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.
Author: Fred Roberts,Barry Tesman
Publisher: CRC Press
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.
Author: Alan Tucker
Publisher: Wiley Global Education
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.
An Introduction to Combinatorics, Second Edition
Author: R.B.J.T. Allenby,Alan Slomson
Publisher: CRC Press
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.
An Introduction to Enumeration and Graph Theory
Author: Mikl¢s B¢na
Publisher: World Scientific
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/.
Author: Mitchel Keller,William T. Trotter
Publisher: Createspace Independent Publishing Platform
Applications of combinatorics in bioformatics, text processing, combinatorial enumeration and fractal analysis.
Author: M. Lothaire
Publisher: Cambridge University Press
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.
Author: John Harris,Jeffry L. Hirst,Michael Mossinghoff
Publisher: Springer Science & Business Media
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.
Author: J. H. van Lint,Richard Michael Wilson
Publisher: Cambridge University Press
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.
Walks, Trees, Tableaux, and More
Author: Richard P. Stanley
Publisher: Springer Science & Business Media
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.
Codes, Ciphers and Discrete Algorithms, Second Edition
Author: Darel W. Hardy,Fred Richman,Carol L. Walker
Publisher: CRC Press
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.
Author: Edward A. Bender,S. Gill Williamson
Publisher: Courier Corporation
Author: Martin J. Erickson
Publisher: John Wiley & Sons
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.?
Concepts and Cases
Author: J Fred Springer
Publisher: Taylor & Francis