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Number Theory in the Spirit of Ramanujan
 
Bruce C. Berndt University of Illinois, Urbana-Champaign, Urbana, IL
Number Theory in the Spirit of Ramanujan
Softcover ISBN:  978-0-8218-4178-5
Product Code:  STML/34
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2145-8
Product Code:  STML/34.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-4178-5
eBook: ISBN:  978-1-4704-2145-8
Product Code:  STML/34.B
List Price: $108.00 $83.50
Number Theory in the Spirit of Ramanujan
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Number Theory in the Spirit of Ramanujan
Bruce C. Berndt University of Illinois, Urbana-Champaign, Urbana, IL
Softcover ISBN:  978-0-8218-4178-5
Product Code:  STML/34
List Price: $59.00
Individual Price: $47.20
eBook ISBN:  978-1-4704-2145-8
Product Code:  STML/34.E
List Price: $49.00
Individual Price: $39.20
Softcover ISBN:  978-0-8218-4178-5
eBook ISBN:  978-1-4704-2145-8
Product Code:  STML/34.B
List Price: $108.00 $83.50
  • 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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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