Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree & 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 & proofs solve problems & write mathematics effectively. All the major methods of proof
- direct method cases induction contradiction & contrapositive
- are featured. Concrete examples are used throughout & you'll get plenty of practice on topics common to many courses such as divisors Euclidean algorithms modular arithmetic equivalence relations & injectivity & 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.