The importance of discrete and combinatorial mathematics continues to increase as the range of applications to computer science, electrical engineering, and the biological sciences grows dramatically. Providing a ready reference for practitioners in the field, the Handbook of Discrete and Combinatorial Mathematics, Second Edition presents additional material on Google's matrix, random graphs, geometric graphs, computational topology, and other key topics. New chapters highlight essential background information on bioinformatics and computational geometry. Each chapter includes a glossary, definitions, facts, examples, algorithms, major applications, and references.
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
