Foundations Of Applied Combinatorics

Author : Edward A. Bender,Stanley Gill Williamson
Publisher : Addison Wesley Publishing Company
Page : 458 pages
File Size : 43,7 Mb
Release : 1991
Category : Mathematics
ISBN : UOM:39015022034725

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Foundations of Applied Combinatorics by Edward A. Bender,Stanley Gill Williamson Pdf

This introduction to combinatorics is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises (some with solutions), notes, and references appear throughout the text. 75 figures. Appendixes.

Author : Edward A. Bender,S. Gill Williamson
Publisher : Courier Corporation
Page : 738 pages
File Size : 52,6 Mb
Release : 2013-01-18
Category : Mathematics
ISBN : 9780486151502

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Foundations of Combinatorics with Applications by Edward A. Bender,S. Gill Williamson Pdf

This introduction to combinatorics, the foundation of the interaction between computer science and mathematics, is suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics. The four-part treatment begins with a section on counting and listing that covers basic counting, functions, decision trees, and sieving methods. The following section addresses fundamental concepts in graph theory and a sampler of graph topics. The third part examines a variety of applications relevant to computer science and mathematics, including induction and recursion, sorting theory, and rooted plane trees. The final section, on generating functions, offers students a powerful tool for studying counting problems. Numerous exercises appear throughout the text, along with notes and references. The text concludes with solutions to odd-numbered exercises and to all appendix exercises.

Author : George Pólya
Publisher : Unknown
Page : 644 pages
File Size : 46,8 Mb
Release : 1981
Category : Mathematics
ISBN : PSU:000006603465

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Applied Combinatorial Mathematics by George Pólya Pdf

Author : Alan Tucker
Publisher : Wiley
Page : 446 pages
File Size : 48,8 Mb
Release : 2003
Category : Combinatorial analysis
ISBN : 0471453021

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Applied Combinatorics by Alan Tucker Pdf

This book is designed for use by students with a wide range of ability and maturity. The stronger the students, the harder the exercises that can be assigned. The book can be used for one-quarter, two-quarter, or one-semester course depending on how much material is used. Combinatorical reasoning underlies all analysis of computer systems. It plays a similar role in discrete operations research problems and in finite probability. This book teaches students in the mathematical sciences how to reason and model combinatorically. It seeks to develop proficiency in basic discrete math problem solving in the way that a calculus textbook develops proficiency in basic analysis problem solving. The three principle aspects of combinatorical reasoning emphasized in this book are: the systematic analysis of different possibilities, the exploration of the logical structure of a problem (e.g. finding manageable subpieces or first solving the problem with three objects instead of n), and ingenuity. Although important uses of combinatorics in computer science, operations research, and finite probability are mentioned, these applications are often used solely for motivation. Numerical examples involving the same concepts use more interesting settings such as poker probabilities or logical games.

Author : Michael Townsend
Publisher : Benjamin-Cummings Publishing Company
Page : 416 pages
File Size : 49,7 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:39015015707907

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Discrete Mathematics by Michael Townsend Pdf

Author : Bruce E. Sagan
Publisher : American Mathematical Soc.
Page : 304 pages
File Size : 40,8 Mb
Release : 2020-10-16
Category : Education
ISBN : 9781470460327

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Combinatorics: The Art of Counting by Bruce E. Sagan Pdf

This book is a gentle introduction to the enumerative part of combinatorics suitable for study at the advanced undergraduate or beginning graduate level. In addition to covering all the standard techniques for counting combinatorial objects, the text contains material from the research literature which has never before appeared in print, such as the use of quotient posets to study the Möbius function and characteristic polynomial of a partially ordered set, or the connection between quasisymmetric functions and pattern avoidance. The book assumes minimal background, and a first course in abstract algebra should suffice. The exposition is very reader friendly: keeping a moderate pace, using lots of examples, emphasizing recurring themes, and frankly expressing the delight the author takes in mathematics in general and combinatorics in particular.

Author : M. Lothaire
Publisher : Cambridge University Press
Page : 646 pages
File Size : 43,5 Mb
Release : 2005-07-11
Category : Computers
ISBN : 0521848024

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Applied Combinatorics on Words by M. Lothaire Pdf

Publisher Description

Author : Philippe Flajolet,Robert Sedgewick
Publisher : Cambridge University Press
Page : 825 pages
File Size : 52,8 Mb
Release : 2009-01-15
Category : Mathematics
ISBN : 9781139477161

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Analytic Combinatorics by Philippe Flajolet,Robert Sedgewick Pdf

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.

Author : Stanley Gill Williamson
Publisher : Courier Corporation
Page : 548 pages
File Size : 50,8 Mb
Release : 2002-01-01
Category : Mathematics
ISBN : 0486420760

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Combinatorics for Computer Science by Stanley Gill Williamson Pdf

Useful guide covers two major subdivisions of combinatorics — enumeration and graph theory — with emphasis on conceptual needs of computer science. Each part is divided into a "basic concepts" chapter emphasizing intuitive needs of the subject, followed by four "topics" chapters that explore these ideas in depth. Invaluable practical resource for graduate students, advanced undergraduates, and professionals with an interest in algorithm design and other aspects of computer science and combinatorics. References for Linear Order & for Graphs, Trees, and Recursions. 219 figures.

Author : Alan Tucker
Publisher : Unknown
Page : 488 pages
File Size : 53,6 Mb
Release : 1995
Category : Mathematics
ISBN : UOM:39015032564653

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Applied Combinatorics by Alan Tucker Pdf

Explains how to reason and model combinatorially. Enables students to develop proficiency in fundamental discrete math problem solving in the manner that a calculus textbook develops competence in basic analysis problem solving. Stresses the systematic analysis of different possibilities, exploration of the logical structure of a problem and ingenuity. This edition contains many new exercises.

Author : Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan
Publisher : Cambridge University Press
Page : 397 pages
File Size : 41,5 Mb
Release : 2009-02-09
Category : Mathematics
ISBN : 9781139476768

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Combinatorics: The Rota Way by Joseph P. S. Kung,Gian-Carlo Rota,Catherine H. Yan Pdf

Gian-Carlo Rota was one of the most original and colourful mathematicians of the 20th century. His work on the foundations of combinatorics focused on the algebraic structures that lie behind diverse combinatorial areas, and created a new area of algebraic combinatorics. Written by two of his former students, this book is based on notes from his influential graduate courses and on face-to-face discussions. Topics include sets and valuations, partially ordered sets, distributive lattices, partitions and entropy, matching theory, free matrices, doubly stochastic matrices, Moebius functions, chains and antichains, Sperner theory, commuting equivalence relations and linear lattices, modular and geometric lattices, valuation rings, generating functions, umbral calculus, symmetric functions, Baxter algebras, unimodality of sequences, and location of zeros of polynomials. Many exercises and research problems are included, and unexplored areas of possible research are discussed. A must-have for all students and researchers in combinatorics and related areas.

Author : Fred Roberts,Barry Tesman
Publisher : CRC Press
Page : 889 pages
File Size : 47,5 Mb
Release : 2009-06-03
Category : Computers
ISBN : 9781420099836

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Applied Combinatorics by Fred Roberts,Barry Tesman Pdf

Now with solutions to selected problems, Applied Combinatorics, Second Edition presents the tools of combinatorics from an applied point of view. This bestselling textbook offers numerous references to the literature of combinatorics and its applications that enable readers to delve more deeply into the topics.After introducing fundamental counting

Author : Ioan Tomescu
Publisher : Wiley-Interscience
Page : 362 pages
File Size : 48,7 Mb
Release : 1985-04-30
Category : Mathematics
ISBN : UOM:39015039010262

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Problems in Combinatorics and Graph Theory by Ioan Tomescu Pdf

Covers the most important combinatorial structures and techniques. This is a book of problems and solutions which range in difficulty and scope from the elementary/student-oriented to open questions at the research level. Each problem is accompanied by a complete and detailed solution together with appropriate references to the mathematical literature, helping the reader not only to learn but to apply the relevant discrete methods. The text is unique in its range and variety -- some problems include straightforward manipulations while others are more complicated and require insights and a solid foundation of combinatorics and/or graph theory. Includes a dictionary of terms that makes many of the challenging problems accessible to those whose mathematical education is limited to highschool algebra.

Author : Miklos Bona
Publisher : CRC Press
Page : 555 pages
File Size : 51,8 Mb
Release : 2015-09-18
Category : Computers
ISBN : 9781482249101

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Introduction to Enumerative and Analytic Combinatorics by Miklos Bona Pdf

Introduction to Enumerative and Analytic Combinatorics fills the gap between introductory texts in discrete mathematics and advanced graduate texts in enumerative combinatorics. The book first deals with basic counting principles, compositions and partitions, and generating functions. It then focuses on the structure of permutations, graph enumerat

Author : Fabrizio Luccio,Linda Pagli,Graham Steel
Publisher : CRC Press
Page : 224 pages
File Size : 40,5 Mb
Release : 2011-07-06
Category : Computers
ISBN : 9781439831380

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Mathematical and Algorithmic Foundations of the Internet by Fabrizio Luccio,Linda Pagli,Graham Steel Pdf

To truly understand how the Internet and Web are organized and function requires knowledge of mathematics and computation theory. Mathematical and Algorithmic Foundations of the Internet introduces the concepts and methods upon which computer networks rely and explores their applications to the Internet and Web. The book offers a unique approach to mathematical and algorithmic concepts, demonstrating their universality by presenting ideas and examples from various fields, including literature, history, and art. Progressing from fundamental concepts to more specific topics and applications, the text covers computational complexity and randomness, networks and graphs, parallel and distributed computing, and search engines. While the mathematical treatment is rigorous, it is presented at a level that can be grasped by readers with an elementary mathematical background. The authors also present a lighter side to this complex subject by illustrating how many of the mathematical concepts have counterparts in everyday life. The book provides in-depth coverage of the mathematical prerequisites and assembles a complete presentation of how computer networks function. It is a useful resource for anyone interested in the inner functioning, design, and organization of the Internet.