TY - BOOK AU - Graham,Ronald L. AU - Nesetril,Jaroslav AU - Butler,Steve TI - Mathematics of Paul Erdos SN - 9781461472575 (v. 1 : acidfree paper) U1 - 510 23 PY - 2013/// CY - New York PB - Springer KW - Erdos, Paul. KW - Mathematics N1 - "List of publications of Paul Erdos, January 2013": v. 2, p. [497]-603; Includes bibliographical references; Vol. 1. : Paul Erdos: Life and Work -- Paul Erdoos Magic -- Part I Early Days -- Introduction -- Some of My Favorite Problems and Results -- 3 Encounters with Paul Erdös -- 4 Did Erdös Save Western Civilization? -- Integers Uniquely Represented by Certain Ternary Forms -- Did Erdös Save Western Civilization? -- Encounters with Paul Erdös -- 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 Erdös-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 Erdös 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 Erdös 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; Vol. 2. : Part I Combinatorics and Graph Theory -- Introduction -- Reconstruction Problems for Digraphs -- Neighborly Families of Boxes and Bipartite Coverings -- On the Isolation of a Common Secret -- Properties of Graded Posets Preserved by Some Operations -- The Dimension of Random Graph Orders -- Hereditary and Monotone Properties of Graphs -- Cycles and Paths in Triangle-Free Graphs -- Problems in Graph Theory from Memphis -- Some Remarks on the Cycle Plus Triangles Problem -- Intersection Representations of the Complete Bipartite Graph -- Reflections on a Problem of Erdös and Hajnal -- The Chromatic Number of the Two-Packing of a Forest -- Part II Ramsey and Extremal Theory -- Introduction -- Ramsey Theory in the Work of Paul Erdös -- Memories on Shadows and Shadows of Memories -- A Bound of the Cardinality of Families Not Containing D-Systems -- Flag Algebras: An Interim Report -- Arrangeability and Clique Subdivisions -- A Finite Partition Theorem with Double Exponential Bound -- Paul Erdös' Influence on Extremal Graph Theory -- Applications of the Probabilistic Method to Partially Ordered Sets -- Part III Infinity -- Introduction -- A Few Remarks on a Conjecture of Erdös on the Infinite Version of Menger's Theorem -- The Random Graph -- Paul Erdös' Set Theory -- Set Theory: Geometric and Real -- On Order-Perfect Lattices -- The PCF Theorem Revisited -- Paul Erdös: The Master of Collaboration -- List of Publications of Paul Erdoos -- N2 - Here is a comprehensive overview of the mathematical life of Paul Erdos (1913-1996), a versatile and prolific mathematician. This second volume covers graph theory and combinatorics, extremal and Ramsey theory, and Erdos's research on set theory. ER -