Sistema Bibliotecario de la Universidad de Quintana Roo

Contents -- Preface -- Alon, N.: Paul Erdȵs and Probabilistic Reasoning -- Benjamini, I.: Euclidean vs. Graph Metric -- Bollobas, B. and Riordan, O.: The Phase Transition in the ErdȵsRȨnyi Random Graph Process -- Bourgain, J.: Around the Sum-product Phenomenon -- Breuillard, E., Green, B. and Tao, T.: Small Doubling in Groups -- Diamond, H. G.: Erdȵs and Multiplicative Number Theory -- Fȭredi, Z. and Simonovits, M.: The History of Degenerate (Bipartite) Extremal Graph Problems -- Gowers, W. T.: Erdȵs and Arithmetic Progressions -- Graham, R. L.: Paul Erdȵs and Egyptian Fractions -- Gyȵry, K.: Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions -- Komjth, P.: Erdȵss Work on Infinite Graphs -- Kunen, K.: The Impact of Paul Erdݥos on Set Theory -- Mauldin, R. D.: Some Problems and Ideas of Erdȵs in Analysis and Geometry -- Montgomery, H. L.: L2 Majorant Principles -- Nesetril, J.: A Combinatorial Classic Sparse Graphs with High Chromatic Number -- Nguyen, H. H. and Vu, V. H.: Small Ball Probability, Inverse Theorems, and Applications -- Pach, J.: The Beginnings of Geometric Graph Theory -- Pintz, J.: Paul Erdȵs and the Difference of Primes -- Pollack, P. and Pomerance, C.: Paul Erdȵs and the Rise of Statistical Thinking in Elementary Number Theory -- Rȵdl, V. and Schacht, M.: Extremal Results in Random Graphs.-Schinzel, A.: Erdȵss Work on the Sum of Divisors Function and on Eulers Function -- Shalev, A.: Some Results and Problems in the Theory of Word Maps -- Tenenbaum, G.: Some of Erdȵs Unconventional Problems in Number Theory, Thirty-four Years Later -- Totik, V.: Erdȵs on Polynomials -- Vertesi, P.: Paul Erdȵs and Interpolation: Problems, Results, New Developments.

Paul Erdȵs was one of the most influential mathematicians of the twentieth century, whose work in number theory, combinatorics, set theory, analysis, and other branches of mathematics has determined the development of large areas of these fields. In 1999, a conference was organized to survey his work, his contributions to mathematics, and the far-reaching impact of his work on many branches of mathematics. On the 100th anniversary of his birth, this volume undertakes the almost impossible task to describe the ways in which problems raised by him and topics initiated by him (indeed, whole branches of mathematics) continue to flourish. Written by outstanding researchers in these areas, these papers include extensive surveys of classical results as well as of new developments.