The Discrete Mathematical Charms of Paul Erdos
A Simple Introduction

A captivating introduction to key results of discrete mathematics through the work of Paul Erd?s, blended with first-hand reminiscences.

Vašek Chvátal (Author)

9781108831833, Cambridge University Press

Hardback, published 26 August 2021

264 pages
25.1 x 17.5 x 1.6 cm, 0.66 kg

'The book … is demanding, but a pleasure to work through. I highly recommend it to everyone with a good background in calculus and elementary number theory.' Franz Lemmermeyer, zbMATH

Paul Erd?s published more papers during his lifetime than any other mathematician, especially in discrete mathematics. He had a nose for beautiful, simply-stated problems with solutions that have far-reaching consequences across mathematics. This captivating book, written for students, provides an easy-to-understand introduction to discrete mathematics by presenting questions that intrigued Erd?s, along with his brilliant ways of working toward their answers. It includes young Erd?s's proof of Bertrand's postulate, the Erd?s-Szekeres Happy End Theorem, De Bruijn-Erd?s theorem, Erd?s-Rado delta-systems, Erd?s-Ko-Rado theorem, Erd?s-Stone theorem, the Erd?s-Rényi-Sós Friendship Theorem, Erd?s-Rényi random graphs, the Chvátal-Erd?s theorem on Hamilton cycles, and other results of Erd?s, as well as results related to his work, such as Ramsey's theorem or Deza's theorem on weak delta-systems. Its appendix covers topics normally missing from introductory courses. Filled with personal anecdotes about Erd?s, this book offers a behind-the-scenes look at interactions with the legendary collaborator.

Foreword
Preface
Acknowledgments
Introduction
1. A glorious beginning – Bertrand's postulate
2. Discrete geometry and spinoffs
3. Ramsey's theorem
4. Delta-systems
5. Extremal set theory
6. Van der Waerden's theorem
7. Extremal graph theory
8. The friendship theorem
9. Chromatic number
10. Thresholds of graph properties
11. Hamilton cycles
Appendix A. A few tricks of the trade
Appendix B. Definitions, terminology, notation
Appendix C. More on Erd?s
References
Index.

Subject Areas: Algorithms & data structures [UMB], History of mathematics [PBX], Combinatorics & graph theory [PBV], Discrete mathematics [PBD]