Fundamental Concepts of Mathematics
Publication Year: 1994
Published by: Hong Kong University Press, HKU
Table of Contents
Fundamental Concepts of Mathematics is the first of several volumes of a proposed series on fundamental mathematics which serve primarily as textbooks for students in preparation for the A-Level or other public examinations. However they go into more depth than what is required by these examinations, and contain topics ...
1. SET NOTATION
Every environment breeds its own language and common words tend to acquire different meanings for different groups of people. For example, a Mediterranean farmer, a chairman of a committee and a young lady may have quite different ideas about the word 'date'. A peasant, a physicist, a mathematician ...
2. MATHEMATICAL INDUCTION
In this chapter we shall study in some detail a very important and useful property of natural numbers - the principle of mathematical induction, upon which is based the well-known technique of the proof by induction. Instead of just recapitulating the standard procedure of this particular method of proof which ...
In this chapter we are interested in counting the different ways in which a given event can occur. There is a great variety of such counting problems that we encounter in every day life and in mathematics. Here we shall discuss a few useful methods that can be applied to such problems. ...
In this chapter we shall put together in a systematic and rigorous manner some results of elementary arithmetic that are familiar to our readers. ...
5. REAL NUMBERS
For the purpose and the scope of this course, it will be sufficient for us to think of the real numbers as the points along a straight line which extends indefinitely in both directions. (Fig. 5.1) This straight line is referred to as the number line. Any finite portion of the number Iine can serve as a ruler with which we may measure ...
6. LIMIT AND CONVERGENCE
Traditionally mathematics is divided into three large categories geometry, algebra and analysis - though at times it is very difficult to put some modern topics of mathematics in one of these categories. A very rough outline of the classification can be given as follows. The study of space inaugurated by the ancient ...
7. COMPLEX NUMBERS
Instead of starting with a formal definition of complex number and then proceeding to study the properties of the new number system, we shall begin with a brief review of our old number systems N, Z, Q and R in order to discover a certain inadequacy in each concerning the provision of solutions of equations. ...
ANSWERS TO EXERCISES
Page Count: 260
Publication Year: 1994
OCLC Number: 794700925
MUSE Marc Record: Download for Fundamental Concepts of Mathematics