The Discrete Mathematical Charms of Paul Erdos
A Simple Introduction

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

Vašek Chvátal (Author)

9781108927406, Cambridge University Press

Paperback / softback, published 26 August 2021

266 pages
24.3 x 16.9 x 1 cm, 0.54 kg

'Chvátal tells the story of many discrete mathematical ideas, centered around the work of Paul Erdős … Chvátal does an exceptional job of putting the mathematical discoveries in their historical context and combining them with photos, personal anecdotes about his time spent with Erdős, and letters between the two. This context, along with the topics chosen and the clear writing, make this book exceptional. … The book can, of course, be used as a graduate-level textbook. But it is far more than that. [It] is a phenomenal reference for discrete mathematicians and a 'simple introduction' to discrete mathematics for any mathematician with the desire to learn about the work and life of Paul Erdős.' Ranjan Rohatgi, Notices of the American Mathematical Society

Paul Erdős 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 Erdős, along with his brilliant ways of working toward their answers. It includes young Erdős's proof of Bertrand's postulate, the Erdős-Szekeres Happy End Theorem, De Bruijn-Erdős theorem, Erdős-Rado delta-systems, Erdős-Ko-Rado theorem, Erdős-Stone theorem, the Erdős-Rényi-Sós Friendship Theorem, Erdős-Rényi random graphs, the Chvátal-Erdős theorem on Hamilton cycles, and other results of Erdős, 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 Erdős, 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 Erdős
References
Index.

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