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1、细心整理1A What is mathematics Mathematics comes from mans 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 m
2、odern 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，比方工农业生产，商业活动， 军事行动和科学技术探究。反过来，数学效劳于实践，并在各个领域中起着特殊重要的作用。 没有应用数学，任何一个此时此刻的科技的分支都不能正常开展。From the early need of man came the concepts of numbers and forms. Then, geometry develop
3、ed 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,
4、i.e. , geometry, trigonometry and algebra, in which only the constants are considered. 很早的时候，人类的须要产生了数和形式的概念，接着，测量土地的须要形成了几何，出于测量的须要产生了三角几何，为了处理更困难的实际问题，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 an
5、d 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 mathemat
6、ical analysis, higher algebra, differential equations, function theory and so on. 17世纪工业的快速开展推动了经济技术的进步， 从而遇到须要处理变量的问题，从常数带变量的跳动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，此时此刻高等数学里面有许多分支，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 al
7、l 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 sign
8、s of addition, subtraction , multiplication, division and equality. 数学家探究的是概念和命题，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.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 ma
9、thematics 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 som
10、e 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，在数学开展历史的很长时间内，逻辑推理始终占据着数学方法的中心地位，此时此刻，由于电子计算机的快速开展和广泛运用，计算机的地位越来越重要，此时此刻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。 1B Equation An equation is a stateme
11、nt 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
12、. 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。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
13、 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。一个等式假设仅仅对其中一个字母的某些值成立，或对其中两个或着多个字母的假设干组相关的值成立，那么它是一个条件等式，简称方程。因此3x-5=7仅当x=4 时成立，而2x-y=0，当x=6,y=2时成
14、立，且对x, y的其他许多对值也成立。A root of an equation is any number or number symbol which satisfies the equation. There are various kinds of equation. They are linear equation, quadratic equation, etc. 方程的根是满足方程的随意数或者数的符号。方程有许多种，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
15、 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 chan
16、ge 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，当然必需移项，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展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。Equation are of very great use. We can use equation in many mathematical problems. We may notice that almost every problem gives us one or more statements that something is equal to something, this gives us equations, with which we may w
