### Features

Includes an extensive glossary for every chapterExtensive list of important formulas and theorems related to the fieldComplete 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

### 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