A=B

Shows how several recently developed computer algorithms can simplify complex summations, presenting the underlying mathematical theory of these methods, the principle theorems and proofs, and the implementation using Maple packages.

**Tag(s):**
Mathematics

**Publication date**: 01 Jan 1996

**ISBN-10**:
1568810636

**ISBN-13**:
9781568810638

**Paperback**:
224 pages

**Views**: 23,371

A=B

Shows how several recently developed computer algorithms can simplify complex summations, presenting the underlying mathematical theory of these methods, the principle theorems and proofs, and the implementation using Maple packages.

Terms and Conditions:

Book excerpts:

'A=B' is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. It's about transforming an important part of mathematics from an art to science. There should no more need to get a brilliant insight in order to evaluate sums of binomial coeficients, and many similar formulas that arise frequently in practice; readers will be able to follow a mechanical procedure and discover the answers quite systematically.

This book shows how several recently developed computer algorithms can simplify complex summations, presenting the underlying mathematical theory of these methods, the principle theorems and proofs, and advice for using two packages of Maple programs available on the official website.

Intended Audience:

Students and professionals interested in combinatorial identities will have great use for this book. People of computer science will be also interested in the authors' unique approach towards automated proofs.

Reviews:

Amazon.com

Peter Paule, RISC-Linz; Austria

Jan Denef, in J. Approximation Theory, October, 1999

Vladik Kreinovich, in SIGACT News, 31, No. 4, 2000

Reproduction of the downloaded version is permitted for any valid educational purpose of an institution of learning, in which case only the reasonable costs of reproduction may be charged. Reproduction for profit or for any commercial purposes is strictly prohibited.

Book excerpts:

'A=B' is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. It's about transforming an important part of mathematics from an art to science. There should no more need to get a brilliant insight in order to evaluate sums of binomial coeficients, and many similar formulas that arise frequently in practice; readers will be able to follow a mechanical procedure and discover the answers quite systematically.

This book shows how several recently developed computer algorithms can simplify complex summations, presenting the underlying mathematical theory of these methods, the principle theorems and proofs, and advice for using two packages of Maple programs available on the official website.

Intended Audience:

Students and professionals interested in combinatorial identities will have great use for this book. People of computer science will be also interested in the authors' unique approach towards automated proofs.

Reviews:

Amazon.com

:) "If you have little experience with hypergeometric functions, yet deal with combinatorial mathematics, you will likely read this book in one (long) sitting; and you'll be glad you did."

:) "This book and the ideas in it should be part of the working knowledge of anyone who uses special functions of hypergeometric or basic hypergeometric type."

Peter Paule, RISC-Linz; Austria

:) "In particular, this book is a must for all those who at least once have struggled with a binomial sum."

Jan Denef, in J. Approximation Theory, October, 1999

:) "The book is written in an exceptionally clear way and can be read by anyone who has had at least one year of university mathematics. The many examples, all verifiable in real time on your PC, make the book very lively. The material is absolutely fascinating, both for undergraduates and for professional mathematicians..."

Vladik Kreinovich, in SIGACT News, 31, No. 4, 2000

:) "Although the book is very technical, it is written in a very popular and understandable way. It starts with the basics, it gently guides the reader through the programs, through the formulas and through the numerous examples..."

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About The Author(s)

No information is available for this author.

Herbert Wilf (1931-2012) was the University of Pennsylvania Thomas A. Scott Emeritus Professor of Mathematics. He was the author of six books and more than 160 research articles. From the 1950's, he was a pioneer in the mathematical programming of early computers, beginning with his work at Nuclear Development Associates, which led to his book Mathematical Methods for Digital Computers, written with A. Ralston. His early work focused on numerical analysis and complex analysis, and led to numerous research papers as well as a textbook, Mathematics for the Physical Sciences.

No information is available for this author.

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