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Generating functions, one of the most important tools in
enumerative combinatorics, are a bridge between discrete
mathematics and continuous analysis. Generating functions have
numerous applications in mathematics, especially in: Combinatorics;
Probability Theory; Statistics; Theory of Markov Chains; and Number
Theory. One of the most important and relevant recent applications
of combinatorics lies in the development of Internet search
engines, whose incredible capabilities dazzle even the
mathematically trained user.
This book is an introductory textbook on the design and analysis of
algorithms. The author uses a careful selection of a few topics to
illustrate the tools for algorithm analysis. Recursive algorithms
are illustrated by Quicksort, FFT, fast matrix multiplications, and
others. Algorithms associated with the network flow problem are
fundamental in many areas of graph connectivity, matching theory,
etc. Algorithms in number theory are discussed with some
applications to public key encryption. This second edition will
differ from the present edition mainly in that solutions to most of
the exercises will be included.
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A = B (Paperback)
Marko Petkovsek, Herbert S. Wilf, Doron Zeilberger
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R1,859
Discovery Miles 18 590
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Ships in 12 - 17 working days
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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 an introductory textbook on the design and analysis of
algorithms. The author uses a careful selection of a few topics to
illustrate the tools for algorithm analysis. Recursive algorithms
are illustrated by Quicksort, FFT, fast matrix multiplications, and
others. Algorithms associated with the network flow problem are
fundamental in many areas of graph connectivity, matching theory,
etc. Algorithms in number theory are discussed with some
applications to public key encryption. This second edition will
differ from the present edition mainly in that solutions to most of
the exercises will be included.
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A = B (Hardcover)
Marko Petkovsek, Herbert S. Wilf, Doron Zeilberger
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R5,341
Discovery Miles 53 410
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Ships in 12 - 17 working days
|
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.
Hardy, Littlewood and P6lya's famous monograph on inequalities [17J
has served as an introduction to hard analysis for many mathema
ticians. Some of its most interesting results center around
Hilbert's inequality and generalizations. This family of
inequalities determines the best bound of a family of operators on
/p. When such inequalities are restricted only to finitely many
variables, we can then ask for the rate at which the bounds of the
restrictions approach the uniform bound. In the context of Toeplitz
forms, such research was initiated over fifty years ago by Szego
[37J, and the chain of ideas continues to grow strongly today, with
fundamental contributions having been made by Kac, Widom, de
Bruijn, and many others. In this monograph I attempt to draw
together these lines of research from the point of view of
sharpenings of the classical inequalities of [17]. This viewpoint
leads to the exclusion of some material which might belong to a
broader-based discussion, such as the elegant work of Baxter,
Hirschman and others on the strong Szego limit theorem, and the
inclusion of other work, such as that of de Bruijn and his
students, which is basically nonlinear, and is therefore in some
sense disjoint from the earlier investigations. I am grateful to
Professor Halmos for inviting me to prepare this volume, and to
Professors John and Olga Todd for several helpful comments.
Philadelphia, Pa. H.S.W.
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