Softcover ISBN:  9781470456238 
Product Code:  MBK/134 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470462109 
Product Code:  MBK/134.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Softcover ISBN:  9781470456238 
eBook: ISBN:  9781470462109 
Product Code:  MBK/134.B 
List Price:  $138.00 $103.50 
MAA Member Price:  $124.20 $93.15 
AMS Member Price:  $110.40 $82.80 
Softcover ISBN:  9781470456238 
Product Code:  MBK/134 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
eBook ISBN:  9781470462109 
Product Code:  MBK/134.E 
List Price:  $69.00 
MAA Member Price:  $62.10 
AMS Member Price:  $55.20 
Softcover ISBN:  9781470456238 
eBook ISBN:  9781470462109 
Product Code:  MBK/134.B 
List Price:  $138.00 $103.50 
MAA Member Price:  $124.20 $93.15 
AMS Member Price:  $110.40 $82.80 

Book Details2020; 519 ppMSC: Primary 05; 11; 33
Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to \(q\)analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view.
The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for selfstudy in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
ReadershipUndergraduate students interested in \(q\)analysis, combinatorics, and number theory.

Table of Contents

Chapters

Inversions

$q$binomial theorems

Partitions I: Elementary theory

Partitions II: Geometry theory

More $q$identities: Jacobi, Guass, and Heine

Ramanujan’s $_1\psi _1$ summation formula

Sums of squares

Ramanujan’s congruences

Some combinatorial results

The RogersRamanujan identities I: Schur

The RogersRamanujan identities II: Rogers

The RogersSelberg function

Bailey’s $_6\psi _6$ sum

Appendix A. A brief guide to notation

Appendix B. Infinite products

Appendix C. Tannery’s theorem


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Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to \(q\)analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view.
The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for selfstudy in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
Undergraduate students interested in \(q\)analysis, combinatorics, and number theory.

Chapters

Inversions

$q$binomial theorems

Partitions I: Elementary theory

Partitions II: Geometry theory

More $q$identities: Jacobi, Guass, and Heine

Ramanujan’s $_1\psi _1$ summation formula

Sums of squares

Ramanujan’s congruences

Some combinatorial results

The RogersRamanujan identities I: Schur

The RogersRamanujan identities II: Rogers

The RogersSelberg function

Bailey’s $_6\psi _6$ sum

Appendix A. A brief guide to notation

Appendix B. Infinite products

Appendix C. Tannery’s theorem