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In the area of combinatorial identities computers are able to find very elegant proofs of difficult theorems unassisted by human intervention. This book shows how several recently developed computer algorithms can master the difficult job of simplifying complex summations.

This book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics. From the table of contents:
* Proof Machines
* Tightening the Target
* The Hypergeometric Database
* The Five Basic Algorithms: Sister Celine's Method, Gosper&'s Algorithm, Zeilberger's Algorithm, The WZ Phenomenon, Algorithm Hyper
* Epilogue: An Operator Algebra Viewpoint
* The WWW Sites and the Software (Maple and Mathematica) Each chapter contains an introduction to the subject and ends with a set of exercises.