离散数学及其应用(英文精编版·原书第8版)

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版做了与时俱进的修改，同时更新了配套教辅资源，成为更加实用的教学工具。英文精编版为满足本科教学需求而缩减了篇幅，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
章节：保留了逻辑和证明、基本结构、计数和高级计数、关系、图、树和布尔代数等内容，删除了算法、数论和密码学、归纳与递归、离散概率、计算模型等内容。
例题：共400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。
练习、复习题和补充练习：共有2000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。

The Adapter's Words
Preface
Online Resources
To the Student
About the Author
List of Symbols
1 The Foundations: Logic and Proofs 1
1.1 Propositional Logic 1
1.2 Applications of Propositional Logic 15
1.3 Propositional Equivalences 22
1.4 Predicates and Quantifiers 34
1.5 Nested Quantifiers 51
1.6 Rules of Inference 62
1.7 Introduction to Proofs 72
1.8 Proof Methods and Strategy 84
End-of-ChapterMaterial (Online)
2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices 101
2.1 Sets 101
2.2 Set Operations 111
2.3 Functions 124
2.4 Sequences and Summations 140
2.5 Cardinality of Sets 153
2.6 Matrices 161
End-of-ChapterMaterial (Online)
3 Counting 169
3.1 The Basics of Counting 169
3.2 The Pigeonhole Principle 182
3.3 Permutations and Combinations 189
3.4 Binomial Coefficients and Identities 197
3.5 Generalized Permutations and Combinations 204
3.6 Generating Permutations and Combinations 215
End-of-ChapterMaterial (Online)
4 Advanced Counting Techniques 221
4.1 Applications of Recurrence Relations 221
4.2 Solving Linear Recurrence Relations 232
4.3 Divide-and-Conquer Algorithms and Recurrence Relations 244
4.4 Generating Functions 253
4.5 Inclusion朎xclusion 268
4.6 Applications of Inclusion朎xclusion 273
End-of-ChapterMaterial (Online)
5 Relations 281
5.1 Relations and Their Properties 281
5.2 n-ary Relations and Their Applications 292
5.3 Representing Relations 302
5.4 Closures of Relations 308
5.5 Equivalence Relations 317
5.6 Partial Orderings 327
End-of-ChapterMaterial (Online)
6 Graphs 343
6.1 Graphs and Graph Models 343
6.2 Graph Terminology and Special Types of Graphs 354
6.3 Representing Graphs and Graph Isomorphism 371
6.4 Connectivity 380
6.5 Euler and Hamilton Paths 393
6.6 Shortest-Path Problems 405
6.7 Planar Graphs 415
6.8 Graph Coloring 423
End-of-ChapterMaterial (Online)
7 Trees 431
7.1 Introduction to Trees 431
7.2 Applications of Trees 442
7.3 Tree Traversal 456
7.4 Spanning Trees 468
7.5 Minimum Spanning Trees 481
End-of-ChapterMaterial (Online)
8 Boolean Algebra 487
8.1 Boolean Functions 487
8.2 Representing Boolean Functions 494
8.3 Logic Gates 497
8.4 Minimization of Circuits 503
End-of-ChapterMaterial (Online)
Suggested Readings (Online)
Answers to Odd-Numbered Exercises (Online)