Kenneth H. Rosen 1972年获密歇根大学数学学士学位，1976年获麻省理工学院数学博士学位，1982年加入贝尔实验室，现为AT&T实验室特别成员，国际知名的计算机数学专家，除本书外，还著有《初等数论及其应用》等书。
目錄：
Contents
The Adapter ''s Words iv
Preface vi
About the Author xi
The Companion Website xii
To the Student xiv
List of Symbols xvii
1 The Foundations： Logic and Proofs1
11 Propositional Logic1
12 Applications of Propositional Logic13
13 Propositional Equivalences20
14 Predicates and Quantifiers32
15 Nested Quantifiers49
16 Rules of Inference59
17 Introduction to Proofs70
18 Proof Methods and Strategy80
End-of-Chapter Material96
2 Basic Structures： Sets, Functions, Sequences, Sums, and Matrices 101
21 Sets101
22 Set Operations111
23 Functions121
24 Sequences and Summations137
25 Cardinality of Sets149
26 Matrices156
End-of-Chapter Material163
3 Counting169
31 The Basics of Counting169
32 The Pigeonhole Principle181
33 Permutations and Combinations188
34 Binomial Coefficients and Identities195
35 Generalized Permutations and Combinations202
36 Generating ermutations and Combinations212
End-of-Chapter Material216
4 Advanced Counting Techniques223
41 Applications of Recurrence Relations223
42 Solving Linear Recurrence Relations233
43 Divide-and-Conquer Algorithms and Recurrence Relations245
44 Generating Functions254
45 Inclusion朎xclusion268
46 Applications of Inclusion朎xclusion273
End-of-Chapter Material279
5 Relations287
51 Relations and Their Properties287
52 n-ary Relations and Their Applications296
53 Representing Relations303
54 Closures of Relations309
55 Equivalence Relations318
56 Partial Orderings327
End-of-Chapter Material340
6 Graphs347
61 Graphs and Graph Models347
62 Graph Terminology and Special Types of Graphs356
63 Representing Graphs and Graph Isomorphism372
64 Connectivity380
65 Euler and Hamilton Paths393
66 Shortest-Path Problems404
67 Planar Graphs414
68 Graph Coloring421
End-of-Chapter Material429
7 Trees439
71 Introduction to Trees439
72 Applications of Trees450
73 Tree Traversal463
74 Spanning Trees475
75 Minimum Spanning Trees486
End-of-Chapter Material491
8 Boolean Algebra497
81 Boolean Functions497
82 Representing Boolean Functions504
83 Logic Gates507
84 Minimization of Circuits513
End-of-Chapter Material525
Suggested Readings 531
Answers to Exercises
內容試閱：
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
購物車/收銀台(0) | 在線留言板
| 付款方式
| 聯絡我們
| 運費計算
| 幫助中心 |
加入書簽
HOME
新書上架
