Discrete Mathematics Its Applications Sixth Edition=离散数学及其应用（英文版·第6版）PDF电子书下载

1 The Foundations：Logic and Proofs 1

1.1 Propositional Logic 1

1.2 Propositional Equivalences 21

1.3 Predicates and Quantifiers 30

1.4 Nested Quantifiers 50

1.5 Rules of Inference 63

1.6 Introduction to Proofs 75

1.7 Proof Methods and Strategy 86

End-of-Chapter Material 104

2 Basic Structures：Sets，Functions，Sequences，and Sums 111

2.1 Sets 111

2.2 Set Operations 121

2.3 Functions 133

2.4 Sequences and Summations 149

End-of-Chapter Material 163

3 The Fundamentals：Algorithms，the Integers，and Matrices 167

3.1 Algorithms 167

3.2 The Growth of Functions 180

3.3 Complexity of Algorithms 193

3.4 The Integers and Division 200

3.5 Primes and Greatest Common Divisors 210

3.6 Integers and Algorithms 219

3.7 Applications of Number Theory 231

3.8 Matrices 246

End-of-Chapter Material 257

4 Induction and Recursion 263

4.1 Mathematical Induction 263

4.2 Strong Induction and Well-Ordering 283

4.3 Recursive Definitions and Structural Induction 294

4.4 Recursive Algorithms 311

4.5 Program Correctness 322

End-of-Chapter Material 328

5 Counting 335

5.1 The Basics of Counting 335

5.2 The Pigeonhole Principle 347

5.3 Permutations and Combinations 355

5.4 Binomial Coefficients 363

5.5 Generalized Permutations and Combinations 370

5.6 Generating Permutations and Combinations 382

End-of-Chapter Material 386

6 Discrete Probability 393

6.1 An Introduction to Discrete Probability 393

6.2 Probability Theory 400

6.3 Bayes’ Theorem 417

6.4 Expected Value and Variance 426

End-of-Chapter Material 442

7 Advanced Counting Techniques 449

7.1 Recurrence Relations 449

7.2 Solving Linear Recurrence Relations 460

7.3 Divide-and-Conquer Algorithms and Recurrence Relations 474

7.4 Generating Functions 484

7.5 Inclusion-Exclusion 499

7.6 Applications of Inclusion-Exclusion 505

End-of-Chapter Material 513

8 Relations 519

8.1 Relations and Their Properties 519

8.2 n-ary Relations and Their Applications 530

8.3 Representing Relations 537

8.4 Closures of Relations 544

8.5 Equivalence Relations 555

8.6 Partial Orderings 566

End-of-Chapter Material 581

9 Graphs 589

9.1 Graphs and Graph Models 589

9.2 Graph Terminology and Special Types of Graphs 597

9.3 Representing Graphs and Graph Isomorphism 611

9.4 Connectivity 621

9.5 Euler and Hamilton Paths 633

9.6 Shortest-Path Problems 647

9.7 Planar Graphs 657

9.8 Graph Coloring 666

End-of-Chapter Material 675

10 Trees 683

10.1 Introduction to Trees 683

10.2 Applications of Trees 695

10.3 Tree Traversal 710

10.4 Spanning Trees 724

10.5 Minimum Spanning Trees 737

End-of-Chapter Material 743

11 Boolean Algebra 749

11.1 Boolean Functions 749

11.2 Representing Boolean Functions 757

11.3 Logic Gates 760

11.4 Minimization of Circuits 766

End-of-Chapter Material 781

12 Modeling Computation 785

12.1 Languages and Grammars 785

12.2 Finite-State Machines with Output 796

12.3 Finite-State Machines with No Output 804

12.4 Language Recognition 817

12.5 Turing Machines 827

End-of-Chapter Material 838

Appendixes 1

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

A-2 Exponential and Logarithmic Functions 7

A-3 Pseudocode 10

Suggested Readings 1

Answers to Odd-Numbered Exercises ？ 1

Index of Biographies 1

Index 2