An error was encountered while trying to add the item to the cart. Please try again.
The following link can be shared to navigate to this page. You can select the link to copy or click the 'Copy To Clipboard' button below.
Copy To Clipboard
Successfully Copied!
Number Theory in the Spirit of Ramanujan

Bruce C. Berndt University of Illinois, Urbana-Champaign, Urbana, IL
Available Formats:
Softcover ISBN: 978-0-8218-4178-5
Product Code: STML/34
List Price: $41.00 Individual Price:$32.80
Electronic ISBN: 978-1-4704-2145-8
Product Code: STML/34.E
List Price: $38.00 Individual Price:$30.40
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: $61.50 Click above image for expanded view Number Theory in the Spirit of Ramanujan Bruce C. Berndt University of Illinois, Urbana-Champaign, Urbana, IL Available Formats:  Softcover ISBN: 978-0-8218-4178-5 Product Code: STML/34  List Price:$41.00 Individual Price: $32.80  Electronic ISBN: 978-1-4704-2145-8 Product Code: STML/34.E  List Price:$38.00 Individual Price: $30.40 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:$61.50
• Book Details

Student Mathematical Library
Volume: 342006; 187 pp
MSC: Primary 11; Secondary 33;

Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics.

The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.

Undergraduate and graduate students interested in number theory, including $q$-series and theta functions.

• Chapters
• Chapter 1. Introduction
• Chapter 2. Congruences for $p(n)$ and $\tau (n)$
• Chapter 3. Sums of squares and sums of triangular numbers
• Chapter 4. Eisenstein series
• Chapter 5. The connection between hypergeometric functions and theta functions
• Chapter 6. Applications of the primary theorem of Chapter 5
• Chapter 7. The Rogers-Ramanujan continued fraction

• Reviews

• ... undergraduates will find no better place to meet the mind behind the towering reputation.

D. V. Feldman, University of New Hampshire for CHOICE Reviews
• This is a delightful little book on selected topics in number theory. ...I highly recommend this book to all mathematicians. It is a great resource both to learn from and to teach from. Even the experts will enjoy his new perspective on these old questions.

Journal of Approximation Theory
• This slender volume is extremely well-written and contains a wealth of material. It is a lucid and accessible introduction to a rich and fascinating area of mathematics, written by the world's leading expert. For anyone with a knowledge of calculus wanting to learn about the mathematical work of Ramanujan, this book is the best place to start.

Shaun Cooper, Massey University - New Zealand Newsletter
• ...“Number theory in the spirit of Ramanujan” is a gem that deserves a place in every mathematician's library.

Zentralblatt MATH
• Request Review Copy
• Get Permissions
Volume: 342006; 187 pp
MSC: Primary 11; Secondary 33;

Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics.

The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.

Undergraduate and graduate students interested in number theory, including $q$-series and theta functions.

• Chapters
• Chapter 1. Introduction
• Chapter 2. Congruences for $p(n)$ and $\tau (n)$
• Chapter 3. Sums of squares and sums of triangular numbers
• Chapter 4. Eisenstein series
• Chapter 5. The connection between hypergeometric functions and theta functions
• Chapter 6. Applications of the primary theorem of Chapter 5
• Chapter 7. The Rogers-Ramanujan continued fraction
• ... undergraduates will find no better place to meet the mind behind the towering reputation.

D. V. Feldman, University of New Hampshire for CHOICE Reviews
• This is a delightful little book on selected topics in number theory. ...I highly recommend this book to all mathematicians. It is a great resource both to learn from and to teach from. Even the experts will enjoy his new perspective on these old questions.

Journal of Approximation Theory
• This slender volume is extremely well-written and contains a wealth of material. It is a lucid and accessible introduction to a rich and fascinating area of mathematics, written by the world's leading expert. For anyone with a knowledge of calculus wanting to learn about the mathematical work of Ramanujan, this book is the best place to start.

Shaun Cooper, Massey University - New Zealand Newsletter
• ...“Number theory in the spirit of Ramanujan” is a gem that deserves a place in every mathematician's library.

Zentralblatt MATH
You may be interested in...
Please select which format for which you are requesting permissions.