；
我为领巾添光彩，标兵集体记我功。

扣分标准
注：每人基本分60分起，学期末核算总分，作为学期评先依据。