Softcover ISBN:  9781470409043 
Product Code:  STML/71 
List Price:  $42.00 
Individual Price:  $33.60 
Electronic ISBN:  9781470416614 
Product Code:  STML/71.E 
List Price:  $39.00 
Individual Price:  $31.20 

Book DetailsStudent Mathematical LibraryVolume: 71; 2014; 183 ppMSC: Primary 05; Secondary 68; 11; 60;
This beautiful book is about how to estimate large quantities—and 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, EötvösLoránd University
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 \(t\) 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 \(n\ln n\), \(n^2\), \(\frac{\ln n}{n}\), \(\sqrt{\ln n}\), \(\frac{1}{n\ln n}\) 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!ReadershipUndergraduate and graduate students interested in asymptotic techniques.

Table of Contents

Chapters

Chapter 0. An infinity of primes

Chapter 1. Stirling’s formula

Chapter 2. Big Oh, little oh and all that

Chapter 3. Integration in Asymptopia

Chapter 4. From integrals to sums

Chapter 5. Asymptotics of binomial coefficients $\binom {n}{k}$

Chapter 6. Unicyclic graphs

Chapter 7. Ramsey numbers

Chapter 8. Large deviations

Chapter 9. Primes

Chapter 10. Asymptotic geometry

Chapter 11. Algorithms

Chapter 12. Potpourri

Chapter 13. Really Big Numbers!


Additional Material

Reviews

The style and the beauty make this book an excellent reading. Keep it on your coffee table or/and bed table and open it often. Asymptopia is a fascinating place.
Péter Hajnal, ACTA Sci. Math.


RequestsReview Copy – for reviewers who would like to review an AMS bookPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
 Book Details
 Table of Contents
 Additional Material
 Reviews
 Requests
This beautiful book is about how to estimate large quantities—and 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, EötvösLoránd University
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 \(t\) 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 \(n\ln n\), \(n^2\), \(\frac{\ln n}{n}\), \(\sqrt{\ln n}\), \(\frac{1}{n\ln n}\) 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!
Undergraduate and graduate students interested in asymptotic techniques.

Chapters

Chapter 0. An infinity of primes

Chapter 1. Stirling’s formula

Chapter 2. Big Oh, little oh and all that

Chapter 3. Integration in Asymptopia

Chapter 4. From integrals to sums

Chapter 5. Asymptotics of binomial coefficients $\binom {n}{k}$

Chapter 6. Unicyclic graphs

Chapter 7. Ramsey numbers

Chapter 8. Large deviations

Chapter 9. Primes

Chapter 10. Asymptotic geometry

Chapter 11. Algorithms

Chapter 12. Potpourri

Chapter 13. Really Big Numbers!

The style and the beauty make this book an excellent reading. Keep it on your coffee table or/and bed table and open it often. Asymptopia is a fascinating place.
Péter Hajnal, ACTA Sci. Math.