数学专业英语课后答案
2.1数学、方程与比例
词组翻译
1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation
2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction
3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart
4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation
5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction
6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place
汉译英
（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。
Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches.
（2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。
No modern scientific and technological branches could be regularly developed without the application of mathematics.
（3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。
Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often.
（4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。
Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered.
（5）方程与算数的等式不同在于它含有可以参加运算的未知量。
Equation is different from arithmetic identity in that it contains unknown quantity which can join operations.
（6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it.
（7）方程很有用，可以用它来解决许多实际应用问题。
Equations are of very great use. We can use equations in many mathematical problems. （8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term.
英译汉
1.Algebra has evolved from the operations and rules of arithmetic.The study of arithmetic begins with addition,multiplication,subtraction,and division of
numbers:4+7,37×682,49-22,40÷8.
In algebra we introduce symbols or letters—such as a,b,c,d,x,y,z—to denote arbitrary numbers and，instead of special cases，we often consider general statements：a+b,cd,x-y,x÷a.
代数是从算术的运算和规则当中逐渐发展起来的，算术的研究是从数的加减乘除开始的。例如4+7，37×682，49-22，40÷8。
在代数学里,我们采用符号或字母。例如a,b,c,d,x,y,z来表示任意的数字，而
不考虑那些特殊情况。我们经常考虑的是一般的表达式，例如a+b,cd,x-y,x÷a。
2.The language of algebra serves a twofold purpose.First,we may use it as a shorthand to abbreviate and simplify long or complicated statements.Second,it proves a convenient means of generalizing many specific statements.
代数的语言有两个作用。第一个是使用它作为一种速记法去缩减和减化那些又长又复杂的表达。第二，它被证明是一种概括许多具体的表达方式的便捷途径。
3.Many expressions involve two or more operations.Grouping symbols tell us which operation is to be done first.The common grouping symbols are
parentheses,(),brackets.[],and the fraction bar,—.For example,in the expression
2(3+4),we do the addition first and then we do the multiplication:2(3+4)=2(7)=14.
许多数学表达式包含两个或更多的运算。分组符号告诉我们哪一个运算先做。常见的分组符号是圆括号，方括号和分数线。例如，在数学表达公式2（3+4）里。我
们先做加法再做乘法2（3+4）=2（7）=14
2.2 几何与三角
词组翻译
1.学会institution，建筑师architect, 机械师machinist, 制图员draftsman, 测量者surveyor, 木匠carpenter
2.点point, 端点endpoint, 线line, 直线straight line, 线段line segment, 曲线curved line, 折线broken line, 射线ray , 平面plane,曲面curved surface
3.立体solid, 柱体cylinder, 立方体cube,球sphere, 棱锥pyramid,圆锥cone ,
4.圆circle,圆心center, 直径diameter, 半径radius, 半圆semicircle, 弦chord, 弧arc, 优弧major arc, 劣弧minor arc
5.角angle, 边side, 三角形triangle, 直角三角形right triangle,斜边hypotenuse, 直
角边right-angle side
6.长度length,宽度breadth/width,厚度thickness, 位置position
7.几何的geometrical,立体的three-dimensional , 弯曲的curved,等距离的equidistant ,无限的infinite
8.培养创造力train originality,必须的毅力necessary perseverance ,
提高鉴赏力raise/improve the appreciation ability
9.消失了的边界vanishing boundaries/landmarks,有序性和优美感orderliness and sense of beauty, 几何图形大量存在geometric forms abound in , 定理成立的先决
条件a prerequisite to a theorem
汉译英
（1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。
Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology.
（2）西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古代的数学家对几何做了许多出色的研究。
The western experts think that geometry had its origin in the measurements by the Babylonians and Egyptians of their lands. Infect, the ancient Chinese mathematicians made much remarkable study for geometry.
（3）几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结论。
In studying geometry, the student is taught to think clearly and critically and he is led away from the practice of blind acceptance of any conclusions.
（4）数学培养学生的分析问题的能力，使他们能应用毅力、创造性和逻辑推理来解决问题。
Studying mathematics can develop the students’ ability to analy ze problems and utilizing perseverance, originality, and logical reasoning in solving the problem.
（5）几何主要不是研究数，而是形，例如三角形，平行四边形和圆，虽然它也与数有关。
Geometry mainly studies hot numbers but figures such as triangles, parallelograms and circles, though it is related with numbers.
（6）一个立体（图形）有长、宽和高；面（曲面或平面）有长和宽，但没有厚度；线（直线或曲线）有长度，但既没有宽度，也没有厚度；点只有位置，却没有大小。
A solid (figure) has length, width and height. A surface (curved surface or plane surface) has length and width, but no thickness. A line (straight line or curved line) has length, but no width and thickness. A point has position, but no dimension.
（7）射线从某个点出发无限延伸；两条从同一点出发的射线构成了角。这两条射线称为这个角的两边，当这两边位于同一直线上且方向相反时，所得的角是平角。
A ray starts from a point and extends infinitely far. Two rays starting from one point form an angle, which are called two edges of the angle. When two edges lie in the same line and have opposite direction named plane angle.
（8）平面上的闭曲线当其中每一点到一个固定点的距离均相等时叫做圆。这个固定点称为圆心，经过圆心且其两个端点在圆周上的线段称为这个圆的直径，直径的一半叫做半径，这条曲线的长度叫做周长。
A circle is a closed curve lying in one plane, all points of which are equidistant from a fixed point. The fixed point called the center. A diameter of a circle is a line segment through the center of the circle with endpoints on the circle. Half of the diameter is called radius. The length of the circle is called circumference.
英译汉 1.In geometry an angle is defined as the set of points determined by two
rays l
1and l
2
having the same endpoint O. 在几何学里从同一点O出发引出的两
条射线l
1和l
2
所组成的点的集合叫做角。
2.In trigonometry we often interpret angles as rotations of rays.To obtain an angle we may start with a fixed ray l
1
having endpoint O,and rotate it about O,in a plane,to a
position specified by ray l
2.We call l
1
the initial side, l
2
the terminal side,and O the
vertex of angle. 在三角学里，我们经常解释角就是射线的旋转。在平面上，我们许会从端点是O的射线l
1
开始让它绕着端点O旋转，转到一个位置，由射
线l
2标注。我们把l
1
叫做角的始边，l
2
叫做角的终边，O叫做角的顶点。
3.A right angle is a 90?angle . An angle θis acute if 0?<θ<90?or obtuse if
90?<θ<180?.A straight angle is a 180?angle .Two acute angles are complementary
if their sum is 90?.Two positive angles are supplementary if their sum is 180?. 直
角就是一个90?的角。如果0?<θ<90?把它叫做锐角，如果90?<θ<180?叫做
钝角。平角就是一个180?的角。如果两个锐角的和是90?，那么这两个角互为
余角。如果两个正角的和是180?，那么这两个角是互为补角。
2.3集合论的基本概念
单词、词组
1.1集set，子集subset，真子集proper subset，全集universal subset，空集void/
empty set，基地集the underlying set
1.2正数positive number，偶数even integer，图形diagram，文氏图Venn diagram，
哑标dummy index，大括号brace
1.3可以被整除的be divisible by，两两不同的distinct from each other，确定的
definite，无关紧要的irrelevant/inessential
1.4一样的结论the same conclusion，等同的效果equivalent effect，用大括号表示集
sets are designated by braces，把这个图形记作A：this diagram is designated by letter A，区别对象to distinguish between objects，证明定理to prove theorems，把结论可视化to visualize conclusions/consequences
汉译英
（1）由小于10 且能被 3 整除的正整数组成的集是整数集的子集。
The set consisting of those positive integers less than 10 which are divisible by 3 is a subset of the set of all integers.
（2）如果方便，我们通过在括号中列举元素的办法来表示集。
When convenient, we shall designate sets by displaying the elements in braces.
（3）用符号?表示集的包含关系，也就是说，式子 A ? B 表示 A 包含于B。
The relation ?is referred to as set inclusion; A?B means that A is contained in B. （4）命题 A ? B 并不排除 B ? A 的可能性。
The statement A?B does not rule out the possibility that B?A.
（5）基础集可根据使用场合不同而改变。
The underlying set may vary from one application to another according to using occasions.
（6）为了避免逻辑上的困难，我们必须把元素x 与仅含有元素x 的集{x}区别开来。
To avoid logical difficulties, we must distinguish between the element x and the set {x} whose only element is x.
（7）图解法有助于将集合之间的关系形象化。
Diagrams often help using visualize relationship between sets.
（8）定理的证明仅仅依赖于概念和已知的结论，而不依赖于图形。
The proofs of theorems rely only on the definitions of the concepts and known result, not on the diagrams.
英译汉
1.If A is the set of all the letters of the alphabet，then listing each of elements would be tedious. So we write A={a,b,c,…,z}.
如果A是所有字母的集合，那么把每一个其中的字母列举出来将是很冗长乏味的，因此我们写出A=｛a，b，c，…,z｝。
2.In the set A，the last element is z. Many sets do not have last elements . Two important sets are N , the set of natural numbers , and W , the set of whose numbers . To list all the elements in these sets would be impossible because they go on forever . So we use three dots and write N={1,2,3,…},W={0,1,2,3,…}.
在集合A里,最后一个元素是z，许多集合没有最后一个元素，两个重要的集合是N，自然数集合，和W，整数的集合。把这两个集合里所有的元素列举出来是不可能的，因为它们是永远持续下去的，所以我们用三个点来表示，集合N写成
N={1,2,3,…}，集合W写成W={0,1,2,3，…}。
3.The whole numbers have many important subsets . A whole number is said to be even if it is divisible by 2；2,6,and 18 are examples of even numbers. A whole number is said to be odd if it is not divisible by 2 ; 1,7,and 13 are examples of odd numbers . The natural numbers greater than 1 are called prime or composite , A number is prime if it is divisible only by 1 and itself , A number is composite if it is divisible by a natural number other than 1 and itself.
整数有许多重要的子集。如果一个整数能被2除开就是偶数；2，6，18就是偶数的例子。一个整数如果不能被2整除就是奇数；1，7，13就是奇数的例子。大于1的自然数叫做素数或者合数，如果一个自然数只能被1和它本身整除，那么这个数就是素数（质数），如果一个自然数除了能被1和它本身整除外，还可以被其他的自然数整除，就叫做合数。
2.4整数、有理数与实数
1.单词
1）Integer rational number irrational number，real number，negative number，the negative，real line，real axis，scale，to the left/right of
2）sum，difference，product，quotient，power，inequality
3）axiom，the field axiom，the order axiom
4）ordered，entirely complete，Euclidean，appropriate，distinguished，illuminating 5）can be deduced formula，formula interchangeably，using a set of formulas，corresponding to an object，proof by induction，the two set to be distinguished
2、汉译英
（1）严格说，这样描述整数是不完整的，因为我们并没有说明“依此类推”或“反复加1” 的含义是什么。
Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”.
（2）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。The sum, difference, or product of two integers is an integer, but the quotient of two integers need not be an integer.
（3）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。
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.
（4）几何经常为一些特定的定理提供证明思路（建议），而且，有时几何的论证比纯分析的（完全依赖于实数公理的）证明更清晰。
The geometry often suggests the method of proof of a particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof (one depending entirely on the axioms for the real numbers).
（5）一个由实数组成的集若满足如下条件则称为开区间（open interval）。
If a set consisting of real numbers satisfies the following conditions we call it an open interval.
（6）实数 a 是-a 的相反数，它们的绝对值相等，且当 a ≠ 0 时，其符号不同。The real number a is the negative number of –a and their absolute values are equal. When a ≠ 0, their notations are different.
（7）每个实数刚好对应着实轴上的一点，反之，对实轴上的每一点，有且只有一个实数与之对应。
Each real number corresponds to exactly one point on this line and, conversely, each point on the line corresponds to one and only one real number.
（8）在几何上，实数之间的次序关系可以在数轴上清楚地表示出来。
In geometry, the ordering relation among the real numbers can be expressed clearly in real axis.
3. 英译汉
1）一个常见的错误是认为x 是一个负数。但x 可以为正数、0 或负数，这取决于x 的值
2）我们在最后一节中介绍的每个属性是唯一的操作，例如，ab =ba和0 + a= a，我们现在考虑一个连接加法和乘法的属性。它被称为分配律或者乘法对加法的分配，用下面的公式表所示：a（b + c) = ab + ac；（b + c) =ba + ca。
3）考虑小数按自然数顺序写出为：123456789101112131415…由于自然数数字不会中止或重复，这是一个无限不循环小数，不能转换为两个整数的比的小数叫做无理数，这组数字是指符号H，H={×：x是无限不循环小数}
2.5 笛卡儿几何学的基本概念
1. 翻译单词、词组、短语
(1)解析几何analytic geometry 笛卡儿几何Cartesian geometry
三维的three-dimensional, 坐标coordinate,坐标系coordinate system, 坐标原点the origin, 横坐标abscissa,坐标轴coordinate axis,纵坐标ordinate，象限quadrant,有序对ordered pair, 尺度scale,单位长度the unit distance
(2)向量vector, 线段line segment, 垂直的perpendicular,水平的horizontal, 竖直的vertical, 相交intersect，交点a point
(3)三角形triangle, 直角三角形right triangle, 斜边hypotenuse, 直角边leg,区域area/region, 多边形的polygonal, 多边形区域polygonal region,抛物线的parabolic, 抛物线弓形parabolic segment circular, 圆的circular，圆域circular region
(4)积分的计算integral calculation, 整数的性质integral quality, 微积分的基本定理basic theorem of calculusp
(5)对符号做适当认定an appropriate regard for signs,
把一个问题转化为另一个问题to reduce a question to another question,
把条件翻译成表达式to translate these conditions into expressions ，
紧密融合在一起inntimately intertwined，
刻画了该曲线的特征to characterize the curve in question
2.汉译英
（1）计算图形的面积是积分的一种重要应用。
The calculation of figure area is the important application of the integral.
（2）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。
On the x-axis a convenient point is chosen to the right of O and its distance from O is called the unit distance.
（3）对xy-平面上的每一个点都指定了一个数对，称为它的坐标。
Each point in the xy-plane is assigned a pair of numbers, called its coordinates.
（4）选取两条互相垂直的直线，其中一条是水平的，另一条是竖立的，把它们的交点记作O，称为原点。
Two perpendicular reference lines are chosen, one horizontal, the other vertical. Their point of intersection, denoted by O, is called the origin.
（5）当我们用一对数（a, b）来表示平面的点时，商定要把横坐标写在第一个位置上。
When we write a pair of numbers such as (a, b) to represent a point, we agree that the abscissa or x-coordinate, a, is written first.
（6）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。
Throughout their historical development, calculus and analytic geometry have been intimately intertwined.
（7）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，而这种研究需用到向量的方法。
A deeper study of analytic geometry is needed to extend the scope and applications of calculus, and this study will be carried out using vector methods.
（8）今后我们要对三维解析几何做详细研究，但目前只限于考虑平面解析几何。We shall discuss three-dimensional Cartesian geometry in more detail later on; for the present we confine our attention to plane analytic geometry.
2.6函数的概念与函数思想
1.1）function，domain，range，the identity function，the absolute-value function，the real-valued
2）cube，volume，edge-length，prime，totality
3)Hooke's law，stretch，displacement，spring，constant，proportional
4）schematic representation，plot，image，output，input
5）it is not difficult to imagine，the idea was much too limited
2.汉译英
（1）常用英语字母和希腊字母来表示函数。
Letters of the English and Greek alphabets are often used to denote functions.
（2）若 f 是一个给定的函数，x 是定义域里的一个元素，那么记号f(x)用来表示由f 确定的对应于x 的值。
If f is a given function and if x is an object of its domain, the notation f(x) is used to designate that object in the range which is associated to x by the function f.
（3）该射线将两个坐标轴的夹角分成两个相等的角。
The ray makes equal angles with the coordinates axes.
（4）可以用许多方式给出函数思想的图解说明。
The function idea may be illustrated schematically in many ways.
（5）容易证明，绝对值函数满足三角不等式。
It is easy to proof that the absolute-value function satisfies the triangle inequality.
（6）对于实数x>0，函数g(x)表示不超过x 的素数的个数。
For a given real number x>0, the function g(x) is defined by the number of primes less than or equal to x.
（7）函数是一种对应，它未必可以表示成一个简单的代数公式。
A function is a correspondence. It is not necessary to be expressed by a simple algebraic formula.
（8）在函数的定义中，关于定义域和值域中的对象，没对其性质做出任何限制。
The function idea places no restriction on the nature of the objects in the domain X and in the range Y.
2.7 序列及其极限序列及其极限
（1）序列各项对n 的相关性常利用下标来表示，写成如下形式： a n , x n 等。The dependence of every team of sequence on n is denoted by using subscript, and we write a n , x n and so on.
（2）以正整数集为定义域的函数称为序列。
A function whose domain is the set of all positive integers is called an infinite sequence. （3）一个复值序列收敛当且仅当它的实部和虚部分别收敛。
A complex-valued sequence converges if and only if both the real part and the imaginary part converge separately.
（4）一个序列{ a n }若满足：对任意正数ε ，存在另一个正数N （N可能与ε 有关）使得a n - L < ε 对所有n ≥ N 成立，就称{ a n }收敛于L。
A sequence { a n } is said to have a limit L if, for every positive number ε , there is another positive number N (which may depend on ε ) such that In this case, we say the sequence { a n } converges to L. an ? L < ε for all n ≥ N.
（5）重要的是，该集的每一个成员都用一个正整数标上记号。这样一来，就可以谈论第一项、第二项和一般项，即第n 项。
The important thing is that each member of the set has been labeled with an integer so that we may speak of the first term, the second term and in general, the nth term.
（6）若无另加申明，本章研究的序列都假定具有实的项或复的项。
Unless otherwise specified, all sequences in this chapter are assumed to have real or complex terms.
（7）作为日常用语，sequence 和series 是同义词；但作为数学术语，它们表示不同的概念。
In everyday usage of the English language, the words “sequence” and “series” are synonyms, but in mathematics these words have special technical meanings.
（8）术语“收敛序列”指的是具有有限极限的序列，因此，极限为无限的序列不是收敛的，而是发散的。
The phrase “convergent sequence” is used only for a sequence whose limit is finite. A sequence with an infinite limit is said to diverge not convergence.
2.8 函数的导数和它的几何意义
（1）差商表示函数 f 在连接x 与x+h 的区间上的平均变化率。
The different quotient is referred to as the average rate of the change of f in the interval joining x to x+h.
（2）速度等于位置函数的导数。
Velocity is equal to the derivative of positing.
（3）由定义导数的过程所提供的几何解释以一种自然的方式导出了关于曲线的切线思想。
The procedure used to define the derivative has a geometric interpretation which leads in a natural way to the idea of a tangent line to a curve.
（4）差商表示直线PQ 与水平线的夹角的正切。
The difference quotient represents the trigonometric tangent of the angle that PQ makes with the horizontal.
（5）在直线运动中，速度的一阶导数称为加速度。
For rectilinear motion, the first derivative of velocity is called acceleration.
（6）我们约定f（0）=f，即函数 f 的零阶导数就等于它本身。
We make the convention that f（0）=f, that is the zeroth derivate is the function itself. （7）在运动的9 秒钟内，物体的速度由v (0) = -144 变成了v (9) =144，也就是说，速度总共增加了每秒288 英尺。
During the 9 seconds of motion the velocity changes from v (0) = -144 to v (9) =144, that is, the total increase in velocity is 288 feet per second.
（8）当α 从0 增加到π/2 时，tan α 所对应的直线趋于竖直位置。As α increases from 0 to π/2 , tan α approach a vertical position.
2.9 微分方程简介
（1）此时，微分方程就有无穷多个解，C的每个值对应一个解。
The differential equation has infinitely many solutions, one for each value of C.
（2）微分方程的阶指的是方程中最高阶导数的阶。
By the order of an equation is meant the order of the highest derivative which appears. （3）我们可以由已知的粒子运动速度或者加速度计算出粒子的位置。
We could try to compute the position of a moving particle from a knowledge of its velocity or acceleration.
（4）如果一个微分方程的未知函数是多元函数，则称为偏微分方程。
Ordinary and partial, depend on whether the unknown is a function of just one variable or of two or more variables.
（5）微分方程的研究直接受到力学、天文学和数学物理的推动。
The study of differential equations has been directly inspired by mechanics, astronomy, and mathematical physics.
（6）许多应用问题要求我们从方程的解集中选出一个在某个点具有指定值的解。In many problems it is necessary to select from the collection of all solutions one having a prescribed value at some point.
（7）确定满足边界条件的解的问题称为边值问题。
The problem of determining such a solution that satisfies boundary condition is called a boundary-value problem.
（8）人们设计许多高速运行的计算机来对各种积分做出近似估计。
Automatic high-speed computing machines are often designed with this kind of problem in mind.
2.10 线性空间中的相关与无关集
（1）该式的两边同时关于t积分，我们就得到一个所需要的结论。
Integrating both sides of this formula with respect to t. we can obtain a conclusion we need.
（2）不难看出，这个命题仅仅建立在该空间是线性的这一事实上，与空间的其他性质无关。
We clearly find that this proposition is based only on the fact that this space is a linear space and not on any other special property of this space.
（3）如果空间不存在有限基，就称该空间是无限维的。
A space is called infinite dimensional if it doesn’t have a finite basis.
（4）假定这个结论对n-1个指数函数成立，我们将证明此结论对n个指数函数也成立。
Assuming the conclusion is true for n-1 exponential functions, we will prove that it is true for n exponential function.
（5）这两个定义在逻辑上是互相等价的。
These two definitions are logically equivalence.
（6）设X是线性空间V中k个元素组成的一个线性无关集合，L（X）是由X张成的子空间。那么，L（X）的每一个元素都可以表示成X的元素的线性组合。Let X be an independent set consisting of k elements in a linear space V and let L（X）be the subspace spanned by X, then each element of L(X) can be expressed as a linear combination of element of X.
（7）设V是一个n维线性空间，考虑它的一个基，其元素按给定的次序排列为错误！未找到引用源。，错误！未找到引用源。，…，错误！未找到引用源。。
Let V be a linear space of dimension n and consider a basis whose elements 错误！未找到引用源。, 错误！未找到引用源。, … , 错误！未找到引用源。are take in a given order.
（8）该线性表示的系数构成一个n元组，它由向量x唯一确定。
The coefficients in this linear representation determine an n-tuple of numbers that is uniquely determined by x.
数学专业英语
数学专业英语课后答案
2.1数学、方程与比例 词组翻译 1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation 2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction 3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart 4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation 5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction 6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place 汉译英 （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。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。
数学专业英语课后答案
2.1 数学、方程与比例 （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。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。 Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。 Equations are of very great use. We can use equations in many mathematical problems. （8）解方程时要进行一系列移项和同解变形，最后求出它的根，即未知量的值。To solve the equation means to move and change the terms about without making the equation untrue, until the root of the equation is obtained, which is the value of unknown term. 2.2 几何与三角 （1）许多专家都认为数学是学习其他科学技术的必备基础和先决条件。 Many experts recognize that mathematics is the necessary foundation and prerequisite of studying other science technology. （2）西方国家的专家认为几何起源于巴比伦和埃及人的土地测量技术，其实中国古代的数学家对几何做了许多出色的研究。 The western experts think that geometry had its origin in the measurements by the Babylonians and Egyptians of their lands. Infect, the ancient Chinese mathematicians made much remarkable study for geometry. （3）几何的学习使学生在思考问题时更周密和审慎，他们将不会盲目接受任何结论。 In studying geometry, the student is taught to think clearly and critically and he is led away from the practice of blind acceptance of any conclusions. （4）数学培养学生的分析问题的能力，使他们能应用毅力、创造性和逻辑推理来解决问题。
数学专业英语课后答案
2.1数学、方程与比例 词组翻译 1.数学分支branches of mathematics，算数arithmetics，几何学geometry，代数学algebra，三角学trigonometry，高等数学higher mathematics，初等数学elementary mathematics，高等代数higher algebra，数学分析mathematical analysis，函数论function theory，微分方程differential equation 2.命题proposition，公理axiom，公设postulate，定义definition，定理theorem，引理lemma，推论deduction 3.形form，数number，数字numeral，数值numerical value，图形figure，公式formula，符号notation(symbol)，记法/记号sign，图表chart 4.概念conception，相等equality，成立/真true，不成立/不真untrue，等式equation，恒等式identity，条件等式equation of condition，项/术语term，集set，函数function，常数constant，方程equation，线性方程linear equation，二次方程quadratic equation 5.运算operation，加法addition，减法subtraction，乘法multiplication，除法division，证明proof，推理deduction，逻辑推理logical deduction 6.测量土地to measure land，推导定理to deduce theorems，指定的运算indicated operation，获得结论to obtain the conclusions，占据中心地位to occupy the centric place 汉译英 （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。 Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. （2）如果没有运用数学，任何一个科学技术分支都不可能正常地发展。 No modern scientific and technological branches could be regularly developed without the application of mathematics. （3）符号在数学中起着非常重要的作用，它常用于表示概念和命题。 Notations are a special and powerful tool of mathematics and are used to express conceptions and propositions very often. （4）17 世纪之前，人们局限于初等数学，即几何、三角和代数，那时只考虑常数。 Before 17th century, man confined himself to the elementary mathematics, i. e. , geometry, trigonometry and algebra, in which only the constants were considered. （5）方程与算数的等式不同在于它含有可以参加运算的未知量。 Equation is different from arithmetic identity in that it contains unknown quantity which can join operations. （6）方程又称为条件等式，因为其中的未知量通常只允许取某些特定的值。Equipment is called an equation of condition in that it is true only for certain values of unknown quantities in it. （7）方程很有用，可以用它来解决许多实际应用问题。
数学专业英语期中测试
数学专业英语期中测试要求 将下列论文的摘要翻译为英语（按照学号顺序每个人分一个题目）。标题字体为黑体，字号三号，“摘要”二字以及“关键字”三字黑体，字号小四，其它字体为宋体，字号小四。行间距都为1.5倍行距。每人把自己要翻译的中文拷贝下来，然后在后面把它翻译为英文(英文字号与中文一样，字体为Times new roman，黑体的地方改为加粗)，写上姓名，学号（格式如下面的例子），打印出来交给我。大家认真做一下，你们写毕业论文要用到，学一学怎样写规范的文章，包括文章的排版（上学期反复强调交给我的matlab程序的打印的格式，结果有人交给我的程序竟然有上百页，字体很大，行距很大，还单面打印！（按照要求做的话只要几页就够了）有些人老是听不进老师讲的话！这样做既劳民伤财又不利于存档）。大家做好以后交到学习委员处，学习委员收齐以后交来给我，期末之前给我就行。 例子 中文标题 （姓名：学号：） 摘要 这是摘要正文…… …… 关键字：关键字1；关键字2；关键字3 English title （name: ,student id: ） Abstract This is the content of the abstract…… …… Keywords: keywords1; keywords2; keywords3;
1.泰勒公式的证明及其应用 摘要 本文先叙述并证明了不同条件下的泰勒公式，并进行了比较。然后讨论了泰勒公式在不同领域中的应用。本文着重论述了带有积分余项，拉格朗日余项和佩亚诺余项三种形式的泰勒公式，并比较了带不同余项的泰勒公式的异同。泰勒公式是数学分析中的重要知识，在理论分析和实际中都有广泛的应用。本文讨论了泰勒公式在10个方面的应用：利用泰勒公式求极限和导数，求无穷远处极限，证明中值公式，中值点的极限，证明不等式，导数的中值，估计关于界的估计，方程中的应用以及在近似计算中的应用。 关键词：泰勒公式；积分余项；佩亚诺余项；拉格朗日余项 2.论中学数学学习中的性别差异及其对成绩的影响 摘要 通过对初、高中两所学校男女学生数学成绩的调查，从智力、非智力、教育、社会环境等方面差异进行分析研究，得出性别差异对学生数学成绩有影响，并且随着年级的升高，男女生的数学成绩存在显著的差异。并提出了提高女生数学成绩应注意的几个方面。 关键词：中学生性别差异数学成绩因性施教 3.论在数学教学中培养学生的创新精神 摘要
数学专业英语一次函数专题
“数学专业英语一次函数专题”教学设计 1. 教学内容及解析 教学内容：与直角坐标系及一次函数相关的英语文献资料 内容解析：本节内容应从两个方面去考虑. 一方面，从数学知识的角度，本节所涉及的是从平面直角坐标系到一次函数的数学知识，都是学生学过的基础知识及其应用，是对于这些知识的拉练式复习，并作为后面用英语叙述解答相关问题知识基础；另一方面，从语言的角度，学生会接触到大量没有接触过，但他们却很熟悉的英语词汇及短语，主动学习的学生可以在老师的指导下快速理解其含义并加入到自己的知识体系中，但需要花时间巩固，是需要读、写、说来巩固的内容. 这也正是本节的重点和难点所在. 2. 教学目标及解析 教学目标：①能根据已有的数学知识和给出的单词对照表，将给出的相关数学定理及结论的英语版本翻译为中文；②能理解并解答用英语表述的相关数学问题；③能将解决数学问题的过程用英语进行书面表述；④初步了解用英语表达与直角坐标系及一次函数相关数学理论的范式. 目标解析：学生掌握基本词汇，并能阅读与本节内容相关的英语文献，是学习和使用数学专业英语的最基本要求，学生需要在学习的过程中逐渐由接受，即阅读或聆听，逐渐向输出，即书面和口头表达的方向发展. 为达到此目标，学生需要在课前独立完成对于本节需要的单词的学习，并阅读一系列简短的相关数学文献，并在这个过程中初步体会数学专业英语的表达范式；在课堂上，在教师的指导下对自己的认知进一步补充，并进行一定量的练习，暴露自己的问题，在教师的帮助下修正问题，完善认知. 3. 教学问题诊断分析 学生在进行语言表达时，往往受到母语的限制，对于非母语的表达方式的接受能力一时难以习惯，而数学对于表达能力则有更高的要求，要求叙述简洁、逻辑清晰，因此本教学设计强调学生在有相当阅读量的积累后，通过自主练习，逐渐感受用英语表达数学理论的基本范式. 教师在教学过程中的主要任务在于为学生提供合适的学习资料，在学生学习的过程中给予提示与指导，及时指出学生的问题并予以纠正. 对于语言的学习，阅读量的积累是至关重要的，教师在课堂上的讲解、学生在课堂上的练习，都只是学习的一部分环节，如果需要帮助学生正确掌握表达数学理论的范式，尽量不留死角，就必须保证课前预习和课后复习的有效性，预习复习材料的充足性，这对教师的教学资料的积累和学生自主学习能力，都是一个挑战. 4. 教学支持条件分析 学情条件：初二8班是实验班，学生有较强的学习热情和好奇心，也知道课前预习、课上参与学习活动、课后复习的重要性，在曾经的数学课程教学中，也有一定的课前预习，课堂讨论的传统，对于本教学设计的各个环节，是可以理解教师的用意，并遵循教师的指导进行学习活动. 在知识层面上，学生已经系统学习过一次函数相关的知识，课程中提供的学习资料都是学生熟悉的数学知识；学生在英语学习上，已经有多年的积累，对于英语语法的学
数学专业英语第二版-课文翻译-converted
2.4 整数、有理数与实数 4－A Integers and rational numbers There exist certain subsets of R which are distinguished because they have special properties not shared by all real numbers. In this section we shall discuss such subsets, the integers and the rational numbers. 有一些R 的子集很著名，因为他们具有实数所不具备的特殊性质。在本节我们将讨论这样的子集，整数集和有理数集。 To introduce the positive integers we begin with the number 1, whose existence is guaranteed by Axiom 4. The number 1+1 is denoted by 2, the number 2+1 by 3, and so on. The numbers 1,2,3,…, obtained in this way by repeated addition of 1 are all positive, and they are called the positive integers. 我们从数字 1 开始介绍正整数，公理 4 保证了 1 的存在性。1+1 用2 表示，2+1 用3 表示，以此类推，由 1 重复累加的方式得到的数字 1,2,3，…都是正的，它们被叫做正整数。 Strictly speaking, this description of the positive integers is not entirely complete because we have not explained in detail what we mean by the expressions “and so on”, or “repeated addition of 1”. 严格地说，这种关于正整数的描述是不完整的，因为我们没有详细解释“等等”或者“1的重复累加”的含义。 Although the intuitive meaning of expressions may seem clear, in careful treatment of the real-number system it is necessary to give a more precise definition of the positive integers. There are many ways to do this. One convenient method is to introduce first the notion of an inductive set. 虽然这些说法的直观意思似乎是清楚的，但是在认真处理实数系统时必须给出一个更准确的关于正整数的定义。有很多种方式来给出这个定义，一个简便的方法是先引进归纳集的概念。 DEFINITION OF AN INDUCTIVE SET. A set of real number s is cal led an i n ductiv e 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. For example, R is an inductive set. So is the set . Now we shall define the positive integers to be those real numbers which belong to every inductive set. 现在我们来定义正整数，就是属于每一个归纳集的实数。 Let P d enote t he s et o f a ll p ositive i ntegers. T hen P i s i tself a n i nductive set b ecause (a) i t contains 1, a nd (b) i t c ontains x+1 w henever i t c ontains x. Since the m embers o f P b elong t o e very inductive s et, w e r efer t o P a s t he s mallest i nductive 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。 This property of P forms the logical basis for a type of reasoning that mathematicians call proof by induction, a detailed discussion of which is given in Part 4 of this introduction.
江西理工大学数学专业英语考试重点2
一、数学符号翻译 12/156 twelve over one hundred and fifty-six 234/567 two hundred and thirty -four over five hundred and sixty-seven 4% four percent 7‰ seven permill 6.79 six point seven nine 52.3 three point two five recurring 85x the eighth root of x to the fifth power 53 x x to the minus three fifths dx x f b a )( f is integrable on [a,b] 32)(dx x f f is integrable on [2,3] x f the partial (derivative) of f with respect to x y f the partial (derivative) of f with respect to y 5lo g 3 the logarithm of five to the base three x a log the logarithm of x to the base a B A A cap B / A meet B / A intersection B B A A cup B / A join B / A union B A a a is an element of A B b b is an element of B 二、名词翻译 function theory 函数论 schematic representation 图解表示 geometry 几何学 trigonometry 三角学 consequence 推论 proposition 命题 theorem 定理 pyramid 棱锥 cone 圆锥 abscissa 横坐标 ordinate 纵坐标 coordinate system 坐标系 coordinate axis 坐标轴 polygonal region 多边形区域 tangent 切线 slope 斜率 complex-valued sequence 复值序列 convergence 收敛 real valued sequence 实值序列 divergence 发散 rational number 有理数 irrational number 无理数 odd number 奇数 even number 偶数 prime 质数、素数 composite 合数 plane 平面 surface 曲面 broken line 折线 Venn diagram 文氏图 universal set 全集 the underlying set 基础集 proper subset 真子集 quadratic equation 二次方程 the absolute-value function 绝对值函数
数学专业英语27528
第一章 数学专业英语的阅读和翻译初级阶段 1.1 数学专业英语的基本特点 一 注意对客观事实与真理的描述： 1. 语句事态的使用上常用一般现在时 例 An equation is a statement of the equality between two equal numbers or number symbols. 2. 被动语态出现频率高“It is …”句型也使用得多 例 It is cleat that any function defined for all positive real x may be used to construct a sequence by restricting x to take only integer values. 3. 主动语态句型也多数用于强调事实，而不是强调行为发出者及其情感 例 1：Given ε> 0，there exits a number N>0. such that ε<-a a n for all n ≥N 例 2：Since h(x) is harmonic on a neighborhood of B(a,r), we have )()()(a h x d x h B =? ?σ “we have ” =one has 可省略 译为 “可以得出”什么结论 二 科学内容的完整性与表达形式的精炼性要求 三 数学的专业性十分典型 1、有的概念可能有几个同义词 如“计算”有： count calculate calculation calculus compute computation 2、同一词根的次和词组很多，如： Integrability 可积性 integrable 可积的 integral 积分，积分的，整数的 integral calculus 积分学 integralization 整化 integrate 积分 3、半专业词汇多是出现频率高 如: function 函数 functional 泛函 power 幂 set 假定，令
数学专业英语第二版的课文翻译
1－A What is mathematics Mathematics comes from man’s social practice, for example, industrial and agricultural production, commercial activities, military operations and scientific and technological researches. And in turn, mathematics serves the practice and plays a great role in all fields. No modern scientific and technological branches could be regularly developed without the application of mathematics. 数学来源于人类的社会实践，比如工农业生产，商业活动，军事行动和科学技术研究。反过来，数学服务于实践，并在各个领域中起着非常重要的作用。没有应用数学，任何一个现在的科技的分支都不能正常发展。From the early need of man came the concepts of numbers and forms. Then, geometry developed out of problems of measuring land , and trigonometry came from problems of surveying . To deal with some more complex practical problems, man established and then solved equation with unknown numbers ,thus algebra occurred. Before 17th century, man confined himself to the elementary mathematics, . , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候，人类的需要产生了数和形式的概念，接着，测量土地的需要形成了几何，出于测量的需要产生了三角几何，为了处理更复杂的实际问题，人类建立和解决了带未知参数的方程，从而产生了代数学，17世纪前，人类局限于只考虑常数的初等数学，即几何，三角几何和代数。The rapid development of industry in 17th century promoted the progress of economics and technology and required dealing with variable quantities. The leap from constants to variable quantities brought about two new branches of mathematics----analytic geometry and calculus, which belong to the higher mathematics. Now there are many branches in higher mathematics, among which are mathematical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速发展推动了经济技术的进步，从而遇到需要处理变量的问题，从常数带变量的跳跃产生了两个新的数学分支-----解析几何和微积分，他们都属于高等数学，现在高等数学里面有很多分支，其中有数学分析，高等代数，微分方程，函数论等。Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful
数学专业英语课后习题2.6
1.1）function，domain，range，the identity function，the absolute-value function，the real-valued function，real variable 2）cube，volume，edge-length，prime，totality 3）Hooke's law，stretch，displacement，spring，constant，proportional 4）schematic representation，plot，image，output，input 5）it is not difficult to imagine，the idea was much too limited 2.（1）常用英语字母和希腊字母来表示函数。 Letters of the English and Greek alphabets are often used to denote functions. （2）若 f 是一个给定的函数，x 是定义域里的一个元素，那么记号f(x)用来表示由 f 确定的对应于x 的值。 If f is a given function and if x is an object of its domain, the notation f(x) is used to designate that object in the range which is associated to x by the function f. （3）该射线将两个坐标轴的夹角分成两个相等的角。 The ray makes equal angles with the coordinates axes. （4）可以用许多方式给出函数思想的图解说明。 The function idea may be illustrated schematically in many ways. （5）容易证明，绝对值函数满足三角不等式。 It is easy to proof that the absolute-value function satisfies the triangle inequality. （6）对于实数x>0，函数g(x)表示不超过x 的素数的个数。 For a given real number x>0, the function g(x) is defined by the number of primes less than or equal to x. （7）函数是一种对应，它未必可以表示成一个简单的代数公式。 A function is a correspondence. It is not necessary to be expressed by a simple algebraic formula. （8）在函数的定义中，关于定义域和值域中的对象，没对其性质做出任何限制。 The function idea places no restriction on the nature of the objects in the domain X and in the range Y. 3.
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. Cha nge 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
关于数学专业英语课程的研究与探讨
第34卷第10期2017年10月 吉林化工学院学报 JOURNAL OF JILIN INSTITUTE OF CHEMICAL TECHNOLOGY V〇1.34N〇.10 Oct.2017 文章编号：1007-2853(2017) 10-0069-03 关于数学专业英语课程的研究与探讨 许洁 (吉林化工学院理学院，吉林吉林132022) 摘要：通过介绍数学专业英语课程开设目的，结合专业本身的特点对数学专业英语课程进行研究，分析 当前数学专业英语课程在教与学过程中存在的问题，并对相应问题的解决提出思考。希望通过对授课 方法，评价体系等方面的改革不断提高数学专业英语的实用性，培养出适应社会发展需要的专业化 人才。 关键词：数学专业英语;教学方法;评价体系 中图分类号：H319 文献标志码：A D0l：10.16039/https://www.wendangku.net/doc/1f12030245.html,22-1249.2017.10.017 随着计算机科学技术的迅速发展，人们进入 了高速发展的信息时代。信息时代拉近了人与人之间的距离，增进了国际间的交流合作。社会生活的信息化、经济的全球化，使英语的重要性日益突出。英语成为许多领域重要的通用语言。绝大多数学科前沿的学术论文都是用英文撰写。许多领域的学术、科技交流会议也以英语作为官方语 言的首选。培养具有国际交流能力的人才势在必行，掌握具有国际交流能力的专业人才又成为高 校培养人才的重中之重。 一、专业英语课程开设的目的 伴随着人类社会进入21世纪，我国的教育也面临着如何进一步与国际接轨的问题。教育部提出了高等学校各专业逐步使用英文教材，培养学生阅读英文版专业文献的能力[1]。为适应人才 培养的需要，高等院校根据各专业的实际情况开 设适应各专业的专业英语、科技外语阅读等课程。通过类似课程的学习使学生增加本专业的专业词汇的英文表达方式。数学，作为古老的学科为适 应新形式下教学改革的需要同样面临着如何与国际接轨的问题。探讨数学专业英语的特点，如何很好的开设这门课程成为很多从事该课程的一线教师关注的热点[2-6]。数学专业英语具有科技英 语的共性、科学内容的客观麵性、表达形式的完整性和简练性要求[7]。数学专业英语作为高等 院校的一门重要课程，是以大学英语为基础，是数学专业的基础课程之一。通过本课程的学习，使学生能够适应国际、国内数学教育的发展，了解本专业的最新发展动态，开拓学生的视野。通过教师讲解，结合学生课后查阅英文资料，培养学生 听、说、写的综合能力，掌握本专业的当前动态和 前沿发展，为进一步的学习、工作打下坚实的 基础。 二、数学专业英语的特点 数学专业英语与许多其他专业的专业英语类似，不能简单的定义为一门专业基础课程或者是 英语课程。数学的专业知识和大学英语课程的基础都是学好数学专业英语的关键。本课程是对于数学专业学生专业英语能力训练和培养的一门重要课程，是对大学高年级学生继公共英语课程之 后的一个重要补充和提高。数学专业英语与大学英语既有区别又有联系。 数学专业英语课程中，数学的专业性十分典 型。数学专业英语以叙述的方式介绍数学的方 法、推导过程及主要结论。其学科本身的特点决 定了其内容通常与特定的时间无关。数学课程或是数学文献中涉及到的结论有时是很久以前给出的，但在叙述的过程中一細现时絲表示。 收稿日期：017-04-05 基金项目：吉林化工学院2016年一般教研项目 作者简介:许洁（1980-)，女，吉林省吉林市人，吉林化工学院副教授，博士，主要从事矩阵代数方面的研究。
数学专业英语(Doc版).19
数学专业英语－Probability The mathematics to which our youngsters are exposed at school is. With rare exceptions, based on the classical yes-or-no, right-or-wrong type of logic. It no rmally doesn’t include one word about probability as a mode of reasoning or as a basis for comparing several alternative conclusions. Geometry, for instance, is strictly devoted to the “if-then”type of reasoning and so to the notion (i dea) that any statement is either correct or incorrect. However, it has been remarked that life is an almost continuous experience o f having to draw conclusions from insufficient evidence, and this is what we h ave to do when we make the trivial decision as to whether or not to carry an umbrella when we leave home for work. This is what a great industry has to do when it decides whether or not to put $50000000 into a new plant abroad. In none of these case and indeed, in practically no other case that you can s uggest, can one proceed by saying:”I know that A, B, C, etc. are completely and reliably true, and therefore the inevitable conclusion is~~”For there is a nother mode of reasoning, which does not say: This statement is correct, and i ts opposite is completely false.”But which say: There are various alternative possibilities. No one of these is certainly correct and true, and no one certainl y incorrect and false. There are varying degrees of plausibility—of probability —for all these alternatives. I can help you understand how these plausibility’s compare; I can also tell you reliable my advice is.” This is the kind of logic, which is developed in the theory of probability. Th is theory deals with not two truth-values—correct or false—but with all the in intermediate truth values: almost certainly true, very probably true, possibly tr ue, unlikely, very unlikely, etc. Being a precise quantities theory, it does not u se phrases such as those just given, but calculates for any question under stud y the numerical probability that it is true. If the probability has the value of 1, the answer is an unqualified “yes”or certainty. If it is zero (0), the answer is an unqualified “no”i.e. it is false or impossible. If the probability is a h alf (0.5), then the chances are even that the question has an affirmative answer. If the probability is tenth (0.1), then the chances are only 1 in 10 that the a nswer is “yes.” It is a remarkable fact that one’s intuition is often not very good at csunati ng answers to probability problems. For ex ample, how many persons must the re are at least two persons in the room with the same birthday (born on the s ame day of the month)? Remembering that there are 356 separate birthdays po ssible, some persons estimate that there would have to be 50, or even 100, pe rsons in the room to make the odds better than even. The answer, in fact, is t hat the odds are better than eight to one that at least two will have the same birthday. Let us consider one more example: Everyone is interested in polls, w hich involve estimating the opinions of a large group (say all those who vote)