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Asymptopia

Joel Spencer New York University, New York, NY
with Laura Florescu, New York University, NY
Available Formats:
Softcover ISBN: 978-1-4704-0904-3
Product Code: STML/71
List Price: $42.00 Individual Price:$33.60
Electronic ISBN: 978-1-4704-1661-4
Product Code: STML/71.E
List Price: $39.00 Individual Price:$31.20
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List Price: $63.00 Click above image for expanded view Asymptopia Joel Spencer New York University, New York, NY with Laura Florescu, New York University, NY Available Formats:  Softcover ISBN: 978-1-4704-0904-3 Product Code: STML/71  List Price:$42.00 Individual Price: $33.60  Electronic ISBN: 978-1-4704-1661-4 Product Code: STML/71.E  List Price:$39.00 Individual Price: $31.20 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$63.00
• Book Details

Student Mathematical Library
Volume: 712014; 183 pp
MSC: Primary 05; Secondary 68; 11; 60;

This beautiful book is about how to estimate large quantities—and why. Building on nothing more than first-year 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 cutting-edge when discovered, and teaches the general methods to be learned from these results.

László Lovász, Eötvös-Loránd 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!

• 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.
• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 712014; 183 pp
MSC: Primary 05; Secondary 68; 11; 60;

This beautiful book is about how to estimate large quantities—and why. Building on nothing more than first-year 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 cutting-edge when discovered, and teaches the general methods to be learned from these results.

László Lovász, Eötvös-Loránd 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.
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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