A Concise Introduction to Pure Mathematics, Second Edition

by Liebeck; Martin

• ISBN13: 9781584885474
• ISBN10: 1584885475
• Edition: 2nd
• Format: Paperback
• Copyright: 2005-11-02
• Publisher: Chapman & Hall/

Summary

A Concise Introduction to Pure Mathematics, Second Edition provides a robust bridge between high school and university mathematics, expanding upon basic topics in ways that will interest first-year students in mathematics and related fields and stimulate further study. Divided into 22 short chapters, this textbook offers a selection of exercises ranging from routine calculations to quite challenging problems.The author discusses real and complex numbers and explains how these concepts are applied in solving natural problems. He introduces topics in analysis, geometry, number theory, and combinatorics.What's New in the Second Edition:· Contains extra material concerning prime numbers, forming the basis for data encryption· Explores "Secret Codes" - one of today's most spectacular applications of pure mathematics· Discusses Permutations and their importance in many topics in discrete mathematicsThe textbook allows for the design of courses with various points of emphasis, because it can be divided into four fairly independent sections related to: an introduction to number systems and analysis; theory of the integers; an introduction to discrete mathematics; and functions, relations, and countability.

Table of Contents

Foreword	ix
Preface	xi
1 Sets and Proofs	1	(12)
2 Number Systems	13	(8)
3 Decimals	21	(6)
4 Inequalities	27	(4)
5 nth Roots and Rational Powers	31	(4)
6 Complex Numbers	35	(12)
7 Polynomial Equations	47	(10)
8 Induction	57	(14)
9 Euler's Formula and Platonic Solids	71	(10)
10 Introduction to Analysis	81	(10)
11 The Integers	91	(8)
12 Prime Factorization	99	(8)
13 More on Prime Numbers	107	(4)
14 Congruence of Integers	111	(10)
15 More on Congruence	121	(10)
16 Secret Codes	131	(6)
17 Counting and Choosing	137	(12)
18 More on Sets	149	(8)
19 Equivalence Relations	157	(6)
20 Functions	163	(10)
21 Permutations	173	(14)
22 Infinity	187	(10)
Further Reading	197	(2)
Index of Symbols	199	(2)
Index	201