Ebook: The Mathematics of Paul Erdős I

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.

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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.

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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.

Content:
Front Matter....Pages i-xix
Front Matter....Pages 47-49
Some of My Favorite Problems and Results....Pages 51-70
Integers Uniquely Represented by Certain Ternary Forms....Pages 71-79
Did Erdős Save Western Civilization?....Pages 81-92
Encounters with Paul Erdős....Pages 93-98
On Cubic Graphs of Girth at Least Five....Pages 99-101
Front Matter....Pages 103-106
Cross-Disjoint Pairs of Clouds in the Interval Lattice....Pages 107-117
Classical Results on Primitive and Recent Results on Cross-Primitive Sequences....Pages 119-132
Dense Difference Sets and Their Combinatorial Structure....Pages 133-146
On Primes Recognizable in Deterministic Polynomial Time....Pages 147-157
Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture....Pages 159-186
On Landau’s Function g(n)....Pages 187-205
On Divisibility Properties of Sequences of Integers....Pages 207-220
On Additive Representative Functions....Pages 221-232
Arithmetical Properties of Polynomials....Pages 233-262
Some Methods of Erdős Applied to Finite Arithmetic Progressions....Pages 263-267
Sur la non-dérivabilité de fonctions périodiques associées à certaines formules sommatoires....Pages 269-287
1105: First Steps in a Mysterious Quest....Pages 289-300
Paul Erdős: Life and Work....Pages 301-308
Erdős Magic....Pages 1-41
Front Matter....Pages 43-46
Games, Randomness and Algorithms....Pages 309-309
On Some Hypergraph Problems of Paul Erdős and the Asymptotics of Matchings, Covers and Colorings....Pages 311-342
The Origins of the Theory of Random Graphs....Pages 343-369
An Upper Bound for a Communication Game Related to Time-Space Tradeoffs....Pages 371-397
How Abelian is a Finite Group?....Pages 399-407
On Small Size Approximation Models....Pages 409-423
The Erdős Existence Argument....Pages 425-433
Front Matter....Pages 435-444
Extension of Functional Equations....Pages 445-446
Remarks on Penrose Tilings....Pages 447-459
Distances in Convex Polygons....Pages 461-481
Unexpected Applications of Polynomials in Combinatorics....Pages 483-492
The Number of Homothetic Subsets....Pages 493-522
On Lipschitz Mappings Onto a Square....Pages 523-532
A Remark on Transversal Numbers....Pages 533-540
In Praise of the Gram Matrix....Pages 541-549
On Mutually Avoiding Sets....Pages 551-557
....Pages 559-563