The Discrete Mathematical Charms of Paul Erd?s: A Simple Introduction
Cambridge University Press, 8/26/2021
EAN 9781108927406, ISBN10: 1108927408
Paperback, 268 pages, 24.4 x 17 x 1.5 cm
Language: English
Originally published in English
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.