一、数学符号翻译12/156 twelve over one hundred and fifty-six234/567 two hundred and thirty -four over five hundred and sixty-seven 4% four percent7‰ seven permill6.79 six point seven nine 52.3 three point two five recurring85xthe eighth root of x to the fifth power 53x x to the minus three fifthsdx x f ba )( 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 yf the partial (derivative) of f with respect to y 5log 3 the logarithm of five to the base threex a log the logarithm of x to the base aB A A cap B / A meet B / A intersection BB A A cup B / A join B / A union BA a a is an element of AB 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parabolic segment 抛物弓形三、中译英（1）17世纪之前，人类局限于初等数学，即几何，三角学和代数，那时只考虑常数。

Before 17th century, man confined himself to the elementary mathematics, i.e., geometry, trigonometry and algebra, inwhich only the constants were considered.（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 integ er, but the quotient of two integers need not be an integer.（3）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.（4）若P(A)>P(B)，则称事件A比事件B有更大的可能性；如果P(A) P(B),则称事件A至少和事件B的可能性一样大。

The event A is called more likely than B if P(A)>P(B), and at least as likely as B if P(A) P(B).（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）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的思想。

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. （7）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.（8）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 not numbers but figures such as triangles, parallelograms and circles, though it is related with numbers.四、英译汉1、Two events are said to be mutually exclusive when both cannot happen at the same time.If E denotes an event,then the event that E does not happen is called the complementary event of E,and is denoted by E .Obviously,E and E are mutually exclusive.Since an event either happens or does not happen,the sum of their probabilities is 1.两个事件若它们不能在同一时间都发生时我们称这两个事件是互斥的。

如果E 表示一个事件，然后 E 不会发生的事件称为 E的补充性事件，并由表示E 。

很明显，E 和E 是互斥的。

因为对于事件发生或不发生，其概率的总和是 1。

2、Thus p q is true if both p and q are true or if both p and q arefalse.The following are English-language equivalents to p q : “ p if and only if q ”,”p is a necessary and sufficient condition for q.”and “p precisely if q.”It is worth emphasizing that the compound proposition p q and its converse q p are quire different;they have different truth tables.因此 p q 是真的，在 p 和 q 同时为真或 同时为假时成立。

以下是英语语言描述，等同于p q : "p 当且仅当 q"，"p 是 q 的必要和充分条件"和"p 准确如果 q."值得强调的是复合命题 p q 和它的逆命题 q p 是不同的，他们有不同的真值表。

3、We now introduce a natural generalization of partial derivatives.In the definition of ),(001y x f ,the numerator of the difference quotient used involves the value of ),(y x f at two points ),x (00y x and ),(00y x .As x approaches zero,the first point approaches the latter along the line y=0y .For ),(002y x f a point ),(00y y x approaches ),(00y x along the line x=0x .We now replace these two special lines by an arbitrary line through ),(00y x .我们现在介绍的偏导数的自然推广。

由),(001y x f 中的定义，所使用的差商的分子涉及),(y x f 在),x (00y x 和),(00y x 两个点的值。

当x 接近零，第一点沿直线y =0y 接近后者。

对于),(002y x f 点),(00y y x 沿直线x =0x 趋向),(00y x 。

现在我们通过一个任意经过点),(00y x 的线来更换这两个特殊的线。

4、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 example of even numbers.A whole number is said to be odd if it is not divisible by 2;1,7and 13 are examples of odd numbers.The natural numbers greater than 1 and 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.整数集有很多重要子集。