对于大学一二年级的教学来说,离散数学是一门很有趣的课程,原因有几个方面。它的内容是数学,但它的大多数应用和超过半数的学生来自于计算机科学。因此,了解本书主题的编写动机,并事先了解它们的应用,是十分重要而必要的策略。此外,这门课程所涵盖的题材广泛,内容丰富,所以教材的内容须精心安排,清晰易懂,并用适当的教学法强调关键概念。同时,也希望学生能够掌握并运用一项重要的新技能:书写数学证明的能力。要写出**的计算机程序,这是一项非常好的训练。
数学系学生可使用本书作为离散数学基本概念的入门书,并作为向更**数学概念发展的基础。如果**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。本书也可作为计算机科学或者计��机工程课程的教材,它为与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连贯的发展和共同的主题。教师很容易通过参考每章的**知识设计出与各章内容相一致的、适当的课程。

Preface
A Word to Students
1 Fundamentals
1.1 Sets and Subsets
1.2 Operations on Sets
1.3 Sequences 13
1.4 Division in the Integers
1.5 Matrices 32
1.6 Mathematical Structures
2 Logic 50
2.1 Propositions and Logical Operations
2.2 Conditional Statements
2.3 Methods of Proof
2.4 Mathematical Induction
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 Computer Representation of 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 Extremal 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
Appendix A:Aigorithms and Psenudocode
Appendix B:Additionol Experiments in Discrete Mathematics
Answers to Odd-Numberde Exercises
Answers to Chapter Self-Tests
Glossary
Index
Photo Credits