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 proof methods – direct method, cases, induction, contradiction, and 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, and injectivity surjectivity of functions. Real students have tested the material 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.