由科曼等编著的《离散数学结构》可作为离散数学基本概念的入门书，并作为向更高级数学概念发展的基础。如果仅限于此，那么书中涉及计算机科学的一些特定应用可以略去或者单独作为重要的例子选用。本书可作为计算机科学或者电子与计算机工程课程的教材，它也为计算机相关的许多基本概念打下基础，并且为这些概念提供延伸、发展和共同的主题。通过参考每章的必备知识，教师很容易设计出与各章内容相一致的、适当的教学大纲。

Preface

A Word to Students

1 Fundamentals

l.1  Sets and Subsets

1.2  Operations on Sets

1.3  Sequences

1.4  Properties of Integers

1.5  Matrices

1.6  Mathematical Structures

2 Logic

2.1  Propositions and Logical Operations

2.2  Conditional Statements

2.3  Methods of Proof

2.4  Mathematical Induction

2.5  Mathematical Statements

2.6  Logic and Problem Solving

3 Counting

3.1  Permutations

3.2  Combinations

3.3  Pigeonhole Principle

3.4  Elements of Probability

3.5  Recurrence Relations

4 Relations and Digraphs

4.1  Product Sets and Partitions

4.2  Relations and Digraphs

4.3  Paths in Relations and Digraphs

4.4  Properties of Relations

4.5  Equivalence Relations

4.6  Data Structures for Relations and Digraphs

4.7  Operations on Relations

4.8  Transitive Closure and Warshall's Algorithm

5 Functions

5.1  Functions

5.2  Functions for Computer Science

5.3  Growth of Functions

5.4  Permutation Functions

6 Order Relations and Structures

6.1  Partially Ordered Sets

6.2  Ex.tremal Elements of Partially Ordered Sets

6.3  Lattices

6.4  Finite Boolean, Algebras

6.5  Functions on Boolean Algebras

6.6  Circuit Design

7 Trees

7.1  Trees

7.2  Labeled Trees

7.3  Tree Searching

7.4  Undirected Trees

7.5  Minimal Spanning Trees

8 Topics in Graph Theory

8.1  Graphs

8.2  Euler Paths and Circuits

8.3  Hamiltonian Paths and Circuits

8.4  Transport Networks

8.5  Matching Problems

8.6  Coloring Graphs

9 Semigroups and Groups

9.1  Binary Operations Revisited

9.2  Semigroups

9.3  Products and Quotients of Semigroups

9.4  Groups

9.5  Products and Quotients of Groups

9.6  Other Mathematical Structures

10 Languages and Finite-State Machines

10.1  Languages

10.2  Representations of Special Grammars and Languages

10.3  Finite-State Machines

10.4  Monoids, Machines, and Languages

10.5  Machines and Regular Languages

10.6  Simplification of Machines

11 Groups and Coding

11.1  Coding of Binary Information and Error Detection

11.2  Decoding and Error Correction

11.3  Public Key Cryptology

Appendix A: Algorithms and Pseudocode

Appendix B: Additional Experiments in Discrete Mathematics

Appendix C: Coding Exercises

Answers to Odd-Numbered Exercises

Answers to Chapter Self-Tests

Glossary G-1

Index 1-1

Photo Credits P-1