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The mathematics of Paul Erdős I

Author: Ronald L Graham; Jaroslav Nešetřil; Steve Butler
Publisher: New York, NY : Springer, 2013.
Edition/Format:   eBook : Document : Biography : English : Second editionView all editions and formats
Database:WorldCat
Summary:
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  Read more...
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Details

Genre/Form: Electronic books
Named Person: Paul Erdős; Paul Erdös; Paul Erdős
Material Type: Biography, Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Ronald L Graham; Jaroslav Nešetřil; Steve Butler
ISBN: 9781461472582 146147258X 1461472571 9781461472575
OCLC Number: 856648293
Description: 1 online resource (xix, 563 pages) : illustrations
Contents: Paul Erdős: Life and Work / Béla Bollobás --
Erdős Magic / Joel Spencer --
Part I. Early Days. Some of My Favorite Problems and Results / Paul Erdős --
Integers Uniquely Represented by Certain Ternary Forms / Irving Kaplansky --
Did Erdős Save Western Civilization? / Cedric A.B. Smith --
Encounters with Paul Erdős / Arthur H. Stone --
On Cubic Graphs of Girth at Least Five / William T. Tutte. Part II. Number Theory. Cross-Disjoint Pairs of Clouds in the Interval Lattice / Rudolf Ahlswede, Ning Cai --
Classical Results on Primitive and Recent Results on Cross-Primitive Sequences / Rudolf Ahlswede, Levan H. Khachatrian --
Dense Difference Sets and Their Combinatorial Structure / Vitaly Bergelson, Paul Erdős, Neil Hindman, Tomasz Łuczak --
Integer Sets Containing No Solution to x+y=3z / Fan R.K. Chung, John L. Goldwasser --
On Primes Recognizable in Deterministic Polynomial Time / Sergei Konyagin, Carl Pomerance --
Ballot Numbers, Alternating Products, and the Erdős-Heilbronn Conjecture / Melvyn B. Nathanson --
On Landau's Function g(n) / Jean-Louis Nicolas --
On Divisibility Properties of Sequences of Integers / András Sárközy --
On Additive Representative Functions / András Sárközy, Vera T. Sós --
Arithmetical Properties of Polynomials / Andrzej Schinzel --
Some Methods of Erdős Applied to Finite Arithmetic Progressions / T.N. Shorey, Robert Tijdeman --
Sur la non-dérivabilité de fonctions périodiques associées à certaines formules sommatoires / Gérald Tenenbaum --
1105: First Steps in a Mysterious Quest / Gérald Tenenbaum. Part III. Randomness and Applications. Games, Randomness and Algorithms / József Beck --
On Some Hypergraph Problems of Paul Erdős and the Asymptotics of Matchings, Covers and Colorings / Jeff Kahn --
The Origins of the Theory of Random Graphs / Michał Karoński, Andrzej Ruciński --
An Upper Bound for a Communication Game Related to Time-Space Tradeoffs / Pavel Pudlák, Jiří Sgall --
How Abelian is a Finite Group? / Lásló Pyber --
On Small Size Approximation Models / Alexander A. Razborov --
The Erdős Existence Argument / Joel Spencer. Part IV. Geometry. Extension of Functional Equations / János Aczél, László Losonczi --
Remarks on Penrose Tilings / N.G. de Bruijn --
Distances in Convex Polygons / Peter Fishburn --
Unexpected Applications of Polynomials in Combinatorics / Larry Guth --
The Number of Homothetic Subsets / Miklós Laczkovich, Imre Z. Ruzsa --
On Lipschitz Mappings Onto a Square / Jiří Matoušek --
A Remark on Transversal Numbers / János Pach --
In Praise of the Gram Matrix / Moshe Rosenfeld --
On Mutually Avoiding Sets / Pavel Valtr.
Responsibility: Ronald L. Graham, Jaroslav Nešetřil, Steve Butler, Editors.

Abstract:

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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