A=B

Rating:
Summary: Marko Petkovsek spins a brillant portrayl of data
Review: Marko Petkovsek may be the first of a new generation of writers who bring life to a dry stle of instructional materials.

A non stop thriller of statistacal information.

A MUST READ.

Rating:
Summary: Prize winning work
Review: The mathematics described in the book "A=B" lead to the awarding of a Steele Prize by the American Mathematical Society to Herbert Wilf and Doron Zeilberger. What the authors have done is to discover a way of using computer algebra and some mathematical ideas they and others had earlier to make it possible to find the sum of most of the hypergeometric and basic hypergeometric series which can be summed. This method also leads to recurrence relations when polynomial series cannot be summed. It does not work for all series, but most of the time it does work. 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.

Rating:
Summary: Prize winning work
Review: The mathematics described in the book "A=B" lead to the awarding of a Steele Prize by the American Mathematical Society to Herbert Wilf and Doron Zeilberger. What the authors have done is to discover a way of using computer algebra and some mathematical ideas they and others had earlier to make it possible to find the sum of most of the hypergeometric and basic hypergeometric series which can be summed. This method also leads to recurrence relations when polynomial series cannot be summed. It does not work for all series, but most of the time it does work. 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.

Rating:
Summary: Witty + Concise + Useful = Excellent
Review: This book is a refreshingly witty and concise look at--of all things--hypergeometric identities. If you have never heard of a binomial coefficient, or shudder at the thought of a double factorial, of fail to see what's so special about special functions, then you are unlikely to derive much pleasure from this volume. On the other hand, if you've encountered gamma functions, Catalan numbers, and Grobner bases, and would delight in discovering deep connections among such vastly different ideas, or if you have wondered how computers can be used to discover or verify monstrous combinatorial identities, then you've stumbled upon a book that is sure to become a favorite.

This book introduces the idea of hypergeometric function, the Swiss army knife of combinatorial mathematics, and proceeds to develop algorithms for their computation as well as numerous applications. The authors also reveal what, exactly, computers can help us to decide, what is a "closed form" solution, what are "canonical" and "normal" forms, and inject relevant philosophical digressions that keep the discussions lively and entertaining. The authors also present snippets of "Mathematica" code so that you can try out many of the basic operations yourself.

The book has concise chapters on Sister Celine's method, Gosper's algorithm, Zeilberger's algorithm, and the WZ algorithm, with sufficient detail that you will likely be able to apply the algorithms yourself (perhaps by downloading the Mathematica packages that the authors point you to). The techniques are invaluable in proving identities in combinatorial mathematics; that is, identities involving binomial coefficients, factorials, rational functions, etc. By means of such techniques, computers "not only find proofs of known identities, they also find completely new identities. Lots of them. Some very pretty. Some not so pretty but very useful. Some neither pretty nor useful, in which case we humans can ignore them."

This is a well-written and highly accessible book about an important (albeit very narrow and specialized) branch of mathematics. 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.

Rating:
Summary: Witty + Concise + Useful = Excellent
Review: This book is a refreshingly witty and concise look at--of all things--hypergeometric identities. If you have never heard of a binomial coefficient, or shudder at the thought of a double factorial, of fail to see what's so special about special functions, then you are unlikely to derive much pleasure from this volume. On the other hand, if you've encountered gamma functions, Catalan numbers, and Grobner bases, and would delight in discovering deep connections among such vastly different ideas, or if you have wondered how computers can be used to discover or verify monstrous combinatorial identities, then you've stumbled upon a book that is sure to become a favorite.

This book introduces the idea of hypergeometric function, the Swiss army knife of combinatorial mathematics, and proceeds to develop algorithms for their computation as well as numerous applications. The authors also reveal what, exactly, computers can help us to decide, what is a "closed form" solution, what are "canonical" and "normal" forms, and inject relevant philosophical digressions that keep the discussions lively and entertaining. The authors also present snippets of "Mathematica" code so that you can try out many of the basic operations yourself.

The book has concise chapters on Sister Celine's method, Gosper's algorithm, Zeilberger's algorithm, and the WZ algorithm, with sufficient detail that you will likely be able to apply the algorithms yourself (perhaps by downloading the Mathematica packages that the authors point you to). The techniques are invaluable in proving identities in combinatorial mathematics; that is, identities involving binomial coefficients, factorials, rational functions, etc. By means of such techniques, computers "not only find proofs of known identities, they also find completely new identities. Lots of them. Some very pretty. Some not so pretty but very useful. Some neither pretty nor useful, in which case we humans can ignore them."

This is a well-written and highly accessible book about an important (albeit very narrow and specialized) branch of mathematics. 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.