Understanding Mathematical Proof

The notion of proof is central to mathematics yet it is one of the most difficult aspects of the subject to teach and master. In particular, undergraduate mathematics students often experience difficulties in understanding and constructing proofs. This text describes the nature of mathematical proof, explores the various techniques that mathematicians adopt to prove their results, and offers advice and strategies for constructing proofs. It will improve students' ability to understand proofs and construct correct proofs of their own.

John Taylor, Rowan Garnier

Introduction. Logic and Reasoning. Sets and Functions. The Structure of Mathematical Proofs. Finding Proofs. Direct Proof: Variations. Existence and Uniqueness. Mathematical Induction. Hints and Solutions to Selected Exercises. Bibliography. Index.