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　　本書是經典的離散數學教材，為全球多所大學廣為采用。本書全面而系統地介紹了離散數學的理論和方法，內容涉及邏輯和證明，集合、函數、序列、求和與矩陣，計數，關系，圖，樹，布爾代數。全書取材廣泛，除包括定義、定理的嚴格陳述外，還配備大量的實例和圖表說明、各種練習和題目。第7版在前六版的基礎上做了大量的改進，使其成為更有效的教學工具。本書可作為高等院校數學、計算機科學和計算機工程等專業的教材或參考書。 

　　PrefaceIn writing this book, I was guided by my long-standing experience and interest in teaching discrete mathematics. For the student, my purpose was to present material in a precise, readable manner, with the concepts and techniques of discrete mathematics clearly presented and demonstrated. My goal was to show the relevance and practicality of discrete mathematics to students, who are often skeptical. I wanted to give students studying computer science all of the mathematical foundations they need for their future studies. I wanted to give mathematics students an understanding of important mathematical concepts together with a sense of why these concepts are important for applications. And most importantly, I wanted to accomplish these goals without watering down the material.For the instructor, my purpose was to design a flexible, comprehensive teaching tool using proven pedagogical techniques in mathematics. I wanted to provide instructors with a package of materials that they could use to teach discrete mathematics effectively and efficiently in the most appropriate manner for their particular set of students. I hope that I have achieved these goals.I have been extremely gratified by the tremendous success of this text. The many improvements in the seventh edition have been made possible by the feedback and suggestions of a large number of instructors and students at many of the more than 600 North American schools, and at any many universities in parts of the world, where this book has been successfully used.This text is designed for a one-or two-term introductory discrete mathematics course taken by students in a wide variety of majors, including mathematics, computer science, and engineering. College algebra is the only explicit prerequisite, although a certain degree of mathematical maturity is needed to study discrete mathematics in a meaningful way. This book has been designed to meet the needs of almost all types of introductory discrete mathematics courses. It is highly flexible and extremely comprehensive. The book is designed not only to be a successful textbook, but also to serve as valuable resource students can consult throughout their studies and professional life.Goals of a Discrete Mathematics CourseA discrete mathematics course has more than one purpose. Students should learn a particular set of mathematical facts and how to apply them; more importantly, such a course should teach students how to think logically and mathematically. To achieve these goals, this text stresses mathematical reasoning and the different ways problems are solved. Five important themes are interwoven in this text: mathematical reasoning, combinatorial analysis, discrete structures, algorithmic thinking, and applications and modeling. A successful discrete mathematics course should carefully blend and balance all five themes.1. Mathematical Reasoning: Students must understand mathematical reasoning in order to read, comprehend, and construct mathematical arguments. This text starts with a discussion of mathematical logic, which serves as the foundation for the subsequent discussions of methods of proof. Both the science and the art of constructing proofs are addressed. The technique of mathematical induction is stressed through many different types of examples of such proofs and a careful explanation of why mathematical induction is a valid proof technique.2. Combinatorial Analysis: An important problem-solving skill is the ability to count or enumerate objects. The discussion of enumeration in this book begins with the basic techniques of counting. The stress is on performing combinatorial analysis to solve counting problems and analyz ealgorithms, not on applying formulae.3. Discrete Structures: A course in discrete mathematics should teach students how to work with discrete structures, which are the abstract mathematical structures used to represent discrete objects and relationships between these objects. These discrete structures include sets, permutations, relations, graphs, trees, and finite-state machines.4. Algor 
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　　Kenneth H. Rosen，1972年獲密歇根大學數學學士學位，1976年獲麻省理工學院數學博士學位，1982年加入貝爾實驗室，現為AT&T實驗室特別成員，國際知名的計算機數學專家，除本書外，還著有《初等數論及其應用》等書。 

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The Adapter 's Words 
Preface　 
About the Author
The Companion Website　 
To the Student　 
List of Symbols　
1 The Foundations: Logic and Proofs. 
1.1 Propositional Logic
1.2 Applications of Propositional Logic
1.3 Propositional Equivalences. 
1.4 Predicates and Quantifiers
1.5 Nested Quantifiers. 
1.6 Rules of Inference. 
1.7 Introduction to Proofs
1.8 Proof Methods and Strategy. 
End-of-Chapter Material. 
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices
2.1 Sets.. 
2.2 Set Operations
2.3 Functions
2.4 Sequences and Summations. 
2.5 Cardinality of Sets
2.6 Matrices
End-of-Chapter Material
3 Counting
3.1 The Basics of Counting
3.2 The Pigeonhole Principle.
3.3 Permutations and Combinations. 
3.4 Binomial Coefficients and Identities
3.5 Generalized Permutations and Combinations. 
3.6 Generating ermutations and Combinations
End-of-Chapter Material
4 Advanced Counting Techniques
4.1 Applications of Recurrence Relations
4.2 Solving Linear Recurrence Relations
4.3 Divide-and-Conquer Algorithms and Recurrence Relations
4.4 Generating Functions
4.5 Inclusion xclusion. 
4.6 Applications of Inclusion xclusion
End-of-Chapter Material.. 
5 Relations. 
5.1 Relations and Their Properties
5.2 n-ary Relations and Their Applications
5.3 Representing Relations. 
5.4 Closures of Relations
5.5 Equivalence Relations.
5.6 Partial Orderings. 
End-of-Chapter Material. 
6 Graphs. 
6.1 Graphs and Graph Models.
6.2 Graph Terminology and Special Types of Graphs
6.3 Representing Graphs and Graph Isomorphism. 
6.4 Connectivity. 
6.5 Euler and Hamilton Paths. 
6.6 Shortest-Path Problems. 
6.7 Planar Graphs.
6.8 Graph Coloring. 
End-of-Chapter Material
7 Trees
7.1 Introduction to Trees.
7.2 Applications of Trees. 
7.3 Tree Traversal.
7.4 Spanning Trees
7.5 Minimum Spanning Trees
End-of-Chapter Material. 
8 Boolean Algebra
8.1 Boolean Functions
8.2 Representing Boolean Functions
8.3 Logic Gates
8.4 Minimization of Circuits
End-of-Chapter Material..
Suggested Readings
Answers to Exercises
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