本书是经典的离散数学教材，被全球数百所大学广为采用。书中全面而系统地介绍了离散数学的理论和方法，主要包括：逻辑和证明，集合、函数、序列、求和与矩阵，算法，数论和密码学，归纳与递归，计数，离散概率，关系，图，树，布尔代数，计算模型。全书取材广泛，除包括定义、定理的严格陈述外，还配备大量的例题、图表、应用实例和练习。第8版做了与时俱进的更新，成为更加实用的教学工具。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，也可作为科技领域从业人员的参考书。

WU

计算机\离散数学

本书是介绍离散数学理论和方法的经典教材，被全球数百所高校采用，获得了极大的成功。第8版做了与时俱进的更新，添加了多重集、字符串匹配算法、同态加密、数据挖掘中的关联规则、语义网络等内容，同时更新了配套教辅资源，成为更加实用的教学工具。本书可作为1～2个学期的离散数学课程教材，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。

本书特色
·例题：共800多道例题，用于阐明概念、建立不同主题之间的关联以及介绍实际应用。
·应用：涉及的领域包括计算机科学、数据网络、心理学、化学、工程学、语言学、生物学、商业和因特网等，展示了离散数学的实用性。
·算法：每一章都介绍了一些关键算法，提供伪代码，并简要分析其计算复杂度。
·历史资料：给出了89位数学家和计算机科学家的简短传记，帮助读者了解不同技术的历史背景和发展轨迹。
·练习、复习题和补充练习：共有4200多道难度各异的练习题，可以满足不同层次学生的需求。此外，还有一些研究性题目，帮助学生通过计算来探索新知识和新想法。

【封底小黄条】
This edition is authorized for sale in the People''s Republic of China only, excluding Hong Kong, Macao SAR and Taiwan.
此英文影印版仅限在中华人民共和国境内（不包括香港、澳门特别行政区及台湾地区）销售。

[美]肯尼思·H. 罗森（Kenneth H. Rosen）著：

1 The Foundations: Logic and Proofs....................................1
1.1 Propositional Logic............................................................1
1.2 Applications of Propositional Logic.............................................17
1.3 Propositional Equivalences....................................................26
1.4 Predicates and Quantifiers.....................................................40
1.5 Nested Quantifiers............................................................60
1.6 Rules of Inference.............................................................73
1.7 Introduction to Proofs.........................................................84
1.8 Proof Methods and Strategy....................................................96
End-of-Chapter Material.....................................................115
2 Basic Structures: Sets, Functions, Sequences, Sums, and atrices....................................121
2.1 Sets........................................................................121
2.2 Set Operations...............................................................133
2.3 Functions...................................................................147
2.4 Sequences and Summations...................................................165
2.5 Cardinality of Sets...........................................................179
2.6 Matrices....................................................................188
End-of-Chapter Material.....................................................195
3 Algorithms.........................................................201
3.1 Algorithms..................................................................201
3.2 The Growth of Functions.....................................................216
3.3 Complexity of Algorithms....................................................231
End-of-Chapter Materia.....................................................244
4 Number Theory and Cryptography..................................251
4.1 Divisibility and Modular Arithmetic...........................................251
4.2 Integer Representations and Algorithms........................................260
4.3 Primes and Greatest Common Divisors........................................271
4.4 Solving Congruences.........................................................290
4.5 Applications of Congruences.................................................303
4.6 Cryptography...............................................................310
End-of-Chapter Materia.....................................................324
5 Induction and Recursion............................................331
5.1 Mathematical Induction......................................................331
5.2 Strong Induction and Well-Ordering...........................................354
5.3 Recursive Definitions and Structural Induction..................................365
5.4 Recursive Algorithms........................................................381
5.5 Program Correctness.........................................................393
End-of-Chapter Materia.....................................................398
6 Counting...........................................................405
6.1 The Basics of Counting.......................................................405
6.2 The Pigeonhole Principle.....................................................420
6.3 Permutations and Combinations...............................................428
6.4 Binomial Coeficients and Identities...........................................437
6.5 Generalized Permutations and Combinations...................................445
6.6 Generating Permutations and Combinations....................................457
End-of-Chapter Materia.....................................................461
7 Discrete Probability.................................................469
7.1 An Introduction to Discrete Probability........................................469
7.2 Probability Theory...........................................................477
7.3 Bayes’Theorem.............................................................494
7.4 Expected Valueand Variance.................................................503
End-of-Chapter Materia.....................................................520
8 Advanced Counting Techniques.....................................527
8.1 Applications of Recurrence Relations..........................................527
8.2 Solving Linear Recurrence Relations..........................................540
8.3 Divide-and-Conquer Algorithms and Recurrence Relations......................553
8.4 Generating Functions........................................................563
8.5 Inclusion–Exclusion.........................................................579
8.6 Applications of Inclusion–Exclusion...........................................585
End-of-Chapter Materia.....................................................592
9 Relations...........................................................599
9.1 Relations and Their Properties................................................599
9.2 n-ary Relations and Their Applications.........................................611
9.3 Representing Relations.......................................................621
9.4 Closures of Relations.........................................................628
9.5 Equivalence Relations........................................................638
9.6 Partial Orderings............................................................650
End-of-Chapter Materia.....................................................665
10 Graphs.............................................................673
10.1 Graphs and Graph Models....................................................673
10.2 Graph Terminology and Special Types of Graphs...............................685
10.3 Representing Graphs and Graph Isomorphism..................................703
10.4 Connectivity................................................................714
10.5 Euler and Hamilton Paths.....................................................728
10.6 Shortest-Path Problems.......................................................743
10.7 Planar Graphs...............................................................753
10.8 Graph Coloring..............................................................762
End-of-Chapter Materia.....................................................771
11 Trees...............................................................781
11.1 Introduction to Trees.........................................................781
11.2 Applications of Trees........................................................793
11.3 Tree Traversal...............................................................808
11.4 Spanning Trees..............................................................821
11.5 Minimum Spanning Trees....................................................835
End-of-Chapter Materia.....................................................841
12 Boolean Algebra....................................................847
12.1 Boolean Functions...........................................................847
12.2 Representing Boolean Functions..............................................855
12.3 Logic Gates.................................................................858
12.4 Minimization of Circuits.....................................................864
End-of-Chapter Materia.....................................................879
13 Modeling Computation .............................................885
13.1 Languages and Grammars....................................................885
13.2 Finite-State Machines with Output.............................................897
13.3 Finite-State Machines with NoOutput.........................................904
13.4 Language Recognition.......................................................917
13.5 Turing Machines.............................................................927
End-of-Chapter Materia.....................................................938
Appendices.........................................................A-1
1 Axioms for the Real Numbers and the Positive Integers..........................A-1
2 Exponential and Logarithmic Functions........................................A-7
3 Pseudocode................................................................A-11
Suggested ReadingsB-1
Answers to Odd-Numbered Exercises S-1
Index of BiographiesI-1
IndexI-2