KENNETH H. ROSEN
AT&T Laboratories
Editor-in-Chief
JOHN G. MICHAELS
SUNY Brockport
Project Editor
JONATHAN L. GROSS
Columbia University
Associate Editor
JERROLD W. GROSSMAN
Oakland University
Associate Editor
DOUGLAS R SHIER
Clemson University
Associate Editor
CONTENTS
1. FOUNDATIONS
1.1 Propositional and Predicate Logic — Jerrold W. Grossman
1.2 Set Theory — Jerrold W. Grossman
1.3 Functions — Jerrold W. Grossman
1.4 Relations — John G. Michaels
1.5 Proof Techniques — Susanna S. Epp
1.6 Axiomatic Program Verification — David Riley
1.7 Logic-Based Computer Programming Paradigms — Mukesh Dalal
2. COUNTING METHODS
2.1 Summary of Counting Problems — John G. Michaels
2.2 Basic Counting Techniques — Jay Yellen
2.3 Permutations and Combinations — Edward W. Packel
2.4 Inclusion/Exclusion — Robert G. Rieper
2.5 Partitions — George E. Andrews
2.6 Burnside/P´olya Counting Formula — Alan C. Tucker
2.7 M¨obius Inversion Counting — Edward A. Bender
2.8 Young Tableaux — Bruce E. Sagan
3. SEQUENCES
3.1 Special Sequences — Thomas A. Dowling and Douglas R. Shier
3.2 Generating Functions — Ralph P. Grimaldi
3.3 Recurrence Relations — Ralph P. Grimaldi
3.4 Finite Differences — Jay Yellen
3.5 Finite Sums and Summation — Victor S. Miller
3.6 Asymptotics of Sequences — Edward A. Bender
3.7 Mechanical Summation Procedures — Kenneth H. Rosen
4. NUMBER THEORY
4.1 Basic Concepts — Kenneth H. Rosen
4.2 Greatest Common Divisors — Kenneth H. Rosen
4.3 Congruences — Kenneth H. Rosen
4.4 Prime Numbers — Jon F. Grantham and Carl Pomerance
4.5 Factorization — Jon F. Grantham and Carl Pomerance
4.6 Arithmetic Functions — Kenneth H. Rosen
4.7 Primitive Roots and Quadratic Residues — Kenneth H. Rosen
4.8 Diophantine Equations — Bart E. Goddard
4.9 Diophantine Approximation — Jeff Shalit
4.10 Quadratic Fields — Kenneth H. Rosen
5. ALGEBRAIC STRUCTURES — John G. Michaels
5.1 Algebraic Models
5.2 Groups
5.3 Permutation Groups
5.4 Rings
5.5 Polynomial Rings
5.6 Fields
5.7 Lattices
5.8 Boolean Algebras
6. LINEAR ALGEBRA
6.1 Vector Spaces — Joel V. Brawley
6.2 Linear Transformations — Joel V. Brawley
6.3 Matrix Algebra — Peter R. Turner
6.4 Linear Systems — Barry Peyton and Esmond Ng
6.5 Eigenanalysis — R. B. Bapat
6.6 Combinatorial Matrix Theory — R. B. Bapat
7. DISCRETE PROBABILITY
7.1 Fundamental Concepts — Joseph R. Barr
7.2 Independence and Dependence — Joseph R. Barr 435
7.3 Random Variables — Joseph R. Barr
7.4 Discrete Probability Computations — Peter R. Turner
7.5 Random Walks — Patrick Jaillet
7.6 System Reliability — Douglas R. Shier
7.7 Discrete-Time Markov Chains — Vidyadhar G. Kulkarni
7.8 Queueing Theory — Vidyadhar G. Kulkarni
7.9 Simulation — Lawrence M. Leemis
8. GRAPH THEORY
8.1 Introduction to Graphs — Lowell W. Beineke
8.2 Graph Models — Jonathan L. Gross
8.3 Directed Graphs — Stephen B. Maurer
8.4 Distance, Connectivity, Traversability — Edward R. Scheinerman
8.5 Graph Invariants and Isomorphism Types — Bennet Manvel
8.6 Graph and Map Coloring — Arthur T. White
8.7 Planar Drawings — Jonathan L. Gross
8.8 Topological Graph Theory — Jonathan L. Gross
8.9 Enumerating Graphs — Paul K. Stockmeyer
8.10 Algebraic Graph Theory — Michael Doob
8.11 Analytic Graph Theory — Stefan A. Burr
8.12 Hypergraphs — Andreas Gyarfas
9. TREES
9.1 Characterizations and Types of Trees — Lisa Carbone
9.2 Spanning Trees — Uri Peled
9.3 Enumerating Trees — Paul Stockmeyer
10. NETWORKS AND FLOWS
10.1 Minimum Spanning Trees — J. B. Orlin and Ravindra K. Ahuja
10.2 Matchings — Douglas R. Shier
10.3 Shortest Paths — J. B. Orlin and Ravindra K. Ahuja
10.4 Maximum Flows — J. B. Orlin and Ravindra K. Ahuja
10.5 Minimum Cost Flows — J. B. Orlin and Ravindra K. Ahuja
10.6 Communication Networks — David Simchi-Levi and Sunil Chopra
10.7 Difficult Routing and Assignment Problems — Bruce L. Golden and Bharat K. Kaku
10.8 Network Representations and Data Structures — Douglas R. Shier
11. PARTIALLY ORDERED SETS
11.1 Basic Poset Concepts — Graham Brightwell and Douglas B. West
11.2 Poset Properties — Graham Brightwell and Douglas B. West
12. COMBINATORIAL DESIGNS
12.1 Block Designs — Charles J. Colbourn and Jeffrey H. Dinitz
12.2 Symmetric Designs & Finite Geometries — Charles J. Colbourn and Jeffrey H. Dinitz
12.3 Latin Squares and Orthogonal Arrays — Charles J. Colbourn and Jeffrey H. Dinitz
12.4 Matroids — James G. Oxley
13. DISCRETE AND COMPUTATIONAL GEOMETRY
13.1 Arrangements of Geometric Objects — Ileana Streinu
13.2 Space Filling — Karoly Bezdek
13.3 Combinatorial Geometry — J´anos Pach
13.4 Polyhedra — Tamal K. Dey
13.5 Algorithms and Complexity in Computational Geometry — Jianer Chen
13.6 Geometric Data Structures and Searching — Dina Kravets 853
13.7 Computational Techniques — Nancy M. Amato
13.8 Applications of Geometry — W. Randolph Franklin
14. CODING THEORY AND CRYPTOLOGY — Alfred J. Menezes and
Paul C. van Oorschot
14.1 Communication Systems and Information Theory
14.2 Basics of Coding Theory
14.3 Linear Codes
14.4 Bounds for Codes
14.5 Nonlinear Codes
14.6 Convolutional Codes
14.7 Basics of Cryptography
14.8 Symmetric-Key Systems
14.9 Public-Key Systems
15. DISCRETE OPTIMIZATION
15.1 Linear Programming — Beth Novick
15.2 Location Theory — S. Louis Hakimi
15.3 Packing and Covering — Sunil Chopra and David Simchi-Levi
15.4 Activity Nets — S. E. Elmaghraby
15.5 Game Theory — Michael Mesterton-Gibbons
15.6 Sperner’s Lemma and Fixed Points — Joseph R. Barr
16. THEORETICAL COMPUTER SCIENCE
16.1 Computational Models — Jonathan L. Gross
16.2 Computability — William Gasarch
16.3 Languages and Grammars — Aarto Salomaa
16.4 Algorithmic Complexity — Thomas Cormen
16.5 Complexity Classes — Lane Hemaspaandra
16.6 Randomized Algorithms — Milena Mihail
17. INFORMATION STRUCTURES
17.1 Abstract Datatypes — Charles H. Goldberg
17.2 Concrete Data Structures — Jonathan L. Gross
17.3 Sorting and Searching — Jianer Chen
17.4 Hashing — Viera Krnanova Proulx
17.5 Dynamic Graph Algorithms — Joan Feigenbaum and Sampath Kannan
BIOGRAPHIES — Victor J. Katz
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