Understanding Mathematical Proof
Chapman and Hall/CRC – 2014 – 414 pages
The concept of a proof is one of the key ideas—some would say the key idea—that sets mathematics apart from other disciplines. But students often have difficulties in understanding proofs and constructing their own proofs. Suitable for a variety of courses or for self-study, this text helps students understand proofs and enhances their ability to construct correct proofs of their own. The book describes the nature of the mathematical proof, explores the various techniques that mathematicians adopt in proving their results, and offers advice and strategies for constructing proofs.
Introduction. Propositional Logic. Predicate Logic. Sets and Functions. Axioms and Formal Proofs. Direct Proofs. Variations on a Theme. Existence and Uniqueness. Mathematical Induction. Hints and Solutions to Selected Exercises.