
Preface  Preview Material  Table of Contents  Index  Supplementary Material 
Student Mathematical Library 2014; 183 pp; softcover Volume: 71 ISBN10: 1470409046 ISBN13: 9781470409043 List Price: US$39 Institutional Members: US$31.20 All Individuals: US$31.20 Order Code: STML/71 See also: Complex Graphs and Networks  Fan Chung and Linyuan Lu Combinatorial Problems and Exercises: Second Edition  Laszlo Lovasz Geometric Approximation Algorithms  Sariel HarPeled  This beautiful book is about how to estimate large quantitiesand why. Building on nothing more than firstyear calculus, it goes all the way into deep asymptotical methods and shows how these can be used to solve problems in number theory, combinatorics, probability, and geometry. The author is a master of exposition: starting from such a simple fact as the infinity of primes, he leads the reader through small steps, each carefully motivated, to many theorems that were cuttingedge when discovered, and teaches the general methods to be learned from these results. László Lovász, LorándEötvösUniversity This is a lovely little travel guide to a country you might not even have heard about  full of wonders, mysteries, small and large discoveries ... and in Joel Spencer you have the perfect travel guide! Günter M. Ziegler, Freie Universität Berlin, coauthor of "Proofs from THE BOOK" 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, Erdős Magic, random graphs, Ramsey numbers, and asymptotic geometry. The author is a disciple of Paul Erdős, who taught him about Asymptopia. Primes less than \(n\), graphs with \(v\) vertices, random walks of \(t\) stepsErdős was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions \(n\ln n\), \(n^2\), \(\frac{\ln n}{n}\), \(\sqrt{\ln n}\), \(\frac{1}{n\ln n}\) all have distinct personalities. Erdős 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! Readership Undergraduate and graduate students interested in asymptotic techniques. 


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