Erdoes Centennial (Bolyai Society Mathematical Studies 25 2013 ed.)

Erdoes Centennial (Bolyai Society Mathematical Studies 25 2013 ed.)

By: Domotor Palvolgyi (editor), Vera T. Sos (editor), Imre Ruzsa (editor), Laszlo Lovasz (editor)Hardback

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Description

Paul Erdoes 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.

Contents

Contents.- Preface.- Alon, N.: Paul Erdoes and Probabilistic Reasoning.- Benjamini, I.: Euclidean vs. Graph Metric.- Bollobas, B. and Riordan, O.: The Phase Transition in the Erdoes-Renyi Random Graph Process.- Bourgain, J.: Around the Sum-product Phenomenon.- Breuillard, E., Green, B. and Tao, T.: Small Doubling in Groups.- Diamond, H. G.: Erdoes and Multiplicative Number Theory.- Furedi, Z. and Simonovits, M.: The History of Degenerate (Bipartite) Extremal Graph Problems.- Gowers, W. T.: Erdoes and Arithmetic Progressions.- Graham, R. L.: Paul Erdoes and Egyptian Fractions.- Gyoery, K.: Perfect Powers in Products with Consecutive Terms from Arithmetic Progressions.- Komjath, P.: Erdoes's Work on Infinite Graphs.- Kunen, K.: The Impact of Paul Erd? os on Set Theory.- Mauldin, R. D.: Some Problems and Ideas of Erdoes 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 Erdoes and the Difference of Primes.- Pollack, P. and Pomerance, C.: Paul Erdoes and the Rise of Statistical Thinking in Elementary Number Theory.- Roedl, V. and Schacht, M.: Extremal Results in Random Graphs.-Schinzel, A.: Erdoes's Work on the Sum of Divisors Function and on Euler's Function.- Shalev, A.: Some Results and Problems in the Theory of Word Maps.- Tenenbaum, G.: Some of Erdoes' Unconventional Problems in Number Theory, Thirty-four Years Later.- Totik, V.: Erdoes on Polynomials.- Vertesi, P.: Paul Erdoes and Interpolation: Problems, Results, New Developments.

Product Details

  • ISBN13: 9783642392856
  • Format: Hardback
  • Number Of Pages: 720
  • ID: 9783642392856
  • ISBN10: 3642392857
  • edition: 2013 ed.

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