Generatingfunctionology
Generatingfunctionology

Author: Herbert S. Wilf

Publisher: Elsevier

Published: 2014-05-10

Total Pages: 193

ISBN-13: 1483276635

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Generatingfunctionology provides information pertinent to generating functions and some of their uses in discrete mathematics. This book presents the power of the method by giving a number of examples of problems that can be profitably thought about from the point of view of generating functions. Organized into five chapters, this book begins with an overview of the basic concepts of a generating function. This text then discusses the different kinds of series that are widely used as generating functions. Other chapters explain how to make much more precise estimates of the sizes of the coefficients of power series based on the analyticity of the function that is represented by the series. This book discusses as well the applications of the theory of generating functions to counting problems. The final chapter deals with the formal aspects of the theory of generating functions. This book is a valuable resource for mathematicians and students.

Generating Functionology
Generating Functionology

Author: Herbert S. Wilf

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 239

ISBN-13: 0080571514

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This is the Second Edition of the highly successful introduction to the use of generating functions and series in combinatorial mathematics. This new edition includes several new areas of application, including the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences. An appendix on using the computer algebra programs MAPLE(r) and Mathematica(r) to generate functions is also included. The book provides a clear, unified introduction to the basic enumerative applications of generating functions, and includes exercises and solutions, many new, at the end of each chapter. Provides new applications on the cycle index of the symmetric group, permutations and square roots, counting polyominoes, and exact covering sequences Features an Appendix on using MAPLE(r) and Mathematica (r) to generate functions Includes many new exercises with complete solutions at the end of each chapter

Analytic Combinatorics
Analytic Combinatorics

Author: Philippe Flajolet

Publisher: Cambridge University Press

Published: 2009-01-15

Total Pages: 825

ISBN-13: 1139477161

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Analytic combinatorics aims to enable precise quantitative predictions of the properties of large combinatorial structures. The theory has emerged over recent decades as essential both for the analysis of algorithms and for the study of scientific models in many disciplines, including probability theory, statistical physics, computational biology, and information theory. With a careful combination of symbolic enumeration methods and complex analysis, drawing heavily on generating functions, results of sweeping generality emerge that can be applied in particular to fundamental structures such as permutations, sequences, strings, walks, paths, trees, graphs and maps. This account is the definitive treatment of the topic. The authors give full coverage of the underlying mathematics and a thorough treatment of both classical and modern applications of the theory. The text is complemented with exercises, examples, appendices and notes to aid understanding. The book can be used for an advanced undergraduate or a graduate course, or for self-study.

Excursions in Calculus
Excursions in Calculus

Author: Robert M. Young

Publisher: Cambridge University Press

Published: 1992

Total Pages: 436

ISBN-13: 9780883853177

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This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.

Mathematics for the Physical Sciences
Mathematics for the Physical Sciences

Author: Herbert S Wilf

Publisher: Courier Corporation

Published: 2013-01-18

Total Pages: 304

ISBN-13: 0486153347

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Topics include vector spaces and matrices; orthogonal functions; polynomial equations; asymptotic expansions; ordinary differential equations; conformal mapping; and extremum problems. Includes exercises and solutions. 1962 edition.

102 Combinatorial Problems
102 Combinatorial Problems

Author: Titu Andreescu

Publisher: Springer Science & Business Media

Published: 2013-11-27

Total Pages: 125

ISBN-13: 0817682228

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"102 Combinatorial Problems" consists of carefully selected problems that have been used in the training and testing of the USA International Mathematical Olympiad (IMO) team. Key features: * Provides in-depth enrichment in the important areas of combinatorics by reorganizing and enhancing problem-solving tactics and strategies * Topics include: combinatorial arguments and identities, generating functions, graph theory, recursive relations, sums and products, probability, number theory, polynomials, theory of equations, complex numbers in geometry, algorithmic proofs, combinatorial and advanced geometry, functional equations and classical inequalities The book is systematically organized, gradually building combinatorial skills and techniques and broadening the student's view of mathematics. Aside from its practical use in training teachers and students engaged in mathematical competitions, it is a source of enrichment that is bound to stimulate interest in a variety of mathematical areas that are tangential to combinatorics.

A = B
A = B

Author: Marko Petkovsek

Publisher: CRC Press

Published: 1996-01-01

Total Pages: 231

ISBN-13: 1439864500

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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 ta

Discrete Mathematics
Discrete Mathematics

Author: László Lovász

Publisher: Springer Science & Business Media

Published: 2006-05-10

Total Pages: 344

ISBN-13: 0387217770

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Aimed at undergraduate mathematics and computer science students, this book is an excellent introduction to a lot of problems of discrete mathematics. It discusses a number of selected results and methods, mostly from areas of combinatorics and graph theory, and it uses proofs and problem solving to help students understand the solutions to problems. Numerous examples, figures, and exercises are spread throughout the book.

Combinatorial Methods with Computer Applications
Combinatorial Methods with Computer Applications

Author: Jonathan L. Gross

Publisher: CRC Press

Published: 2016-04-19

Total Pages: 664

ISBN-13: 1584887443

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Combinatorial Methods with Computer Applications provides in-depth coverage of recurrences, generating functions, partitions, and permutations, along with some of the most interesting graph and network topics, design constructions, and finite geometries. Requiring only a foundation in discrete mathematics, it can serve as the textbook in a combinat

GKS Theory and Practice
GKS Theory and Practice

Author: Peter R. Bono

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 314

ISBN-13: 3642729304

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Eurographics, the European Association for Computer Graphics, has always been an important forum for discussions and presentation of results concerning the first ISO Graphical Standard, GKS (the Graphical Kernel System) and later of its three-dimensional extension, GKS-3D. This book is a collection of those articles which have appeared within the framework of Eurographics in the past 5 years, and which still contain, even after several years, valid and interesting results concerning the problems arising in connection with GKS. Some of these papers help the reader to gain a deeper understanding of the standard; others deal with general implementation problems, and finally there are some presentations of specific algorithms usable also for a GKS or GKS-3D implementation. The book may be of a particular interest to those specialists who intend to implement a GKS package or some similar graphics subsystem and who can therefore make direct use of the experiences reflected in this collection. The book should also be a valuable supplement in university courses concerned with teaching the principles of implementing device-independent computer graphics.