How to Think Like a Mathematician: A Companion to Undergraduate
Publisher: Cambridge University | Pages: 278 | 2009-02-23 | ISBN 0521895464 | PDF | 2 MBLooking for a head start in your undergraduate degree in mathematics?Maybe you've already started your degree and feel bewildered by thesubject you previously loved? Don't panic! This friendly companion willease your transition to real mathematical thinking.
thebook you will develop an arsenal of techniques to help you unlock themeaning of definitions, theorems and proofs, solve problems, and writemathematics effectively. All the major methods of proof - directmethod, cases, induction, contradiction and contrapositive - arefeatured. Concrete examples are used throughout, and you'll get plentyof practice on topics common to many courses such as divisors,Euclidean algorithms, modular arithmetic, equivalence relations, andinjectivity and surjectivity of functions. The material has been testedby real students over many years so all the essentials are covered.With over 300 exercises to help you test your progress, you'll soonlearn how to think like a mathematician.
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