Probabilistic Methods in Combinatorics

Science & Math

Paul Erdős

Joel Spencer

Mathematics

Academic Press

Paul Erdös, who has been called the world's greatest problem poser and solver, has published more papers than any mathematician alive. The aim of this selection from his vast output is to bring together his most important papers. Over 80 contributions are included, which are grouped into four parts and sixteen chapters as follows: Papers of Special Interest: an early gem—problems; Graph Theory: representation of graphs—coloring of graphs—extremal graph theory—circuits—assorted graph theory; Combinatorial Analysis; Ramsey's theorem—property B—systems of sets—block designs—tournaments—information theory; Miscellany: random objects—Latin squares—geometry. Erdös is a kind of mathematical wandering scholar. Over the past 40 years, he has traveled to more than 200 universities throughout the world, posing problems and giving lectures: "I have no permanent position or address."

Paul Erdös : The Art of Counting

The MIT Press

Ten Lectures on the Probabilistic Method (Cbms-Nsf Regional Conference Series in Applied Mathematics, No 52)

Society for Industrial & Applied Mathematics

Asymptotics in one form or another are part of the landscape for every mathematician. The objective of this book is to present the ideas of how to approach asymptotic problems that arise in discrete mathematics, analysis of algorithms, and number theory. A broad range of topics is covered, including distribution of prime integers, Erd?s Magic, random graphs, Ramsey numbers, and asymptotic geometry. The author is a disciple of Paul Erd?s, who taught him about Asymptopia. Primes less than n , graphs with v vertices, random walks of t steps - Erd?s was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions nlnn , n 2 , lnn n , lnn ? ? ? ? , 1 nlnn all have distinct personalities. Erd?s knew these functions as personal friends. It is the author's hope that these insights may be passed on, that the reader may similarly feel which function has the right temperament for a given task. This book is aimed at strong undergraduates, though it is also suitable for particularly good high school students or for graduates wanting to learn some basic techniques. Asymptopia is a beautiful world. Enjoy!

Asymptopia (Student Mathematical Library) (Student Mathematical Library, 71)

American Mathematical Society

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Books by Joel Spencer