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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