Looking to get a head start on your mathematics undergraduate degree? Perhaps you’ve already begun your degree and find the subject you once liked confusing? Not to worry! This helpful companion will make your move to using genuine mathematical reasoning easier. As you progress through the book, you’ll build up a toolkit of strategies that will enable you to decipher definitions, theorems, and proofs, solve issues and write mathematics clearly. There are examples of every significant form of proof, including direct method, cases, induction, contradiction, and contrapositive. The course makes extensive use of concrete examples and gives you lots of practice in areas including divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and the injectivity and surjectivity of functions. All the essentials are addressed because the information has been put to the test over many years by actual pupils. You’ll quickly develop mathematical thinking skills thanks to the more than 300 activities that help you gauge your progress.