books tagged “combinatorics”

books tagged “combinatorics”

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More editions of Handbook of Discrete and Combinatorial Mathematics:

  • Handbook of Discrete and Computational Geometry
    by Joseph O'Rourke, Jacob E. Goodman
    ISBN 0849385245 (0-8493-8524-5)
    Hardcover, CRC Pr I Llc

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    Book summary:

    Jacob E. Goodman, co-founder and editor of Discrete & Computational Geometry, the preeminent journal on this area in the international mathematics and computer science community, joins forces with the distinguished computer scientist Joseph O'Rourke and other well-known authorities to produce the definitive handbook on these two interrelated fields.

    Over the past decade or so, researchers and professionals in discrete geometry and the newer field of computational geometry have developed a highly productive collaborative relationship, where each area benefits from the methods and insights of the other. At the same time that discrete and computational geometry are becoming more closely identified, applications of the results of this work are being used in an increasing number of widely differing areas, from computer graphics and linear programming to manufacturing and robotics. The authors have answered the need for a comprehensive handbook
    for workers in these and related fields, and for other users of the body of results.

    While much information can be found on discrete and computational geometry, it is scattered among many sources, and individual books and articles are often narrowly focused. Handbook of Discrete and Computational Geometry brings together, for the first time, all of the major results in both these fields into one volume. Thousands of results - theorems, algorithms, and tables - throughout the volume definitively cover the field, while numerous applications from many different fields demonstrate practical usage. The material is presented clearly enough to assist the novice, but in enough depth to appeal to the specialist. Every technical term is clearly defined in an easy-to-use glossary. Over 200 figures illustrate the concepts presented and provide supporting examples. Information on current geometric software - what it does, how efficiently it does it, and where to find it - is also included. [via]

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  • Schuster, Heinz Georg: Handbook of Graphs and Networks: From the Genome to the Internet
    Handbook of Graphs and Networks: From the Genome to the Internet
    by Heinz Georg Schuster, Stefan Bornholdt
    ISBN 3527403361 (3-527-40336-1)
    Hardcover, Vch Verlagsgesellschaft Mbh

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  • Hopf Algebras and Their Actions on Rings
    by Susan Montgomery
    ISBN 0821807382 (0-8218-0738-2)
    Softcover, Amer Mathematical Society

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    Book summary:

    The last ten years have seen a number of significant advances in Hopf algebras. The best known is the introduction of quantum groups, which are Hopf algebras that arose in mathematical physics and now have connections to many areas of mathematics. In addition, several conjectures of Kaplansky have been solved, the most striking of which is a kind of Lagrange's theorem for Hopf algebras. Work on actions of Hopf algebras has unified earlier results on group actions, actions of Lie algebras, and graded algebras. This book brings together many of these recent developments from the viewpoint of the algebraic structure of Hopf algebras and their actions and coactions. Quantum groups are treated as an important example, rather than as an end in themselves. The two introductory chapters review definitions and basic facts; otherwise, most of the material has not previously appeared in book form. Providing an accessible introduction to Hopf algebras, this book would make an excellent graduate textbook for a course in Hopf algebras or an introduction to quantum groups. [via]

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  • Soifer, Alexander: How Does One Cut a Triangle?
    How Does One Cut a Triangle?
    by Alexander Soifer, Yrui Soifer
    ISBN 0940263017 (0-940263-01-7)
    Softcover, Center of Excellence in

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  • Erickson, Martin J.: Introduction to Combinatorics
    Introduction to Combinatorics
    by Martin J. Erickson
    ISBN 0471154083 (0-471-15408-3)
    Hardcover, Wiley-Interscience

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  • Introduction to Graph Theory
    by Douglas Brent West
    ISBN 0131437372 (0-13-143737-2)
    Hardcover, Prentice Hall

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    Book summary:

    Flexibly designed for CS students needing math review. Also covers some advanced, cutting edge topics (running 120 pages and intended for grad students) in the last chapter (8). This text fits senior year or intro. grad course for CS and math majors. [via]

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  • Introduction to Graph Theory
    by Douglas B. West
    ISBN 0130144002 (0-13-014400-2)
    Hardcover, Prentice Hall PTR

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    Book summary:

    This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity. An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs. For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

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  • Brualdi, Richard A.: Introductory Combinatorics
    Introductory Combinatorics
    by Richard A. Brualdi
    ISBN 0131001191 (0-13-100119-1)
    Hardcover, Prentice Hall

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    Book summary:

    Introductory Combinatorics emphasizes combinatorial ideas, including the pigeon-hole principle, counting techniques, permutations and combinations, Polya counting, binomial coefficients, inclusion-exclusion principle, generating functions and recurrence relations, and combinatortial structures (matchings, designs, graphs). Written to be entertaining and readable, this book's lively style reflects the author's joy for teaching the subject. It presents an excellent treatment of Polya's Counting Theorem that doesn't assume the student is familiar with group theory. It also includes problems that offer good practice of the principles it presents. The third edition of Introductory Combinatorics has been updated to include new material on partially ordered sets, Dilworth's Theorem, partitions of integers and generating functions. In addition, the chapters on graph theory have been completely revised. A valuable book for any reader interested in learning more about combinatorics. [via]

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  • Lando, S. K.: Lectures on Generating Functions
    Lectures on Generating Functions
    by S. K. Lando
    ISBN 0821834819 (0-8218-3481-9)
    Softcover, Amer Mathematical Society

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  • BEWERSDORFF, JORG: Luck, Logic, And White Lies: The Mathematics Of Games
    Luck, Logic, And White Lies: The Mathematics Of Games
    by JORG BEWERSDORFF, David Kramer
    ISBN 1568812108 (1-56881-210-8)
    Softcover, A K Peters Ltd

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  • Morris, S. Brent: Magic Tricks Card Shuffling and Dynamic Computer Memories
    Magic Tricks Card Shuffling and Dynamic Computer Memories
    by S. Brent Morris
    ISBN 0883855275 (0-88385-527-5)
    Softcover, Mathematical Assn of Amer

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  • Math Structures for Computer Science
    by Judith L. Gersting
    ISBN 0716783061 (0-7167-8306-1)
    Hardcover, College Board, The

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    Book summary:

    The algorithms in this text have been rewritten in a language-neutral pseudocode making the book useful to computer science students. Each chapter begins with a "motivating problem" which occurs later as an exercise. Tables and bullet notes have been added througout, with examples. [via]

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  • Montenegro, Ravi: Mathematical Aspects of Mixing Times in Markov Chains
    Mathematical Aspects of Mixing Times in Markov Chains
    by Ravi Montenegro, Prasad Tetali
    ISBN 1933019298 (1-933019-29-8)
    Softcover, Now Pub

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  • Gersting, Judith L.: Mathematical Structures for Computer Science
    Mathematical Structures for Computer Science
    by Judith L. Gersting
    ISBN 0716782596 (0-7167-8259-6)
    Hardcover, W H Freeman & Co

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  • Mathematical Structures for Computer Science: A Modern Approach to Discrete Mathematics
    by Judith L. Gersting
    ISBN 071676864X (0-7167-6864-X)
    Hardcover, W H Freeman & Co

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    Book summary:

    Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of Mathematical Structures for Computer Science covers all the topics in the CC2001 suggested curriculum for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes: Importance of logical thinking Power of mathematical notation Usefulness of abstractions [via]

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  • Knuth, Donald Ervin: Mathematics for the Analysis of Algorithms
    Mathematics for the Analysis of Algorithms
    by Donald Ervin Knuth, Daniel H. Greene
    ISBN 3764330465 (3-7643-3046-5)
    Hardcover, Birkhauser

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  • Mathematics of Choice: Or, How to Count Without Counting
    by Ivan Morton Niven
    ISBN 0883856158 (0-88385-615-8)
    Softcover, Mathematical Assn of Amer

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    Book summary:

    A study of combinatorics--formulas used in solving problems that ask how many. Counting lies at the heart of most mathematics, and this book's subtitle says it all-How to count without counting. This is the whole art of combinatorics: permutations, combinations, binomial coefficients, the inclusion- exclusion principle, combinatorial probability, partitions of numbers, generating polynomials, the pigeonhole principle, and much more. The exercises in this book can all easily be done by hand on paper. [via]

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  • Nesetril, Jaroslav: Mathematics of Ramsey Theory
    Mathematics of Ramsey Theory
    by Jaroslav Nesetril, Vojtech Rodl
    ISBN 3540181911 (3-540-18191-1)
    Hardcover, Springer-Verlag

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  • Aldous, D.J.: Microsurveys in Discrete Probability: Dimacs Workshop, June 2-6, 1997
    Microsurveys in Discrete Probability: Dimacs Workshop, June 2-6, 1997
    by D.J. Aldous, James Propp
    ISBN 0821808273 (0-8218-0827-3)
    Hardcover, Amer Mathematical Society

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  • Modern Graph Theory
    by Bela Bollobas
    ISBN 0387984887 (0-387-98488-7)
    Softcover, Springer Verlag

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    Book summary:

    An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader. [via]

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  • Modern Graph Theory
    by Sheldon J. Axler, F. W. Gehring, P. R. Halmos
    ISBN 0387984917 (0-387-98491-7)
    Hardcover, Springer

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    Book summary:

    The time has now come when graph theory should be part of the education of every serious student of mathematics and computer science, both for its own sake and to enhance the appreciation of mathematics as a whole. This book is an in-depth account of graph theory, written with such a student in mind; it reflects the current state of the subject and emphasizes connections with other branches of pure mathematics. The volume grew out of the author's earlier book, Graph Theory -- An Introductory Course, but its length is well over twice that of its predecessor, allowing it to reveal many exciting new developments in the subject. Recognizing that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavor of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory such as coloring, matching, extremal theory, and algebraic graph theory, the book presents a detailed account of newer topics, including Szemer\'edi's Regularity Lemma and its use, Shelah's extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. In no other branch of mathematics is it as vital to tackle and solve challenging exercises in order to master the subject. To this end, the book contains an unusually large number of well thought-out exercises: over 600 in total. Although some are straightforward, most of them are substantial, and others will stretch even the most able reader. [via]

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  • Johnson, David S.: Network Flows and Matching: First Dimacs Implementation Challenge
    Network Flows and Matching: First Dimacs Implementation Challenge
    by David S. Johnson, Catherine C. McGeoch
    ISBN 0821865986 (0-8218-6598-6)
    Hardcover, Amer Mathematical Society

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  • Chen, C. C.: Principles and Techniques in Combinatorics
    Principles and Techniques in Combinatorics
    by C. C. Chen, K. M. Koh
    ISBN 9810211392 (981-02-1139-2)
    Softcover, World Scientific Publishing Company, Incorporated

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  • The Probabilistic Method
    by Noga Alon, Joel H. Spencer
    ISBN 0471370460 (0-471-37046-0)
    Hardcover, Wiley-Interscience

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    Book summary:

    The leading reference on probabilistic methods in combinatorics-now expanded and updated

    When it was first published in 1991, The Probabilistic Method became instantly the standard reference on one of the most powerful and widely used tools in combinatorics. Still without competition nearly a decade later, this new edition brings you up to speed on recent developments, while adding useful exercises and over 30% new material. It continues to emphasize the basic elements of the methodology, discussing in a remarkably clear and informal style both algorithmic and classical methods as well as modern applications.

    The Probabilistic Method, Second Edition begins with basic techniques that use expectation and variance, as well as the more recent martingales and correlation inequalities, then explores areas where probabilistic techniques proved successful, including discrepancy and random graphs as well as cutting-edge topics in theoretical computer science. A series of proofs, or "probabilistic lenses," are interspersed throughout the book, offering added insight into the application of the probabilistic approach. New and revised coverage includes:
    * Several improved as well as new results
    * A continuous approach to discrete probabilistic problems
    * Talagrand's Inequality and other novel concentration results
    * A discussion of the connection between discrepancy and VC-dimension
    * Several combinatorial applications of the entropy function and its properties
    * A new section on the life and work of Paul Erd?s-the developer of the probabilistic method [via]

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  • Erdos, Paul: The Probabilistic Method
    The Probabilistic Method
    by Paul Erdos, Noga Alon, Joel H. Spencer
    ISBN 0471535885 (0-471-53588-5)
    Hardcover, John Wiley & Sons Inc

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  • Habib, M.: Probabilistic Methods for Algorithmic Discrete Mathematics
    Probabilistic Methods for Algorithmic Discrete Mathematics
    by M. Habib, C. McDiarmid, J. Ramirez-Alfonsin, B Reed
    ISBN 3540646221 (3-540-64622-1)
    Hardcover, Springer Verlag

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  • Proofs from the Book
    by Gunter M. Ziegler, Martin Aigner
    ISBN 3540636986 (3-540-63698-6)
    Hardcover, Springer Verlag

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    Book summary:

    The (mathematical) heroes of this book are "perfect proofs": brilliant ideas, clever connections and wonderful observations that bring new insight and surprising perspectives on basic and challenging problems from Number Theory, Geometry, Analysis, Combinatorics, and Graph Theory. Thirty beautiful examples are presented here. They are candidates for The Book in which God records the perfect proofs - according to the late Paul Erd/s, who himself suggested many of the topics in this collection. The result is a book which will be fun for everybody with an interest in mathematics, requiring only a very modest (undergraduate) mathematical background. For this revised and expanded second edition several chapters have been revised and expanded, and three new chapters have been added. According to the great mathematician Paul Erd/s, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connections, and wonderful observations, bringing new insight and surprising perspectives to problems from number theory, geometry, sis, com binatorics, and graph theory. As a result, this book will be fun reading for anyone with an interest in mathematics. [via]

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  • Proofs from the Book
    by Martin Aigner, Günter M. Ziegler, K. H. Hofmann
    ISBN 3540404600 (3-540-40460-0)
    Hardcover, Springer London, Limited

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    From the Reviews:

    "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. Some of the proofs are classics, but many are new and brilliant proofs of classical results. ...Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999

    "... the style is clear and entertaining, the level is close to elementary ... and the proofs are brilliant. ..." LMS Newsletter, January 1999

    This third edition offers two new chapters, on partition identities, and on card shuffling. Three proofs of Euler's most famous infinite series appear in a separate chapter. There is also a number of other improvements, such as an exciting new way to "enumerate the rationals".

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  • Quinn, Jennifer: Proofs That Really Count: The Art of Combinatorialproof
    Proofs That Really Count: The Art of Combinatorialproof
    by Jennifer Quinn, Arthur T. Benjamin
    ISBN 0883853337 (0-88385-333-7)
    Hardcover, Mathematical Assn of Amer

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  • Chung, Fan R.K.: Spectral Graph Theory
    Spectral Graph Theory
    by Fan R.K. Chung
    ISBN 0821803158 (0-8218-0315-8)
    Softcover, Amer Mathematical Society

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  • Stable Marriage and Its Relation to Other Combinatorial Problems: An Introduction to the Mathematical Analysis of Algorithms
    by Donald E. Knuth
    ISBN 0821806033 (0-8218-0603-3)
    Softcover, Amer Mathematical Society

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    Book summary:

    The book uses the appealing theory of stable marriage to introduce and illustrate a variety of important concepts and techniques of computer science and mathematics: data structures, control structures, combinatorics, probability, analysis, algebra, and especially the analysis of algorithms.

    The presentation is elementary, and the topics are interesting to nonspecialists. The theory is quite beautiful and developing rapidly. Exercises with answers, an annotated bibliography, and research problems are included. The text would be appropriate as supplementary reading for undergraduate research seminars or courses in algorithmic analysis and for graduate courses in combinatorial algorithms, operations research, economics, or analysis of algorithms.

    Donald E. Knuth is one of the most prominent figures of modern computer science. His works in The Art of Computer Programming are classic. He is also renowned for his development of TeX and METAFONT. In 1996, Knuth won the prestigious Kyoto Prize, considered to be the nearest equivalent to a Nobel Prize in computer science. [via]

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  • Spencer, Joel H.: The Strange Logic of Random Graphs
    The Strange Logic of Random Graphs
    by Joel H. Spencer
    ISBN 3540416544 (3-540-41654-4)
    Hardcover, Springer Verlag

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  • Sagan, Bruce Eli: The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
    The Symmetric Group: Representations, Combinatorial Algorithms, and Symmetric Functions
    by Bruce Eli Sagan
    ISBN 0387950672 (0-387-95067-2)
    Hardcover, Springer Verlag

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  • Andrews, George E.: The Theory of Partitions
    The Theory of Partitions
    by George E. Andrews
    ISBN 052163766X (0-521-63766-X)
    Softcover, Cambridge University Press

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  • Berlekamp, Elwyn R.: Winning Ways for Your Mathematical Plays
    Winning Ways for Your Mathematical Plays
    by Elwyn R. Berlekamp, Richard K. Guy, John Horton Conway
    ISBN 1568811306 (1-56881-130-6)
    Softcover, A K Peters Ltd

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  • Fulton, William: Young Tableaux : With Applications to Representation Theory and Geometry
    Young Tableaux : With Applications to Representation Theory and Geometry
    by William Fulton, C. M. Series, J. W. Bruce
    ISBN 0521567246 (0-521-56724-6)
    Softcover, Cambridge University Press

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