The Mathematics of Paul Erdős I, 2nd Edition

  • Published By:
  • ISBN-10: 146147258X
  • ISBN-13: 9781461472582
  • DDC: 510
  • Grade Level Range: College Freshman - College Senior
  • 563 Pages | eBook
  • Original Copyright 2013 | Published/Released June 2014
  • This publication's content originally published in print form: 2013

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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.

Table of Contents

Front Cover.
Half Title Page.
Other Frontmatter.
Title Page.
Copyright Page.
Preface to the Second Edition.
Preface to the First Edition.
1: Paul Erdős: Life and Work.
2: Erdős Magic.
3: Early Days.
4: Some of My Favorite Problems and Results.
5: Integers Uniquely Represented by Certain Ternary Forms.
6: Did Erdős Save Western Civilization?.
7: Encounters with Paul Erdős.
8: On Cubic Graphs of Girth at Least Five.
9: Number Theory.
10: Cross-Disjoint Pairs of Clouds in the Interval Lattice.
11: Classical Results on Primitive and Recent Results on Cross-Primitive Sequences.
12: Dense Difference Sets and Their Combinatorial Structure.
13: Integer Sets Containing No Solution to X + Y = 3z.
14: On Primes Recognizable in Deterministic Polynomial Time.
15: Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture.
16: On Landau’s Function G(N).
17: On Divisibility Properties of Sequences of Integers.
18: On Additive Representative Functions.
19: Arithmetical Properties of Polynomials.
20: Some Methods of Erdős Applied to Finite Arithmetic Progressions.
21: Sur La Non-D´erivabilit´e De Fonctions P´eriodiques Associ´ees `a Certaines Formules Sommatoires.
22: 1105: First Steps in a Mysterious Quest.
23: Randomness and Applications.
24: Games, Randomness and Algorithms.
25: On Some Hypergraph Problems of Paul Erdős and the Asymptotics of Matchings, Covers and Colorings.
26: The Origins of the Theory of Random Graphs.
27: An Upper Bound for a Communication Game Related to Time-Space Tradeoffs.
28: How Abelian Is a Finite Group?.
29: On Small Size Approximation Models.
30: The Erdős Existence Argument.
31: Geometry.
32: Extension of Functional Equations.
33: Remarks on Penrose Tilings.
34: Distances in Convex Polygons.
35: Unexpected Applications of Polynomials in Combinatorics.
36: The Number of Homothetic Subsets.
37: On Lipschitz Mappings onto a Square∗.
38: A Remark on Transversal Numbers.
39: In Praise of the Gram Matrix.
40: On Mutually Avoiding Sets∗.