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.
1 A Classical Beginning
2 Multiple Proofs
3 Number Theory
4 Mathematical Induction
5 Discrete Mathematics
6 Proofs Without Words
7 Theory of Games
8 Pick's Theorem
9 Lattice-Point Polygons
10 Polygonal Dissection Congruence Theorem
11 Functions and Relations
12 Graph Theory
13 Infinity
14 Order Theory
15 Real Analysis
Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. The author of Proof and the Art of Mathematics (MIT Press), he is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

About

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.

Table of Contents

1 A Classical Beginning
2 Multiple Proofs
3 Number Theory
4 Mathematical Induction
5 Discrete Mathematics
6 Proofs Without Words
7 Theory of Games
8 Pick's Theorem
9 Lattice-Point Polygons
10 Polygonal Dissection Congruence Theorem
11 Functions and Relations
12 Graph Theory
13 Infinity
14 Order Theory
15 Real Analysis

Author

Joel David Hamkins is Professor of Logic at Oxford University and Sir Peter Strawson Fellow in Philosophy at University College, Oxford. The author of Proof and the Art of Mathematics (MIT Press), he is the creator of the popular blog Mathematics and Philosophy of the Infinite. He is a prominent contributor to MathOverflow, where he has posted more than 1,000 mathematical arguments.

Books for Asian American and Native Hawaiian/Pacific Islander Heritage Month

Every May we celebrate the rich history and culture of Asian Americans, Native Hawaiians, and Pacific Islanders. Browse a curated selection of fiction and nonfiction books by AANHPI creators that we think your students will love. Find our full collection of titles for Higher Education here.

Read more