A Concise Introduction to Pure Mathematics

"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. The second edition contains extra material concerning prime numbers, forming the basis for data encryption. It explores 'Secret Codes' - one of today's most spectacular applications of pure mathematics. It discusses Permutations and their importance in many topics in discrete mathematics. The 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.

ISBN 1439835985   Weight (grammes) 458 ISBN13 9781439835982 (What's this?)   Published in Bosa Roca Publisher Taylor & Francis Inc   Series title Chapman Hall/CRC Mathematics Series Imprint CRC Press Inc   Previous ISBN 9781584885474 Format Paperback   Height (mm) 235 Publication date 09 Aug 2010   Width (mm) 156 DEWEY 510   Spine width (mm) 18 DEWEY edition DC22   Academic level Tertiary education Pages 268

		Foreword
		Preface
1		Sets and Proofs		1
2		Number Systems		13
3		Decimals		21
4		Inequalities		27
5		nth Roots and Rational Powers		33
6		Complex Numbers		37
7		Polynomial Equations		49
8		Induction		59
9		Euler's Formula and Platonic Solids		73
10		The Integers		83
11		Prime Factorization		91
12		More on Prime Numbers		99
13		Congruence of Integers		103
14		More on Congruence		113
15		Secret Codes		123
16		Counting and Choosing		129
17		More on Sets		141
18		Equivalence Relations		149
19		Functions		155
20		Permutations		165
21		Infinity		179
22		Introduction to Analysis: Bounds		189
23		More Analysis: Limits		197
24		Yet More Analysis: Continuity		207
		Solutions to Odd-Numbered Exercises		215
		Further Reading		245
		Index of Symbols		247
		Index		249

It would in fact be difficult to find in this excellent book three consecutive pages that do not contain material useful to students or practitioners. ! A diligent, active reader of this outstanding book will have the best foundation at minimum cost for making meaningful contributions to mathematics, science, or engineering. --Computing Reviews, November 2011 Now in an updated and expanded third edition, A Concise Introduction to Pure Mathematics provides an informed and informative presentation into a representative selection of fundamental ideas in mathematics ! . Of special note is the inclusion of solutions to all of the odd-numbered exercises. An ideal, accessible, elegant, student-friendly, and highly recommended choice for classroom textbooks for high school and college level mathematics curriculums, A Concise Introduction to Pure Mathematics is further enhanced with a selective bibliography, an index of symbols, and a comprehensive index. --Library Bookwatch, December 2010 This book displays a unique combination of lightness and rigor, leavened with the right dose of humor. When I used it for a course, students could not get enough, and I have been recommending independent study from it to students wishing to take a core course in analysis without having taken the prerequisite course. The material is very well chosen and arranged, and teaching from Liebeck's book has in many different ways been among my most rewarding teaching experiences during the last decades. --Boris Hasselblatt, Tufts University, Medford, Massachusetts, USA In addition to preparing students to go on in mathematics, it is also a wonderful choice for a student who will not necessarily go on in mathematics but wants a gentle but fascinating introduction into the culture of mathematics. ! This book will give a student the understanding to go on in further courses in abstract algebra and analysis. The notion of a proof will no longer be foreign, but also mathematics will not be viewed as some abstract black box. At the very least, the student will have an appreciation of mathematics. As usual, Liebeck's writing style is clear and easy to read. This is a book that could be read by a student on his or her own. There is a wide selection of problems ranging from routine to quite challenging. --From the Foreword by Robert Guralnick, University of Southern California, Los Angeles, USA Praise for Previous Editions: The book will continue to serve well as a transitional course to rigorous mathematics and as an introduction to the mathematical world ! . --Gerald A. Heuer, Zentralblatt MATH, 2009 !a pleasure to read ! a very welcome and highly accessible book. --Michael Ward, The Mathematical Gazette, March 2007

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