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How to Think Like a Mathematician - A Companion to Undergraduate Mathematics - (Malestrom)

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

Publisher: Cambridge University | Pages: 278 | 2009-02-23 | ISBN 0521895464 | PDF 



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.

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