Generatingfunctionology
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Generatingfunctionology
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Author : Herbert S. Wilf
language : en
Publisher: CRC Press
Release Date : 2005-12-20
Generatingfunctionology written by Herbert S. Wilf and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-12-20 with Computers categories.
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 - 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.
Generatingfunctionology
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Author : Herbert S. Wilf
language : en
Publisher: Elsevier
Release Date : 2014-05-10
Generatingfunctionology written by Herbert S. Wilf and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.
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
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Author : Herbert S. Wilf
language : en
Publisher: Elsevier
Release Date : 2013-10-22
Generating Functionology written by Herbert S. Wilf and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-10-22 with Mathematics categories.
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
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Author : Philippe Flajolet
language : en
Publisher: Cambridge University Press
Release Date : 2009-01-15
Analytic Combinatorics written by Philippe Flajolet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-01-15 with Mathematics categories.
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
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Author : Robert M. Young
language : en
Publisher: Cambridge University Press
Release Date : 1992
Excursions In Calculus written by Robert M. Young and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book explores the interplay between the two main currents of mathematics, the continuous and the discrete.
102 Combinatorial Problems
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Author : Titu Andreescu
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
102 Combinatorial Problems written by Titu Andreescu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
"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 Course In Enumeration
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Author : Martin Aigner
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-28
A Course In Enumeration written by Martin Aigner and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-28 with Mathematics categories.
Combinatorial enumeration is a readily accessible subject full of easily stated, but sometimes tantalizingly difficult problems. This book leads the reader in a leisurely way from basic notions of combinatorial enumeration to a variety of topics, ranging from algebra to statistical physics. The book is organized in three parts: Basics, Methods, and Topics. The aim is to introduce readers to a fascinating field, and to offer a sophisticated source of information for professional mathematicians desiring to learn more. There are 666 exercises, and every chapter ends with a highlight section, discussing in detail a particularly beautiful or famous result.
A Book Of Abstract Algebra
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Author : Charles C Pinter
language : en
Publisher: Courier Corporation
Release Date : 2010-01-14
A Book Of Abstract Algebra written by Charles C Pinter and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-14 with Mathematics categories.
Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Experimental Mathematics In Action
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Author : David Bailey
language : en
Publisher: CRC Press
Release Date : 2007-05-31
Experimental Mathematics In Action written by David Bailey and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-31 with Mathematics categories.
With the continued advance of computing power and accessibility, the view that "real mathematicians don't compute" no longer has any traction for a newer generation of mathematicians. The goal in this book is to present a coherent variety of accessible examples of modern mathematics where intelligent computing plays a significant role and in so doi
Combinatorial Methods With Computer Applications
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2007-11-16
Combinatorial Methods With Computer Applications written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-16 with Mathematics categories.
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 combinatorial methods course or in a combined graph theory and combinatorics course. After an introduction to combinatorics, the book explores six systematic approaches within a comprehensive framework: sequences, solving recurrences, evaluating summation expressions, binomial coefficients, partitions and permutations, and integer methods. The author then focuses on graph theory, covering topics such as trees, isomorphism, automorphism, planarity, coloring, and network flows. The final chapters discuss automorphism groups in algebraic counting methods and describe combinatorial designs, including Latin squares, block designs, projective planes, and affine planes. In addition, the appendix supplies background material on relations, functions, algebraic systems, finite fields, and vector spaces. Paving the way for students to understand and perform combinatorial calculations, this accessible text presents the discrete methods necessary for applications to algorithmic analysis, performance evaluation, and statistics as well as for the solution of combinatorial problems in engineering and the social sciences.