The Discrete Mathematical Charms of Paul Erdos

A Simple Introduction

Vašek Chvátal

• Publisher: Cambridge University Press
• Year: 2021
• Print ISBN: 9781108831833
• eBook ISBN: 9781108934916
• Topic: Mathematics
• Subtopic: Discrete Mathematics
• Index: Mathematics

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.

Table of contents

• Cover
• Half-title Page
• Frontispiece
• Title Page
• Copyright Page
• Dedication
• Epigraph
• Contents
• 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 ERDOS
• Bibliography
• Index