Asymptopia
Spencer, Joel
Asymptopia - Rhode Island : American Mathematical Society, 2014. - xiv, 183p. : illustrations ; 22 cm. - Student mathematical library ; volume 71 .
Includes bibliographical references (pages 179-180) and index.
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 steps—Erdős was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions nlnn, n2, lnnn, lnn−−−√, 1nlnn 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.
9781470438432
Combinatorial analysis.
Combinatorial enumeration problems.
Asymptotic expansions.
Ramsey numbers--Asymptotic theory.
Combinatorics -- Instructional exposition (textbooks, tutorial papers, etc.).
Combinatorics -- Enumerative combinatorics -- Asymptotic enumeration.
Combinatorics -- Graph theory -- Random graphs.
Computer science -- Algorithms -- Analysis of algorithms.
Number theory -- Elementary number theory -- Primes.
Probability theory and stochastic processes -- Combinatorial probability -- Combinatorial probability.
511.35 / SPE-A
Asymptopia - Rhode Island : American Mathematical Society, 2014. - xiv, 183p. : illustrations ; 22 cm. - Student mathematical library ; volume 71 .
Includes bibliographical references (pages 179-180) and index.
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 steps—Erdős was fascinated by the limiting behavior as the variables approached, but never reached, infinity. Asymptotics is very much an art. The various functions nlnn, n2, lnnn, lnn−−−√, 1nlnn 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.
9781470438432
Combinatorial analysis.
Combinatorial enumeration problems.
Asymptotic expansions.
Ramsey numbers--Asymptotic theory.
Combinatorics -- Instructional exposition (textbooks, tutorial papers, etc.).
Combinatorics -- Enumerative combinatorics -- Asymptotic enumeration.
Combinatorics -- Graph theory -- Random graphs.
Computer science -- Algorithms -- Analysis of algorithms.
Number theory -- Elementary number theory -- Primes.
Probability theory and stochastic processes -- Combinatorial probability -- Combinatorial probability.
511.35 / SPE-A
