Mathematics of Paul Erdős I

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 Nešetřil 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.

• VOLUME I.- Paul Erdős — Life and Work.- Paul Erdős Magic.- Part I Early Days.-  Introduction.- Some of My Favorite Problems and Results.- 3 Encounters with Paul Erdős.- 4 Did Erdős Save Western Civilization?.- Integers Uniquely Represented by Certain Ternary Forms.- Did Erdős Save Western Civilization?.- Encounters with Paul Erdős.- 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 Erdős-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 Erdős 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 Erdős 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.