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Discrete Mathematics Its Applications Sixth Edition=离散数学及其应用（英文版·第6版）PDF|Epub|txt|kindle电子书版本网盘下载

Kenneth H. Rosen 著
出版社：机械工业出版社
ISBN：7111239352
出版时间：2008
标注页数：890页
文件大小：126MB
文件页数：917页
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图书目录

1 The Foundations：Logic and Proofs1

1.1 Propositional Logic1

1.2 Propositional Equivalences21

1.3 Predicates and Quantifiers30

1.4 Nested Quantifiers50

1.5 Rules of Inference63

1.6 Introduction to Proofs75

1.7 Proof Methods and Strategy86

End-of-Chapter Material104

2 Basic Structures：Sets，Functions，Sequences，and Sums111

2.1 Sets111

2.2 Set Operations121

2.3 Functions133

2.4 Sequences and Summations149

End-of-Chapter Material163

3 The Fundamentals：Algorithms，the Integers，and Matrices167

3.1 Algorithms167

3.2 The Growth of Functions180

3.3 Complexity of Algorithms193

3.4 The Integers and Division200

3.5 Primes and Greatest Common Divisors210

3.6 Integers and Algorithms219

3.7 Applications of Number Theory231

3.8 Matrices246

End-of-Chapter Material257

4 Induction and Recursion263

4.1 Mathematical Induction263

4.2 Strong Induction and Well-Ordering283

4.3 Recursive Definitions and Structural Induction294

4.4 Recursive Algorithms311

4.5 Program Correctness322

End-of-Chapter Material328

5 Counting335

5.1 The Basics of Counting335

5.2 The Pigeonhole Principle347

5.3 Permutations and Combinations355

5.4 Binomial Coefficients363

5.5 Generalized Permutations and Combinations370

5.6 Generating Permutations and Combinations382

End-of-Chapter Material386

6 Discrete Probability393

6.1 An Introduction to Discrete Probability393

6.2 Probability Theory400

6.3 Bayes’ Theorem417

6.4 Expected Value and Variance426

End-of-Chapter Material442

7 Advanced Counting Techniques449

7.1 Recurrence Relations449

7.2 Solving Linear Recurrence Relations460

7.3 Divide-and-Conquer Algorithms and Recurrence Relations474

7.4 Generating Functions484

7.5 Inclusion-Exclusion499

7.6 Applications of Inclusion-Exclusion505

End-of-Chapter Material513

8 Relations519

8.1 Relations and Their Properties519

8.2 n-ary Relations and Their Applications530

8.3 Representing Relations537

8.4 Closures of Relations544

8.5 Equivalence Relations555

8.6 Partial Orderings566

End-of-Chapter Material581

9 Graphs589

9.1 Graphs and Graph Models589

9.2 Graph Terminology and Special Types of Graphs597

9.3 Representing Graphs and Graph Isomorphism611

9.4 Connectivity621

9.5 Euler and Hamilton Paths633

9.6 Shortest-Path Problems647

9.7 Planar Graphs657

9.8 Graph Coloring666

End-of-Chapter Material675

10 Trees683

10.1 Introduction to Trees683

10.2 Applications of Trees695

10.3 Tree Traversal710

10.4 Spanning Trees724

10.5 Minimum Spanning Trees737

End-of-Chapter Material743

11 Boolean Algebra749

11.1 Boolean Functions749

11.2 Representing Boolean Functions757

11.3 Logic Gates760

11.4 Minimization of Circuits766

End-of-Chapter Material781

12 Modeling Computation785

12.1 Languages and Grammars785

12.2 Finite-State Machines with Output796

12.3 Finite-State Machines with No Output804

12.4 Language Recognition817

12.5 Turing Machines827

End-of-Chapter Material838

Appendixes1

A-1 Axioms for the Real Numbers and the Positive Integers1

A-2 Exponential and Logarithmic Functions7

A-3 Pseudocode10