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An Introduction to $q$-analysis

Warren P. Johnson Connecticut College, New London, CT
Available Formats:
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 Electronic 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
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $103.50 MAA Member Price:$93.15
AMS Member Price: $82.80 Click above image for expanded view An Introduction to$q$-analysis Warren P. Johnson Connecticut College, New London, CT Available Formats:  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
 Electronic 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 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:$103.50 MAA Member Price: $93.15 AMS Member Price:$82.80
• Book Details

2020; 519 pp
MSC: 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.

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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
2020; 519 pp
MSC: 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.

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
Review Copy – for reviewers who would like to review an AMS book
Desk Copy – for instructors who have adopted an AMS textbook for a course
Examination Copy – for faculty considering an AMS textbook for a course
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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