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1、Mathematical English,Chapter 2 精读课文-入门必读,Key points: useful terms and definitions of Mathematics, equation and geometry Difficult points: Some geometrical terms,Requirements:,掌握所讲课文的生词和词组 2. 理解并掌握课外作业里面的汉译英 3. 理解所讲段落的翻译技巧与方法,New Words & Expressions: geometry n. 几何学 function theory 函数论 trigonometry n
2、. 三角学 conception n. 概念 algebra n. 代数学 proposition 命题 equation 方程,等式 definition 定义 mathematical analysis 数学分析 logical deduction 逻辑推理,推论Roman-number n. 罗马数字 notation 符号, 记号 higher mathematics 高等数学 constant n. 常量 differential equation 微分方程 variable adj. 变化的, n.变量 formula 公式 even number 偶数 equation of c
3、ondition 条件等式 linear equation 线性等式 arithmetic 算术, 算术的 identity 恒等式 algebraic 代数的 numerical 数值的, 数字的 term 项, 术语, 命名为 operation 运算 fraction 分数 dimension 大小,维数,尺寸,2.1 Mathematics, Equation and Ratio,Mathematics comes from mans social practice, for example, industrial and agricultural production, commer
4、cial 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
5、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。,1A What is mathematics,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 m
6、ore 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, i.e. , 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，
7、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。,1A What is mathematics,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 t
8、o 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
9、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。,1A What is mathematics,Mathematicians study conceptions and propositions, Axioms, postulates, definitions and theorems are all propositions. Notations are a special and powerful tool of ma
10、thematics and are used to express conceptions and propositions very often. 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 equal
11、ity. 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。公式，图表都是不同的符号,1A What is mathematics,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 lo
12、gical deductions. 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
13、 by logical deductions, for example, the proof of most of geometrical theorems. 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，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，大多数几何定理的证明。,1A What is mathematics,回顾： 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 。 符号在数学中起着非常重要的作用，它常用于表
14、示概念和命题。,1A What is mathematics,An equation is a statement of the equality between two equal numbers or number symbols. 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 bec
15、ome alike on the performance of the indicated operation. 等式是关于两个数或者数的符号相等的一种描述。等式有两种恒等式和条件等式。算术或者代数恒等式是等式。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。,1B Equation,An identity involving letters is true for any set of numerical values of the letters in it. 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=0 is true for x=6 and y=2 and for many other pairs of values for x and y. 含有字母的恒等式对其中字母的任一组数值都成立。一个等式若仅仅对其中一个字母
