The Mathematics of Paul Erdős I

  • Ronald L. Graham
  • Jaroslav Nešetřil
  • Steve Butler

Table of contents

  1. Front Matter
    Pages i-xix
  2. Béla Bollobás
    Pages 1-41
  3. Joel Spencer
    Pages 43-46
  4. I. Early Days

    1. Front Matter
      Pages 47-49
    2. Cedric A. B. Smith
      Pages 81-92
    3. Arthur H. Stone
      Pages 93-98
    4. William T. Tutte
      Pages 99-101
  5. II. Number Theory

    1. Front Matter
      Pages 103-106
    2. Rudolf Ahlswede, Ning Cai
      Pages 107-117
    3. Rudolf Ahlswede, Levan H. Khachatrian
      Pages 119-132
    4. Vitaly Bergelson, Paul Erdős, Neil Hindman, Tomasz Łuczak
      Pages 133-146
    5. Fan R. K. Chung, John L. Goldwasser
      Pages 147-157
    6. Sergei Konyagin, Carl Pomerance
      Pages 159-186
    7. Jean-Louis Nicolas
      Pages 207-220
    8. András Sárközy
      Pages 221-232
    9. András Sárközy, Vera T. Sós
      Pages 233-262
    10. Andrzej Schinzel
      Pages 263-267

About this book

Introduction

This is the most comprehensive survey of the mathematical life of the legendary Paul Erdős (1913-1996), one of the most versatile and prolific mathematicians of our time. For the first time, all the main areas of Erdős' research are covered in a single project. Because of overwhelming response from the mathematical community, the project now occupies over 1000 pages, arranged into two volumes. These volumes contain both high level research articles as well as key articles that survey some of the cornerstones of Erdős' work, each written by a leading world specialist in the field. A special chapter "Early Days", rare photographs, and art related to Erdős complement this striking collection. A unique contribution is the bibliography on Erdős' publications: the most comprehensive ever published. This new edition, dedicated to the 100th anniversary of Paul Erdős' birth, contains updates on many of the articles from the two volumes of the first edition, several new articles from prominent mathematicians, a new introduction, more biographical information about Paul Erdős, and an updated list of publications.

The first volume contains the unique chapter "Early Days", which features personal memories of Paul Erdős by a number of his colleagues. The other three chapters cover number theory, random methods, and geometry. All of these chapters are essentially updated, most notably the geometry chapter that covers the recent solution of the problem on the number of distinct distances in finite planar sets, which was the most popular of Erdős' favorite geometry problems.

Keywords

Erdős existence argument Erdős–Turán Paul Erdős Ramsey theory additive representation functions extremal theory incidence problems sum-product phenomena

Editors and affiliations

  • Ronald L. Graham
    • 1
  • Jaroslav Nešetřil
    • 2
  • Steve Butler
    • 3
  1. 1.Dept. Comp. Sci. & EngineeringUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of Applied MathematicsCharles University Department of Applied MathematicsPragueCzech Republic
  3. 3.Department of MathematicsIowa State UniversityAmesUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-7258-2
  • Copyright Information Springer Science+Business Media New York 2013
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-7257-5
  • Online ISBN 978-1-4614-7258-2
  • About this book
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