Looking for a head start in your undergraduate degree in mathematics? Maybeyou’ve already started your degree and feel bewildered by the subject you previouslyloved? Don’t panic! This friendly companion will ease your transition to realmathematical thinking.Working through the book you will develop an arsenal of techniques to help youunlock the meaning of definitions, theorems and proofs, solve problems, and writemathematics effectively. All the major methods of proof – direct method, cases,induction, contradiction and contrapositive – are featured. Concrete examples areused throughout, and you’ll get plenty of practice on topics common to many coursessuch as divisors, Euclidean Algorithm, modular arithmetic, equivalence relations,and injectivity and surjectivity of functions.The material has been tested by real students over many years so all the essentialsare covered. With over 300 exercises to help you test your progress, you’ll soon learnhow to think like a mathematician.Essential for any starting undergraduate in mathematics, this book can also help ifyou’re studying engineering or physics and need access to undergraduatemathematics topics, or if you’re taking a subject that requires logic such as computerscience, philosophy or linguistics.