广西大学专业英语题库

一、英文表示：加减乘除等常见数学运算。

如31 52a-+x二、英语名词定义1.Equation2.Function3.The limit of a sequence {}f(n)(for exampleLnf=∞→)(limn4.The derivative of function f(x)5.Statistical population6、A B ⊆7、The event A is said to be certain8、Monotonic sequence英译汉1.This device for representing real numbers geometrically is a very worthwhile aid that helps us to discover and understand better certain properties of real numbers. However, the readers should realize that all properties of real numbers that are to be accepted as theorems must be deducible from the axioms without any reference to geometry. This does not mean that one should not make use of geometry in studying properties of real numbers. On the contrary ,the geometry often suggests the method of proof of particular theorem, and sometimes a geometric argument is more illuminating than a purely analytic proof(one depending entirely on the axioms for the real numbers).In this book, geometric arguments are used to large to help motivate or clarify a particular discuss.2.Equations are of very great use. We can use equations in many mathematical problems. We may notice that almost every problem gives us one or more statement that something is equal to something; this gives us equations, with which we may work if we need to. To solve an equation means to find the value of the unknown term. To do this, we must change the terms about until the unknown term stand alone on one side 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, on matter which side.3.The study of differential equation is one part of mathematics that, perhaps more than any other, has been directly inspired by mechanics, astronomy, and mathematical physics. Its history began in the 17th century when Newton, Leibniz, and the Bernoullis solved some simple differential equations arising from problems in geometry and mechanics. These early discoveries, beginning about 1690,gradually led to the development of a lot of “s pecial tricks”for solving certain special kings of differential equations, Although these special tricks are applicable in relatively few cases, they do enable us to solve many differential equations that arise in mechanics and geometry.4. A large variety of scientific problems arise in which one tries to determine something from its rate of change. For example, we could try to compute the position of a moving particle from a knowledge of its velocity or acceleration. Or a radioactive substance may be disintegrating at a known rate and we may be required to determine the amount of material preset after a give time. In example like these, we are trying to determine an unknown function from prescribed information expressed in the form of an equation involving are least one of the derivatives of the unknown function. These equations are called differential equations, and their study forms one of the most challenging branches of mathematics.5. In discussing any branch of mathematics, be it analysis, algebra, or geometry, it is helpful to use the notationand terminology of set theory. This subject, which was developed by Boole and Cantor in the latter part of the 19th century, has had a profound influence on the development of mathematics in the in the 20th century. It has unified many seemingly disconnected ideas and has helped to reduce many mathematical concepts to their logical foundations in an elegant and systematic way. In mathematics, the word “set” is used to represent a collection of objects viewed as a single entity. The individual objects in the collection are called elements or members of the set, and they are said to belong to or to be contained in the set. The set is said to contain or be composed of its elements. In many applications it is convenient to deal with abstract sets. Abstract set theory has been developed to deal with such collections of arbitrary objects, and from this generality the theory derives its power.6. In discussions involving probability, one often sees phrases from everyday language such as “two events are equally likely,” “an event is impossible,” or “an event is certain to occur.” Expre ssions of this sort have intuitive appeal and it is both pleasant and helpful to be able to employ such colorful language in mathematical discussions. Before we can do so, however, it is necessary to explain the meaning of this language in terms of the fundamental concepts of our theory. Because of the way probability is used in practice, it is convenient to imagine that each probability space (S, B, P) is associated with a real or conceptual experiment. The universal set S can then be thought of as the collection of all conceivable outcomes of the experiment, as in the example of coin tossing discussed in the foregoing section. Each element of S is called an outcome or a sample and the subsets of S that occur in the Boolean algebra B are called event. The reasons for this terminology will become more apparent when we treat some examples.7、Not only are matrix methods useful in solving simultaneous equations , but they are also useful in discovering whether or not the set of equations are consistent, in the sense that they lead to solutions, and in discovering whether or not the set of equations are determinate, in the sense that they lead to unique solution.8、In many problems it is necessary to select from the collection of all solutions one having a prescribed value at some point. The prescribed value is called an initial condition, and the problem of determining such a solution is called an initial-value problem. This terminology originated in mechanics where, as in the above example , the prescribed value represents the displacement at some initial time.9、The impossible event must be assigned probability zero because P is a finitely additive measure. However, there may be events with probability zero that are not impossible.汉译英（1）数学来源于人类的社会实践，例如，工农业生产，商业活动，军事行动及科技研究。