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Discrete Mathematics and Its Applications2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

Discrete Mathematics and Its Applications
  • Kenneth H.Rosen 著
  • 出版社：
  • ISBN：0394367685
  • 出版时间：未知
  • 标注页数：598页
  • 文件大小：156MB
  • 文件页数：727页
  • 主题词：

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图书目录

1The Foundations： Logic， Sets， and Functions1

1.1 Logic2

1.2 Propositional Equivalences11

1.3 Predicates and Quantifiers17

1.4 Sets25

1.5 Set Operations33

1.6 Functions45

1.7 Sequences and Summations57

1.8 The Growth of Functions63

Key Terms and Results72

Supplementary Exercises74

Computer Projects76

2The Fundamentals： Algorithms， The Integers， and Matrices77

2.1 Algorithms78

2.2 Complexity of Algorithms84

2.3 The Integers and Division91

2.4 Integers and Algorithms102

2.5 Matrices112

Key Terms and Results124

Supplementary Exercises126

Computer Projects127

3Mathematical Reasoning129

3.1 Methods of Proof130

3.2 Mathematical Induction141

3.3 Recursive Definitions156

3.4 Recursive Algorithms166

3.5 Program Correctness175

Key Terms and Results178

Supplementary Exercises179

Computer Projects182

4Counting184

4.1 The Basics of Counting185

4.2 The Pigeonhole Principle194

4.3 Permutations and Combinations200

4.4 Discrete Probability209

4.5 Generalized Permutations and Combinations215

4.6 Generating Permutations and Combinations223

Key Terms and Results228

Supplementary Exercises229

Computer Projects232

5Advanced Counting Techniques233

5.1 Recurrence Relations234

5.2 Solving Recurrence Relations242

5.3 Divide-and-Conquer Relations250

5.4 Inclusion-Exclusion256

5.5 Applications of Inclusion-Exclusion264

Key Terms and Results273

Supplementary Exercises274

Computer Projects277

6Relations278

6.1 Relations and Their Properties279

6.2 n-ary Relations and Their Applications289

6.3 Representing Relations297

6.4 Closures of Relations305

6.5 Equivalence Relations317

6.6 Partial Orderings326

Key Terms and Results341

Supplementary Exercises344

Computer Projects347

7Graphs348

7.1 Introduction to Graphs349

7.2 Graph Terminology357

7.3 Representing Graphs367

7.4 Connectivity378

7.5 Euler and Hamilton Paths387

7.6 Shortest Path Problems401

7.7 Planar Graphs411

7.8 Graph Coloring421

Key Terms and Results431

Supplementary Exercises433

Computer Projects438

8Trees439

8.1 Introduction to Trees440

8.2 Applications of Trees454

8.3 Tree Traversal460

8.4 Trees and Sorting477

8.5 Spanning Trees486

8.6 Minimal Spanning Trees499

Key Terms and Results506

Supplementary Exercises508

Computer Projects512

9Boolean Algebra513

9.1 Boolean Functions514

9.2 Representing Boolean Functions520

9.3 Logic Gates525

9.4 Minimization of Circuits532

Key Terms and Results546

Supplementary Exercises547

Computer Projects550

10Modeling Computation551

10.1 Languages and Grammars552

10.2 Finite-State Machines with Output563

10.3 Finite-State Machines with No Output573

10.4 Language Recognition582

Key Terms and Results594

Supplementary Exercises595

Computer Projects598

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