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. 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 “=”. 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，图形和图表都是不同的符号……..
第二章 精读课文——入门必修
数学与计: useful terms and definitions of Mathematics,
equation
Difficult points:
Some mathematical terms
Requirements: 1. 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
1－A What is mathematics
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－B Equation
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 become 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都是 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。
2.1 数学、方程与比例 Mathematics, Equation and Ratio New Words & Expressions:
algebra 代数学 algebraic 代数的 arithmetic 算术, 算术的 axiom 公理 conception 概念，观点 constant 常数 logical deduction 逻辑推理 division 除，除法 formula 公式 trigonometry 三角学 geometrical 几何的 identity 恒等式 measure 测量，测度 numerical 数值的, 数字的 operation 运算 postulate 公设 proposition 命题 subtraction 减，减法 term 项，术语 variable 变化的，变量
There are various kinds of equations. They are linear equation, quadratic equation, etc.
方程的根是满足方程的任意数或者数的符号。求方程根的过 程被称为解方程。 方程有很多种，例如： 线性方程，二次方程等。
To solve an equation means to find the value of the unknown term. To do this , we must, of course, change the terms about until the unknown term stands alone on one side of the equation, thus making it equal to something on the other side. We then obtain the value of the unknown and the answer to the question. To solve the equation, therefore, means to move and change the terms about without making the equation untrue, until only the unknown quantity is left on one side ,no matter which side. 解方程意味着求未知项的值，为了求未知项的值，当然必须 移项，直到未知项单独在方程的一边，令其等于方程的另一 边，从而求得未知项的值，解决了问题。 因此解方程意味着进行一系列的移项和同解变形，直到未知 量被单独留在方程的一边，无论那一边。
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。 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。
A root of an equation is any number or number symbol which satisfies the equation. To obtain the root or roots of an equation is called solving an equation.
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, 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。 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。
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. 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. 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，证 明大多数的几何定理。