A equals B

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. 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.. In the area of combinatorial identities computers are able to find very elegant proofs of difficult theorems unassisted by human intervention. This autonomy means that not only is it possible to use a PC to find such a proof, but also the proof can be checked easily. This book shows how several recently developed computer algorithms can master the difficult job of simplifying complex summations and if there is no such simplification they will prove this to be the case. The authors present the underlying mathematical theory of these methods, the principle theorems and proofs, and include a package of computer programs that can do these tasks This book is helpful for mathematicians and computer scientists working in finite mathematics. It presents a breakthrough method for analyzing complex summations, and contains practical applications and conceptual developments having applications in other areas of mathematics.