### HANDBOOK OF DISCRETE AND COMBINATORIAL MATHEMATICS

## Monday, December 22, 2008

__HANDBOOK OF DISCRETE AND COMBINATORIAL MATHEMATICS
__

Download link is given at the bottom of the post:

BY:

KENNETH H. ROSEN

AT&T Laboratories

Editor-in-Chief

JOHN G. MICHAELS

SUNY Brockport

Project Editor

JONATHAN L. GROSS

Associate Editor

JERROLD W. GROSSMAN

Associate Editor

DOUGLAS R SHIER

Associate Editor

CRC Press

The importance of discrete and combinatorial mathematics has increased dramatically

within the last few years. The purpose of the Handbook of Discrete and Combinatorial

Mathematics is to provide a comprehensive reference volume for computer scientists,

engineers, mathematicians, and others, such as students, physical and social scientists,

and reference librarians, who need information about discrete and combinatorial math-

ematics.

This book is the ﬁrst resource that presents such information in a ready-reference form

designed for use by all those who use aspects of this subject in their work or studies.

The scope of this book includes the many areas generally considered to be parts of

discrete mathematics, focusing on the information considered essential to its application

in computer science and engineering. Some of the fundamental topic areas covered

include:

Logic and set theory graph theory

Enumeration trees

Integer sequences network sequences

Recurrence relations combinatorial designs

Generating functions computational geometry

Number theory coding theory and cryptography

Abstract algebra discrete optimization

Linear algebra automata theory

Discrete probability theory data structures and algorithms.

__Format:__

The material in the Handbook is presented so that key information can be located

and used quickly and easily. Each chapter includes a glossary that provides succinct deﬁnitions of the most important terms from that chapter. Individual topics are cov-ered in sections and subsections within chapters, each of which is organized into clearly identiﬁable parts: deﬁnitions, facts, and examples. The deﬁnitions included are care-fully crafted to help readers quickly grasp new concepts. Important notation is also highlighted in the deﬁnitions. Lists of facts include:

• Information about how material is used and why it is important

• Historical information

• Key theorems

• The latest results

• The status of open questions

• Tables of numerical values, generally not easily computed

• Summary tables

• Key algorithms in an easily understood pseudocode

• Information about algorithms, such as their complexity

• Major applications

• Pointers to additional resources, including websites and printed material.

Facts are presented concisely and are listed so that they can be easily found and understood. Extensive cross-references linking parts of the handbook are also provided.

Readers who want to study a topic further can consult the resources listed.

The material in the Handbook has been chosen for inclusion primarily because it is important and useful. Additional material has been added to ensure comprehensiveness so that readers encountering new terminology and concepts from discrete mathematics in their explorations will be able to get help from this book.

Examples are provided to illustrate some of the key deﬁnitions, facts, and algorithms. Some curious and entertaining facts and puzzles that some readers may ﬁnd intriguing are also included. Each chapter of the book includes a list of references divided into a list of printed resources and a list of relevant websites.

Elaborated contents:

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

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 —

8. GRAPH THEORY

8.1 Introduction to Graphs —

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

c 2000 by CRC Press LLC10. 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.

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

## 1 comments:

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