数学专业英语(吴炯圻)

第二版 课文翻译及课后习题

New Words & Expressions:

algebra 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

2.1 数学、方程与比例

Mathematics, Equation and Ratio

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Mathematics comes from man’s social practice, for example, industrial and agricultural

production, commercial activities, military operations and scientific and technological researches.

1－A What is 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。

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.

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。

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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.

很早的时候，人类的需要产生了数和形的概念。接着，测量土地问题形成了几何学，测量问

题产生了三角学。为了处理更复杂的实际问题，人类建立和解决了带未知数的方程，从而产

生了代数学。

Before 17th century, man confined himself to the elementary mathematics, i.e. , geometry,

trigonometry and algebra, in which only the constants are considered.

17世纪前，人类局限于只考虑常数的初等数学，即几何学，三角学和代数学。

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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.

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。从常量到

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。

第二版 课文翻译及课后习题

Now there are many branches in higher mathematics, among which are mathematical analysis,

higher algebra, differential equations, function theory and so on.

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。

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Mathematicians study conceptions and propositions, Axioms, postulates, definitions and

theorems are all propositions. Notations are a special and powerful tool of mathematics and are

used to express conceptions and propositions very often.

数学家研究的是概念和命题，公理，公设，定义和定理都是命题。符号是数学中一个特殊而

有用的工具，常用于表达概念和命题。

Formulas ,figures and charts are full of different symbols. Some of the best known symbols of

mathematics are the Arabic numerals 1,2,3,4,5,6,7,8,9,0 and the signs of addition “+”,

subtraction “-” , multiplication “×”, division “÷” and equality “=”.

公式，图形和图表都是不同的符号 ..

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The conclusions in mathematics are obtained mainly by logical deductions and computation. For

a long period of the history of mathematics, the centric place of mathematics methods was

occupied by the logical deductions.

数学结论主要由逻辑推理和计算得到。在数学发展历史的很长时间内，逻辑推理一直占据着

数学方法的中心地位。

Now , since electronic computers are developed promptly and used widely, the role of

computation becomes more and more important. In our times, computation is not only used to

deal with a lot of information and data, but also to carry out some work that merely could be

done earlier by logical deductions, for example, the proof of most of geometrical theorems.

现在，由于电子计算机的迅速发展和广泛使用，计算机的地位越来越重要。现在计算机不仅

用于处理大量的信息和数据，还可以完成一些之前只能由逻辑推理来做的工作，例如，证明

大多数的几何定理。

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回顾：

1. 如果没有运用数学，任何一个科学技术分支都不可能正常的发展。

2. 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。

1－A What is mathematics

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An equation is a statement of the equality between two equal numbers or number symbols.

1－B Equation

等式是关于两个数或者数的符号相等的一种描述。

Equation are of two kinds---- identities and equations of condition.

An arithmetic or an algebraic identity is an equation. In such an equation either the two

members are alike, or become alike on the performance of the indicated operation.

等式有两种－恒等式和条件等式。算术或者代数恒等式都是等式。这种等式的两端要么一样，

第二版 课文翻译及课后习题

要么经过执行指定的运算后变成一样。

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An identity involving letters is true for any set of numerical values of the letters in it.

含有字母的恒等式对其中字母的任一组数值都成立。

An equation which is true only for certain values of a letter in it, or for certain sets of related

values of two or more of its letters, is an equation of condition, or simply an equation. Thus

3x-5=7 is true for x=4 only; and 2x-y=10 is true for x=6 and y=2 and for many other pairs of values

for x and y.

一个等式若仅仅对其中一个字母的某些值成立，或对其中两个或者多个字母的若干组 …… 此处隐藏：4174字，全部文档内容请下载后查看。喜欢就下载吧 ……