離散數學及其應用（英文精編版·原書第8版）

本書是經典的離散數學教材，被全球數百所大學廣為採用。英文精編版為滿足本科教學需求而縮減了篇幅，保留的主要內容包括：邏輯和證明，集合、函數、序列、求和與矩陣，計數，關係，圖，樹，布林代數。
 
全書取材廣泛，除包括定義、定理的嚴格陳述外，還配備大量的例題、圖表、應用實例和練習。第8版做了與時俱進的更新，成為更加實用的教學工具。
 
本書可作為高等院校數學、電腦科學和電腦工程等專業的教材，也可作為科技領域從業人員的參考書。

The Adapter's Words
Preface
Online Resources
To the Student
About the Author
List of Symbols

1 The Foundations: Logic and Proofs1
1.1　Propositional Logic1
1.2　Applications of Propositional Logic15
1.3　Propositional Equivalences22
1.4　Predicates and Quantifiers34
1.5　Nested Quantifiers51
1.6　Rules of Inference62
1.7　Introduction to Proofs72
1.8　Proof Methods and Strategy84
End-of-ChapterMaterial (Online)

2 Basic Structures: Sets, Functions, Sequences, Sums, and Matrices101
2.1　Sets101
2.2　Set Operations111
2.3　Functions124
2.4　Sequences and Summations140
2.5　Cardinality of Sets153
2.6　Matrices161
End-of-ChapterMaterial (Online)

3 Counting169
3.1　The Basics of Counting169
3.2　The Pigeonhole Principle182
3.3　Permutations and Combinations189
3.4　Binomial Coefficients and Identities197
3.5　Generalized Permutations and Combinations204
3.6　Generating Permutations and Combinations215
End-of-ChapterMaterial (Online)

4 Advanced Counting Techniques221
4.1　Applications of Recurrence Relations221
4.2　Solving Linear Recurrence Relations232
4.3　Divide-and-Conquer Algorithms and Recurrence Relations244
4.4　Generating Functions253
4.5　Inclusion朎xclusion268
4.6　Applications of Inclusion朎xclusion273
End-of-ChapterMaterial (Online)

5 Relations281
5.1　Relations and Their Properties281
5.2　n-ary Relations and Their Applications292
5.3　Representing Relations302
5.4　Closures of Relations308
5.5　Equivalence Relations317
5.6　Partial Orderings327
End-of-ChapterMaterial (Online)

6 Graphs343
6.1　Graphs and Graph Models343
6.2　Graph Terminology and Special Types of Graphs354
6.3　Representing Graphs and Graph Isomorphism371
6.4　Connectivity380
6.5　Euler and Hamilton Paths393
6.6　Shortest-Path Problems405
6.7　Planar Graphs415
6.8　Graph Coloring423
End-of-ChapterMaterial (Online)

7 Trees431
7.1　Introduction to Trees431
7.2　Applications of Trees442
7.3　Tree Traversal456
7.4　Spanning Trees468
7.5　Minimum Spanning Trees481
End-of-ChapterMaterial (Online)

8 Boolean Algebra487
8.1　Boolean Functions487
8.2　Representing Boolean Functions494
8.3　Logic Gates497
8.4　Minimization of Circuits503
End-of-ChapterMaterial (Online)
Suggested Readings (Online)
Answers to Odd-Numbered Exercises (Online)

肯尼士·H.羅森（Kenneth H. Rosen）於1972年獲密歇根大學安娜堡分校數學學士學位，1976年獲麻省理工學院數學博士學位。Rosen曾就職於科羅拉多大學、俄亥俄州立大學、緬因大學和蒙茅斯大學，教授離散數學、演算法設計和電腦安全方面的課程；他還曾加盟貝爾實驗室，並且是AT&T貝爾實驗室的傑出技術人員。他的著作《初等數論及其應用》和《離散數學及其應用》均被翻譯成多種語言，在全球數百所大學中廣為採用。