Handbook of Discrete and Combinatorial Mathematics

Handbook of Discrete and Combinatorial Mathematics

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ISBN 9780849301490
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Features

  • Includes an extensive glossary for every chapter
  • Extensive list of important formulas and theorems related to the field
  • Complete explanations and descriptions of every algorithm
  • Many reference pages to web connections are included throughout the book
  • Summary

    The importance of discrete mathematics has increased dramatically within the last few years but until now, it has been difficult-if not impossible-to find a single reference book that effectively covers the subject. To fill that void, The Handbook of Discrete and Combinatorial Mathematics presents a comprehensive collection of ready reference material for all of the important areas of discrete mathematics, including those essential to its applications in computer science and engineering. Its topics include:

  • Logic and foundations
  • Counting
  • Number theory
  • Abstract and linear algebra
  • Probability
  • Graph theory
  • Networks and optimization
  • Cryptography and coding
  • Combinatorial designs
    The author presents the material in a simple, uniform way, and emphasizes what is useful and practical. For easy reference, he incorporates into the text:
  • Many glossaries of important terms
  • Lists of important theorems and formulas
  • Numerous examples that illustrate terms and concepts
  • Helpful descriptions of algorithms
  • Summary tables
  • Citations of Web pages that supplement the text
    If you have ever had to find information from discrete mathematics in your work-or just out of curiosity-you probably had to search through a variety of books to find it. Never again. The Handbook of Discrete Mathematics is now available and has virtually everything you need-everything important to both theory and practice.
  • Table of Contents

    Foundations, edited by J. Gross
    Propositional and Predicate Logic
    Set Theory
    Functions
    Relations
    Proof Techniques
    Axiomatic Program Verification
    Logic-Based Computer Programming Paradigms
    Counting Methods, edited by J. Gross
    Summary of Counting Problems
    Basic Counting Techniques
    Permutations and Combinations
    Inclusion/Exclusion
    Partitions
    Burnside/Polya Counting
    Mobius Inversion Counting
    Young Tableaux
    Sequences, edited by D. Shier and J. Gross
    Special Sequences
    Generating Functions
    Recurrence Relations
    Finite Differences
    Finite Sums and Summation
    Asymptotes of Sequences
    Number Theory, edited by K. Rosen
    Basics
    Primes and Factorization
    Multiplicative Functions
    Quadratic Residues and Primitive Roots
    Diophantine Equations
    Diophantine Approximation
    Algebraic Number Theory
    Algebraic Structures, edited by J. Michaels
    Algebraic Models
    Groups
    Permutation Groups
    Rings
    Polynomial Rings
    Fields
    Lattices
    Boolean Algebra
    Linear Algebra, edited by D. Shier
    Vector Spaces
    Linear Transformations
    Matrix Algebra
    Linear Systems
    Eigenanalysis
    Combinatorial Matrix Theory
    Transforms
    Discrete Probability, edited by D. Shier
    Fundamental Concepts
    Independence and Dependence
    Random Variables
    Probabilistic and Combinatorial Computations
    Random Walks
    System Reliability
    Discrete-Time Markov Chains
    Queuing Theory
    Simulation
    Graph Theory, edited by J. Gross
    Generalities
    Paths and Circuits
    Isomorphism
    Graph and Map Coloring
    Planarity
    Topological Graph Theory
    Graphical Enumeration
    Directed Graphs
    Algebraic Graph Theory
    Analytic Graph Theory
    Hypergraphs
    Trees, edited by J. Gross
    Characterization of Trees
    Spanning Trees
    Enumerating Trees
    Applications of Trees to Networks
    Networks and Flows, edited by D. Shier
    Minimum Spanning Trees
    Shortest Paths
    Matchings
    Maximum Flows
    Minimum Cost Flows
    Communication Networks
    Heuristic Approaches
    Network Representations and Data Structures
    Partially Ordered Sets, edited by J. Gross
    Fundamental Definitions and Examples
    Further Development
    Connections to Other Areas
    Combinatorial Designs, edited by J. Michaels
    Block Designs and Finite Geometries
    Symmetric Designs and Finite Geometries
    Latin Squares and Orthogonal Arrays
    Matroids
    Discrete and Computational Geometry, edited by J. Michaels
    Arrangements of Geometric Objects
    Space Filling
    Combinatorial Results in Geometry
    Polyhedra
    Algorithms and Complexity in Computational Geometry
    Geometric Data Structures and Searching
    Computational Techniques
    Applications of Geometry
    Coding Theory and Cryptology, edited by K. Rosen
    Basic Concepts of Coding Theory
    Linear Codes
    Bounds
    Convolutional Code
    Cryptology: Definitions
    Private Key Schemes
    Public Key Schemes
    Discrete Optimization, edited by D. Shier
    Linear Programming
    Algorithmic Strategies
    Location Theory
    Packing and Covering
    Activity Nets
    Game Theory
    Sperner's Lemma and Fixed-Point Theorems
    Theoretical Computer Science, edited by J. Gross
    Formal Languages
    Machine Models
    Computability
    Algorithmic Complexity
    Complexity Classes
    Randomized Algorithms
    Information Structures, edited by J. Gross
    Abstract Data Types
    Concrete Data Structures
    Sorting and Searching
    Hashing
    Dynamic Graph Algorithms

    Editorial Reviews

    "No other book covers such a wide range of topics in discrete mathematics…a useful resource."
    --CHOICE Magazine

    "I like the book's format. There are glossaries at the beginning of each chapter. Each subsection begins with definitions and goes on to "facts", then algorithms (boxed and in pseudo -code), lists of mathematical objects, illuminating pictures, examples, lists of applications, and, finally, bibliography and web sources. This handbook will appeal both to pure and to applied mathematicians. Its 17 chapters, and 115 subsections were produced by 77 individuals, kept nicely in line (no mean task) by five editors who, in turn, got the go-ahead signal and the prestige of an advisory editorial board of 23 distinguished authorities.
    --SIAM News -June 2001

    "intended to provide a user a quick and concise look up facility for definitions, basic facts, algorithms, standard examples, tables, printed references and URLs for the various objects of discrete mathematics. Thus it will be a valuable supplement in any library."
    -Monatshefte fur Mathematics, Volume 134, No. 3, 2002

    "…a valuable reference tool for professionals and students using discrete mathematics…The coverage is vast…This book is a must-buy for research libraries."
    --Journal of Mathematical Psychology, February 2002

     
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