| Softcover ISBN: | 978-1-4704-5623-8 |
| Product Code: | MBK/134 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-6210-9 |
| Product Code: | MBK/134.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Softcover ISBN: | 978-1-4704-5623-8 |
| eBook: ISBN: | 978-1-4704-6210-9 |
| 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: | 978-1-4704-5623-8 |
| Product Code: | MBK/134 |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| eBook ISBN: | 978-1-4704-6210-9 |
| Product Code: | MBK/134.E |
| List Price: | $69.00 |
| MAA Member Price: | $62.10 |
| AMS Member Price: | $55.20 |
| Softcover ISBN: | 978-1-4704-5623-8 |
| eBook ISBN: | 978-1-4704-6210-9 |
| 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 |
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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 self-study 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.
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Table of Contents
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Chapters
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Inversions
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$q$-binomial theorems
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Partitions I: Elementary theory
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Partitions II: Geometry theory
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More $q$-identities: Jacobi, Guass, and Heine
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Ramanujan’s $_1\psi _1$ summation formula
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Sums of squares
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Ramanujan’s congruences
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Some combinatorial results
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The Rogers-Ramanujan identities I: Schur
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The Rogers-Ramanujan identities II: Rogers
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The Rogers-Selberg function
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Bailey’s $_6\psi _6$ sum
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Appendix A. A brief guide to notation
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Appendix B. Infinite products
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Appendix C. Tannery’s theorem
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Additional Material
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RequestsReview Copy – for publishers of book reviewsDesk Copy – for instructors who have adopted an AMS textbook for a courseExamination Copy – for faculty considering an AMS textbook for a coursePermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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 self-study 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 Rogers-Ramanujan identities I: Schur
-
The Rogers-Ramanujan identities II: Rogers
-
The Rogers-Selberg function
-
Bailey’s $_6\psi _6$ sum
-
Appendix A. A brief guide to notation
-
Appendix B. Infinite products
-
Appendix C. Tannery’s theorem
