本书是介绍离散数学理论和方法的经典教材，已经成为采用率最高的离散数学教材。仅在美国就被600多所高校用作教材，获得了极大的成功。中文版也已被国内大学广泛采用为教材。第6版在前五版的基础上做了大量的改进，使其成为更有效的教学工具。

本书可作为1至2个学期的离散数学课入门教材，适用于数学、计算机科学、计算机工程、信息技术等专业的学生。

Preface             fii

About the Author         xiv

To the Student          xv

LIST OF SYMBOLS       xviii

1 The Foundations: Logic and Proofs

1.1 Propositional Logic

1.2 Propositional Equivalences

1.3 Predicates and Quantifiers

1.4 Nested Quantifiers

1.5 Rules oflnference

1.6 Introduction to Proofs

1.7 Proof Methods and Strategy

 End-of-Chapter Material

2 Basic Structures: Sets, Functions, Sequences, and Sums

2.1 Sets

2.2 Set Operations

2.3 Functions

2.4 Sequences and Summations

 End-of-Chapter Material

3 The Fundamentals: Algorithms, the Integers, and Matrices

3.1 Algorithms

3.2 The Growth of Functions

3.3 Complexity of Algorithms

3.4 The Integers and Division

3.5 Primes and Greatest Common Divisors

3.6 Integers and Algorithms

3.7 Applications of Number Theory

3.8 Matrices

 End-of-Chapter Material

4 Induction and Recursion

4.1 Mathematical Induction

4.2 Strong Induction and Well-Ordering

4.3 Recursive Definitions and Structural Induction

4.4 Recursive Algorithms

4.5 Program Correctness

 End-of-Chapter Material

5 Counting

5.1 The Basics of Counting

5.2 The Pigeonhole Principle

5.3 Permutations and Combinations

5.4 Binomial Coefficients

5.5 Generalized Permutations and Combinations

5.6 Generating Permutations and Combinations

 End-of-Chapter Material

6 Discrete Probability

6.1 An Introduction to Discrete Probability

6.2 Probability Theory

6.3 Bayes' Theorem

6.4 Expected Value and Variance

 End-of-Chapter Material

7 Advanced Counting Techniques

7.1 Recurrence Relations

7.2 Solving Linear Recurrence Relations

7.3 Divide-and-Conquer Algorithms and Recurrence Relations

7.4 Generating Functions

7.5 Inclusion-Exclusion

7.6 Applications of Inclusion-Exclusion

 End-of-Chapter Material

8 Relations

8.1 Relations and Their Properties

8.2 n-ary Relations and Their Applications

8.3 Representing Relations

8.4 Closures of Relations

8.5 Equivalence Relations

8.6 Partial Orderings

 End-of-Chapter Material

9 Graphs

9.1 Graphs and Graph Models

9.2 Graph Terminology and Special Types of Graphs

9.3 Representing Graphs and Graph Isomorphism

9.4 Connectivity

9.5 Euler and Hamilton Paths

9.6 Shortest-Path Problems

9.7 Planar Graphs

9.8 Graph Coloring

 End-of-Chapter Material

10 Trees

10.1 Introduction to Trees

10.2 Applications of Trees

10.3 Tree Traversal

10.4 Spanning Trees

10.5 Minimum Spanning Trees

 End-of-Chapter Material

11 Boolean Algebra

11.1 Boolean Functions

11.2 Representing Boolean Functions

11.3 Logic Gates

11.4 Minimization of Circuits

  End-of-Chapter Material

12 Modeling Computation

12.1 Languages and Grammars

12.2 Finite-State Machines with Output

12.3 Finite-State Machines with No Output

12.4 Language Recognition

12.5 Turing Machines

  End-of-Chapter Material

  Appendixes

A-1 Axioms for the Real Numbers and the Positive Integers

A-2 Exponential and Logarithmic Functions

A-3 Pseudocode

Suggested Readings B-1

Answers to Odd-Numbered Exercises @ S-1

Index of Biographies I-1

Index I-2