Proof and the Art of Mathematics

Proof and the Art of Mathematics

By Joel David Hamkins

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs.

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Summary

An introduction to writing proofs, presented through compelling mathematical statements with interesting elementary proofs.

This book offers an introduction to the art and craft of proof writing. The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision.

The book is organized around mathematically rich topics (rather than methods of proof), allowing students to learn to write proofs with material that is itself intrinsically interesting. Students will find the early chapters the easiest. Chapter 4 explains the method of mathematical induction, which is used in many arguments throughout the book. Later chapters offer chapter-length developments of major theorems, and the final chapters are more abstract. The book is generously illustrated; an extended chapter on proofs-without-words shows the power of figures and diagrams to communicate mathematical ideas—but also acknowledges the dangers of such an approach. Each chapter includes exercises, and sample answers are provided at the end of the book.

Pre-Order Paperback

$30.00 X ISBN: 9780262539791 240 pp. | 7 in x 9 in 112 color illus., 8 b&w illus.

Endorsements

  • For anyone wanting to experience the joy of mathematics, Joel Hamkins' book is a perfect place to start. He makes it clear that a theorem statement is merely a travel brochure, while its many and varied proofs are the actual adventures.

    John Baez

    Professor of Mathematics at the University of California, Riverside; author of Gauge Fields, Knots and Gravity and Quantum Techniques in Stochastic Mechanics

  • Any book that tries to teach the art of proofs has to take 'teaching,' 'art,' and 'proofs' very seriously. Hamkins's book excels in all three aspects, and beautifully brings them together. The book is a pleasure, and it will be an excellent teacher for the art of proofs.

    Günter M. Ziegler

    Freie Universität Berlin; coauthor of Proofs from THE BOOK