One idea that defines mathematics is “proof,” and it still does. The book aims to clarify what mathematicians mean by proofs and how they are presented by addressing axiom systems, formal proofs, propositional and predicate logic, basic logic, and propositional and predicate logic. The writers all cover the main methods of direct and indirect evidence, such as induction, existence and uniqueness proofs, proof by contradiction, constructive and non-constructive proofs, etc. There are numerous examples drawn from analysis and contemporary algebra. Those who are studying and interested in the idea of mathematical “proof” will find the book instructive and interesting because of its extraordinarily clear style and presentation.

Rowan Garnier and John Taylor