How to Think Like a Mathematician: A Companion to Undergraduate Mathematics

How to Think Like a Mathematician: A Companion to Undergraduate Mathematics
by Kevin Houston (Author)
Publisher: Cambridge University Press; 1st edition (12 Feb. 2009)
Language: English
Hardcover: 278 pages
ISBN-10: 0521895464
ISBN-13: 9780521895460
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Book Description
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.