How to Think Like a Mathematician

Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.

ISBN	0521895464	Pages	278
ISBN13	9780521895460 (What's this?)	Volumes	1
Publisher	Cambridge University Press	Weight (grammes)	690
Imprint	Cambridge University Press	Published in	Cambridge
Format	Hardback	Height (mm)	246
Publication date	12 Feb 2009	Width (mm)	189
Library of Congress	QA1	Spine width (mm)	19
DEWEY	510	Academic level	Undergraduate
DEWEY edition	DC22

I	Study skills for mathematicians	1
II	How to think logically	51
III	Definitions, theorems and proofs	97
IV	Techniques of proof	137
V	Mathematics that all good mathematicians need	185
VI	Closing remarks	241
	Appendices	257
	Index	263

"In this book, Houston has created a primer on the fundamental abstract ideas of mathematics; the primary emphasis is on demonstrating the many principles and tactics used in proofs. The material is explained in ways that are comprehensible, which will be a great help for people who seem to hit the wall regarding what to do when confronted with the creation of a proof... In this book, Houston takes a systematic and gentle approach to explaining the ideas of mathematics and how tactics of reasoning can be combined with those ideas to generate what would be considered a convincing proof." Charles Ashbacher, Journal of Recreational Mathematics "The author provides concise, crisp explanations, including definitions, examples, tips, remarks, warnings, and idea-reinforcing questions. Houston expresses thoughts clearly and concisely, and includes succinct remarks to make points, clarify arguments, and reveal subleties." W.R. Lee, Choice Magazine

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A Companion to Undergraduate Mathematics