本书从算法分析和问题求解的角度,全面系统地介绍了离散数学的基础概念及相关知识,并在其前一版的基础上进行了修改与扩展。书中通过大量实例,深入浅出地讲解了数理逻辑、组合算法、图论、布尔代数、网络模型、形式语言与自动机理论等与计算机科学密切相关的前沿课题,既着重于各部分内容之间的紧密联系,又深入探讨了相关的概念、理论、算法和实际应用。本书内容叙述严谨、推演详尽,各章配有相当数量的习题与书后的提示和答案,为读者迅速掌握相关知识提供了有效的帮助。
本书既可作为计算机科学及计算数学等专业的本科生和研究生教材,也可作为工程技术人员和相关人员的参考书。

Preface
1 Sets and Logic
1.1 Sets
1.2 Propositions
1.3 Conditional Propositions and Logical Equivalence
1.4 Arguments and Rules of Inference
1.5 Quantifiers
1.6 Nested Quantifiers
Problem-Solving Corner: Quantifiers
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
2 Proofs
2.1 Mathematical Systems, Direct Proofs, and Counterexamples
2.2 More Methods of Proof
Problem-Solving Corner: Proving Some Properties of Real Numbers
2.3 Resolution Proofst
2.4 Mathematical Induction
Problem-Solving Corner: Mathematical Induction
2.5 Strong Form of Induction and the Well-Ordering Property
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
3 Functions, Sequences, and Relations
3.1 Functions
Problem-Solving Corner: Functions
3.2 Sequences and Strings
3.3 Relations
3.4 Equivalence Relations
Problem-Solving Corner: Equivalence Relations
3.5 Matrices of Relations
3.6 Relational Databasest
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
4 Algorithms
4.1 Introduction
4.2 Examples of Algorithms
4.3 Analysis of Algorithms
Problem-Solving Corner: Design and Analysis of an Algorithm
4.4 Recursive Algorithms
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
5 Introduction to Number Theory
5.1 Divisors
5.2 Representations of Integers and Integer Algorithms
5.3 The Euclidean Algorithm
Problem-Solving Corner: Making Postage
5.4 The RSA Public-Key Cryptosystem
Notes
Chapter Review
Chapter Self-Test
Computer Exercises
6 Counting Methods and the Pigeonhole Principle
6.1 Basic Principles 265
Problem-Solving Corner: Counting
……
7 Recurence Relations
8 Graph Theory
9 Trees
10 Network Models
11 Boolean Algebras and Combinatorial Circuits
12 Automata, Grammars, and languages
13 Computational Geometry
A Matrices
B Algebra Review
C Pesudocode
References
Hints and Solutions to Selected Exer……

本书是“国外计算机科学教材系列”之一,全书共分13个章节,全面系统地介绍了离散数学的基础概念及相关知识,并在其前一版的基础上进行了修改与扩展。另外,书中还为各章配有相当数量的习题与书后的提示和答案,为读者迅速掌握相关知识提供了有效的帮助。可供各大专院校作为教材使用,也可供从事相关工作的人员作为参考用书使用。