Synopses & Reviews
"Proof" has been and remains one of the concepts which characterises mathematics. Covering basic propositional and predicate logic as well as discussing axiom systems and formal proofs, the book seeks to explain what mathematicians understand by proofs and how they are communicated. The authors explore the principle techniques of direct and indirect proof including induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. Many examples from analysis and modern algebra are included. The exceptionally clear style and presentation ensures that the book will be useful and enjoyable to those studying and interested in the notion of mathematical "proof."
Description
Includes bibliographical references (p. [273]-274) and index.
Table of Contents
Proofs: Mathematical and Non-Mathematical.
Propositional Logic.
Predicate Logic.
Axiom Systems and Formal Proof.
Direct Proof.
Direct Proofs: Variations.
Existence and Uniqueness Proofs.
Further Proof Techniques.
Mathematical Induction.
Appendix.
References and Further Reading.
Hints and Solutions to Selected Exercises.
Index.