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

How to Think Like a Mathematician: A Companion to Undergraduate Mathematics by Houston, Kevin. Paperback edition. ISBN: 9780521719780.

Looking for a head start in your undergraduate degree in mathematics? Maybe youve already started your degree and feel bewildered by the subject you previously loved? Dont 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 youll 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, youll soon learn how to think like a mathematician.