作者：(美)肯尼思H.罗森(Kenneth
页数：537
出版社：机械工业出版社
出版日期：2017
ISBN：9787111555360
电子书格式：pdf/epub/txt
内容简介
本书是经典的离散数学教材，为全球多所大学广为采用。本书全面而系统地介绍了离散数学的理论和方法，内容涉及逻辑和证明，集合、函数、序列、求和与矩阵，计数，关系，图，树，布尔代数。全书取材广泛，除包括定义、定理的严格陈述外，还配备大量的实例和图表说明、各种练习和题目。第7版在前六版的基础上做了大量的改进，使其成为更有效的教学工具。本书可作为高等院校数学、计算机科学和计算机工程等专业的教材或参考书。
作者简介
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。
本书特色
本书是经典的离散数学教材，为全球多所大学广为采用。本书全面而系统地介绍了离散数学的理论和方法，内容涉及逻辑和证明，集合、函数、序列、求和与矩阵，计数，关系，图，树，布尔代数。全书取材广泛，除包括定义、定理的严格陈述外，还配备大量的实例和图表说明、各种练习和题目。第7版在前六版的基础上做了大量的改进，使其成为更有效的教学工具。本书可作为高等院校数学、计算机科学和计算机工程等专业的教材或参考书。
目录
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
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
