Applied Combinatorics, Second Edition

Author: Fred Roberts,Barry Tesman

Publisher: CRC Press

ISBN: 9781420099836

Category: Computers

Page: 848

View: 6755

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 rules and the tools of graph theory and relations, the authors focus on three basic problems of combinatorics: counting, existence, and optimization problems. They discuss advanced tools for dealing with the counting problem, including generating functions, recurrences, inclusion/exclusion, and Pólya theory. The text then covers combinatorial design, coding theory, and special problems in graph theory. It also illustrates the basic ideas of combinatorial optimization through a study of graphs and networks.
Posted in Computers

Applied Combinatorics, 6th Edition

Author: Alan Tucker

Publisher: Wiley Global Education

ISBN: 1118210115

Category: Mathematics

Page: 496

View: 642

The new 6th edition of Applied Combinatorics builds on the previous editions with more in depth analysis of computer systems in order to help develop proficiency in basic discrete math problem solving. As one of the most widely used books in combinatorial problems, this edition explains how to reason and model combinatorically while stressing the systematic analysis of different possibilities, exploration of the logical structure of a problem, 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.
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How to Count

An Introduction to Combinatorics, Second Edition

Author: R.B.J.T. Allenby,Alan Slomson

Publisher: CRC Press

ISBN: 1420082612

Category: Mathematics

Page: 444

View: 4672

Emphasizes a Problem Solving Approach A first course in combinatorics Completely revised, How to Count: An Introduction to Combinatorics, Second Edition shows how to solve numerous classic and other interesting combinatorial problems. The authors take an easily accessible approach that introduces problems before leading into the theory involved. Although the authors present most of the topics through concrete problems, they also emphasize the importance of proofs in mathematics. New to the Second Edition This second edition incorporates 50 percent more material. It includes seven new chapters that cover occupancy problems, Stirling and Catalan numbers, graph theory, trees, Dirichlet’s pigeonhole principle, Ramsey theory, and rook polynomials. This edition also contains more than 450 exercises. Ideal for both classroom teaching and self-study, this text requires only a modest amount of mathematical background. In an engaging way, it covers many combinatorial tools, such as the inclusion-exclusion principle, generating functions, recurrence relations, and Pólya’s counting theorem.
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A Walk Through Combinatorics

An Introduction to Enumeration and Graph Theory

Author: Mikl¢s B¢na

Publisher: World Scientific

ISBN: 9814335231

Category: Mathematics

Page: 546

View: 9510

Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.
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Applied Combinatorics

Author: Mitchel Keller,William T. Trotter

Publisher: Createspace Independent Publishing Platform

ISBN: 9781973702719

Category:

Page: 392

View: 4301

This is a text with more than enough material for a one-semester introduction to combinatorics. The original target audience was primarily computer science majors, but the topics included make it suitable for a variety of different students. Topics include Basic enumeration: strings, sets, binomial coefficients Recursion and mathematical induction Graph theory Partially ordered sets Additional enumeration techniques: inclusion-exclusion, generating functions, recurrence relations, and Polya theory. Graph algorithms: minimum weight spanning trees, Dijkstra's algorithm, network flows This text is open source and available under a Creative Commons license. To access the free HTML and PDF versions of the text, visit http://rellek.net/appcomb/.
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Applied Combinatorics on Words

Author: M. Lothaire

Publisher: Cambridge University Press

ISBN: 9780521848022

Category: Computers

Page: 610

View: 2253

Applications of combinatorics in bioformatics, text processing, combinatorial enumeration and fractal analysis.
Posted in Computers

Combinatorics and Graph Theory

Author: John Harris,Jeffry L. Hirst,Michael Mossinghoff

Publisher: Springer Science & Business Media

ISBN: 0387797114

Category: Mathematics

Page: 381

View: 452

These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
Posted in Mathematics

A Course in Combinatorics

Author: J. H. van Lint,Richard Michael Wilson

Publisher: Cambridge University Press

ISBN: 9780521006019

Category: Mathematics

Page: 602

View: 8407

This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.
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Algebraic Combinatorics

Walks, Trees, Tableaux, and More

Author: Richard P. Stanley

Publisher: Springer Science & Business Media

ISBN: 1461469988

Category: Mathematics

Page: 223

View: 9379

Written by one of the foremost experts in the field, Algebraic Combinatorics is a unique undergraduate textbook that will prepare the next generation of pure and applied mathematicians. The combination of the author’s extensive knowledge of combinatorics and classical and practical tools from algebra will inspire motivated students to delve deeply into the fascinating interplay between algebra and combinatorics. Readers will be able to apply their newfound knowledge to mathematical, engineering, and business models. The text is primarily intended for use in a one-semester advanced undergraduate course in algebraic combinatorics, enumerative combinatorics, or graph theory. Prerequisites include a basic knowledge of linear algebra over a field, existence of finite fields, and group theory. The topics in each chapter build on one another and include extensive problem sets as well as hints to selected exercises. Key topics include walks on graphs, cubes and the Radon transform, the Matrix–Tree Theorem, and the Sperner property. There are also three appendices on purely enumerative aspects of combinatorics related to the chapter material: the RSK algorithm, plane partitions, and the enumeration of labeled trees. Richard Stanley is currently professor of Applied Mathematics at the Massachusetts Institute of Technology. Stanley has received several awards including the George Polya Prize in applied combinatorics, the Guggenheim Fellowship, and the Leroy P. Steele Prize for mathematical exposition. Also by the author: Combinatorics and Commutative Algebra, Second Edition, © Birkhauser.
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Bijective Combinatorics

Author: Nicholas Loehr

Publisher: CRC Press

ISBN: 1439848866

Category: Computers

Page: 612

View: 1409

Bijective proofs are some of the most elegant and powerful techniques in all of mathematics. Suitable for readers without prior background in algebra or combinatorics, Bijective Combinatorics presents a general introduction to enumerative and algebraic combinatorics that emphasizes bijective methods. The text systematically develops the mathematical tools, such as basic counting rules, recursions, inclusion-exclusion techniques, generating functions, bijective proofs, and linear-algebraic methods, needed to solve enumeration problems. These tools are used to analyze many combinatorial structures, including words, permutations, subsets, functions, compositions, integer partitions, graphs, trees, lattice paths, multisets, rook placements, set partitions, Eulerian tours, derangements, posets, tilings, and abaci. The book also delves into algebraic aspects of combinatorics, offering detailed treatments of formal power series, symmetric groups, group actions, symmetric polynomials, determinants, and the combinatorial calculus of tableaux. Each chapter includes summaries and extensive problem sets that review and reinforce the material. Lucid, engaging, yet fully rigorous, this text describes a host of combinatorial techniques to help solve complicated enumeration problems. It covers the basic principles of enumeration, giving due attention to the role of bijective proofs in enumeration theory.
Posted in Computers

Applied Algebra

Codes, Ciphers and Discrete Algorithms, Second Edition

Author: Darel W. Hardy,Fred Richman,Carol L. Walker

Publisher: CRC Press

ISBN: 1420071432

Category: Mathematics

Page: 410

View: 2520

Using mathematical tools from number theory and finite fields, Applied Algebra: Codes, Ciphers, and Discrete Algorithms, Second Edition presents practical methods for solving problems in data security and data integrity. It is designed for an applied algebra course for students who have had prior classes in abstract or linear algebra. While the content has been reworked and improved, this edition continues to cover many algorithms that arise in cryptography and error-control codes. New to the Second Edition A CD-ROM containing an interactive version of the book that is powered by Scientific Notebook®, a mathematical word processor and easy-to-use computer algebra system New appendix that reviews prerequisite topics in algebra and number theory Double the number of exercises Instead of a general study on finite groups, the book considers finite groups of permutations and develops just enough of the theory of finite fields to facilitate construction of the fields used for error-control codes and the Advanced Encryption Standard. It also deals with integers and polynomials. Explaining the mathematics as needed, this text thoroughly explores how mathematical techniques can be used to solve practical problems. About the Authors Darel W. Hardy is Professor Emeritus in the Department of Mathematics at Colorado State University. His research interests include applied algebra and semigroups. Fred Richman is a professor in the Department of Mathematical Sciences at Florida Atlantic University. His research interests include Abelian group theory and constructive mathematics. Carol L. Walker is Associate Dean Emeritus in the Department of Mathematical Sciences at New Mexico State University. Her research interests include Abelian group theory, applications of homological algebra and category theory, and the mathematics of fuzzy sets and fuzzy logic.
Posted in Mathematics

Combinatorial Problems and Exercises

Author: L. Lovász

Publisher: Elsevier

ISBN: 0080933092

Category: Mathematics

Page: 636

View: 5501

The aim of this book is to introduce a range of combinatorial methods for those who want to apply these methods in the solution of practical and theoretical problems. Various tricks and techniques are taught by means of exercises. Hints are given in a separate section and a third section contains all solutions in detail. A dictionary section gives definitions of the combinatorial notions occurring in the book. Combinatorial Problems and Exercises was first published in 1979. This revised edition has the same basic structure but has been brought up to date with a series of exercises on random walks on graphs and their relations to eigenvalues, expansion properties and electrical resistance. In various chapters the author found lines of thought that have been extended in a natural and significant way in recent years. About 60 new exercises (more counting sub-problems) have been added and several solutions have been simplified.
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Foundations of Combinatorics with Applications

Author: Edward A. Bender,S. Gill Williamson

Publisher: Courier Corporation

ISBN: 0486151506

Category: Mathematics

Page: 480

View: 3106

Suitable for upper-level undergraduates and graduate students in engineering, science, and mathematics, this introductory text explores counting and listing, graphs, induction and recursion, and generating functions. Includes numerous exercises (some with solutions), notes, and references.
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Introduction to Combinatorics

Author: Martin J. Erickson

Publisher: John Wiley & Sons

ISBN: 1118030893

Category: Mathematics

Page: 208

View: 7180

Posted in Mathematics

Introduction to Combinatorics

Author: A. B. Slomson

Publisher: CRC Press

ISBN: 9780412353703

Category: Mathematics

Page: 270

View: 4670

The growth in digital devices, which require discrete formulation of problems, has revitalized the role of combinatorics, making it indispensable to computer science. Furthermore, the challenges of new technologies have led to its use in industrial processes, communications systems, electrical networks, organic chemical identification, coding theory, economics, and more. With a unique approach, Introduction to Combinatorics builds a foundation for problem-solving in any of these fields. Although combinatorics deals with finite collections of discrete objects, and as such differs from continuous mathematics, the two areas do interact. The author, therefore, does not hesitate to use methods drawn from continuous mathematics, and in fact shows readers the relevance of abstract, pure mathematics to real-world problems. The author has structured his chapters around concrete problems, and as he illustrates the solutions, the underlying theory emerges. His focus is on counting problems, beginning with the very straightforward and ending with the complicated problem of counting the number of different graphs with a given number of vertices. Its clear, accessible style and detailed solutions to many of the exercises, from routine to challenging, provided at the end of the book make Introduction to Combinatorics ideal for self-study as well as for structured coursework.
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Introduction to Enumerative and Analytic Combinatorics, Second Edition

Author: Miklos Bona

Publisher: CRC Press

ISBN: 1482249103

Category: Computers

Page: 534

View: 1991

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 enumeration, and extremal combinatorics. Lastly, the text discusses supplemental topics, including error-correcting codes, properties of sequences, and magic squares. Strengthening the analytic flavor of the book, this Second Edition: Features a new chapter on analytic combinatorics and new sections on advanced applications of generating functions Demonstrates powerful techniques that do not require the residue theorem or complex integration Adds new exercises to all chapters, significantly extending coverage of the given topics Introduction to Enumerative and Analytic Combinatorics, Second Edition makes combinatorics more accessible, increasing interest in this rapidly expanding field.
Posted in Computers

Applied Policy Research

Concepts and Cases

Author: J Fred Springer

Publisher: Taylor & Francis

ISBN: 1135215413

Category:

Page: N.A

View: 339

Where many textbooks on policy research focus on methodological and statistical theories, leaving students to wonder how they will apply those theories to future policy positions, this innovative textbook takes theories of policy research and puts them into practice, demystifying the subject by translating it into real-world situations in which students can actively engage. Beginning with an orientation and overview of policy research, outlining the processes of policy analysis and evaluation from start to finish, Applied Policy Research, 2e walks students through an examination of case studies to demonstrate how these theories play out in real policy situations. New to this edition: A rewritten Part I that includes several new chapters incorporating the latest developments in applicable policy research design, implementation, and products to provide a framework for conducting policy research. A matrix at the start of Part II to easily identify how each of the fifteen case-study chapters correspond with concepts and topics presented in Part I, showing the reader where to look for a specific real-life example of a given topic or concept. Each case is drawn from real instances of policy research to provide students with an opportunity to consider and learn how to grapple with the challenges posed by the needs of public programs and agencies. Cases include local, state, and nonprofit agencies as well as federal-state-local intergovernmental "hybrids." Each chapter is presented in a uniform format: (1) a detailed description of a policy research problem; (2) a discussion of the unique challenges posed by the problem; (3) a description of the policy research techniques used; (4) a summary of the outcomes or conclusions associated with the research as it was conducted; and (5) conclusions about the implications or lessons for policy research. Illustrative figures help students understand the stages of policy research, and end-of-chapter tools such as discussion questions, assignments and activities, and case studies "at a glance" help students master not only the particulars of each case but the broader skills needed in future research. Applied Policy Research, Second Edition will be essential reading in all policy research courses with a focus on practical outcomes and student preparation for public service.?
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Handbook of Discrete and Combinatorial Mathematics

Author: Kenneth H. Rosen

Publisher: CRC Press

ISBN: 135164405X

Category: Mathematics

Page: 1612

View: 5205

Handbook of Discrete and Combinatorial Mathematics provides a comprehensive reference volume for mathematicians, computer scientists, engineers, as well as students and reference librarians. The material is presented so that key information can be located and used quickly and easily. Each chapter includes a glossary. Individual topics are covered in sections and subsections within chapters, each of which is organized into clearly identifiable parts: definitions, facts, and examples. Examples are provided to illustrate some of the key definitions, facts, and algorithms. Some curious and entertaining facts and puzzles are also included. Readers will also find an extensive collection of biographies. This second edition is a major revision. It includes extensive additions and updates. Since the first edition appeared in 1999, many new discoveries have been made and new areas have grown in importance, which are covered in this edition.
Posted in Mathematics