Ronald L. Graham is currently Professor of Mathematics and Irwin and Joan Jacobs Professor of Computer and Information Sciences at the University of California, San Diego, and Chief Scientist at the California Institute for Telecommunications and Information Technology.

Jaroslav Nešet¿il is currently Professor of Mathematics and Director of the Institute of Theoretical Computer Science at Charles University, Prague.

Steve Butler is currently Assistant Professor of Mathematics at Iowa State University.

New and extensively revised edition with approximately 100 pages of new material

Contains new articles from prominent mathematicians such as Larry Guth, Alexander Razborov and Joel Spencer

Includes new introductions to all the individual parts, with an update of scientific activity in the last 20 years

The first book bringing together articles surveying the legacy of Paul Erdos in all fields of his activity

Features Paul Erdos' influence in number theory, random structures and geometry, with the most general collection of recent surveys available

VOLUME I.- Paul Erd¿s - Life and Work.- Paul Erd¿s Magic.- Part I Early Days.- Introduction.- Some of My Favorite Problems and Results.- 3 Encounters with Paul Erd¿s.- 4 Did Erd¿s Save Western Civilization?.- Integers Uniquely Represented by Certain Ternary Forms.- Did Erd¿s Save Western Civilization?.- Encounters with Paul Erd¿s.- On Cubic Graphs of Girth at Least Five.- Part II Number Theory.- Introduction.- Cross-disjoint Pairs of Clouds in the Interval Lattice.- Classical Results on Primitive and Recent Results on Cross-Primitive Sequences.- Dense Difference Sets and their Combinatorial Structure.- Integer Sets Containing No Solution to x+y=3z.- On Primes Recognizable in Deterministic Polynomial Time.- Ballot Numbers, Alternating Products, and the Erd¿s-Heilbronn Conjecture.- On Landau's Function g(n).- On Divisibility Properties on Sequences of Integers.- On Additive Representation Functions.- Arithmetical Properties of Polynomials.- Some Methods of Erd¿s Applied to Finite Arithmetic Progressions.- Sur La Non-Dérivabilité de Fonctions Périodiques Associées à Certaines Formules Sommatoires.- 1105: First Steps in a Mysterious Quest.- Part III Randomness and Applications.- Introduction.- Games, Randomness, and Algorithms.- The Origins of the Theory of Random Graphs.- An Upper bound for a Communication Game Related to Time-space Tradeoffs.- How Abelian is a Finite Group?.- One Small Size Approximation Models.- The Erd¿s Existence Argument.- Part IV Geometry.- Introduction.- Extension of Functional Equations.- Remarks on Penrose Tilings.- Distances in Convex Polygons.- Unexpected Applications of Polynomials in Combinatorics.- The Number of Homothetic Subsets.- On Lipschitz Mappings Onto a Square.- A Remark on Transversal Numbers.- In Praise of the Gram Matrix.- On Mutually Avoiding Sets.- Bibliography.