The Mathematics of Paul Erdős I

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-D?rivabilit? de Fonctions P?riodiques Associ?es ? 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.