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离散数学 第5版PDF|Epub|txt|kindle电子书版本网盘下载
- （美）多西（Dossey，J.A.）等著 著
- 出版社： 北京：机械工业出版社
- ISBN：7111201671
- 出版时间：2007
- 标注页数：665页
- 文件大小：96MB
- 文件页数：686页
- 主题词：离散数学
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图书目录
1 AN INTRODUCTION TO COMBINATORIAL PROBLEMS AND TECHNIQUES1
1.1 The Time to Complete a Project2
1.2 A Matching Problem10
1.3 A Knapsack Problem16
1.4 Algorithms and Their Efficiency23
Historical Notes35
Supplementary Exercises37
Computer Projects39
Suggested Readings40
2 SETS,RELATIONS,AND FUNCTIONS41
2.1 Set Operations41
2.2 Equivalence Relations47
2.3 Partial Ordering Relations54
2.4 Functions65
2.5 Mathematical Induction76
2.6 Applications84
Historical Notes93
Supplementary Exercises95
Computer Projects98
Suggested Readings98
3 CODING THEORY99
3.1 Congruence100
3.2 The Euclidean Algorithm106
3.3 The RSA Method113
3.4 Error-Detecting and Error-Correcting Codes122
3.5 Matrix Codes132
3.6 Matrix Codes that Correct All Single-Digit Errors140
Historical Notes147
Supplementary Exercises149
Computer Projects152
Suggested Readings153
4 GRAPHS154
4.1 Graphs and Their Representations154
4.2 Paths and Circuits164
4.3 Shortest Paths and Distance181
4.4 Coloring a Graph193
4.5 Directed Graphs and Multigraphs202
Historical Notes219
Supplementary Exercises220
Computer Projects226
Suggested Readings227
5 TREES228
5.1 Properties of Trees228
5.2 Spanning Trees238
5.3 Depth-First Search253
5.4 Rooted Trees266
5.5 Binary Trees and Traversals274
5.6 Optimal Binary Trees and Binary Search Trees287
Historical Notes306
Supplementary Exercises308
Computer Projects311
Suggested Readings312
6 MATCHING313
6.1 Systems of Distinct Representatives313
6.2 Matchings in Graphs319
6.3 A Matching Algorithm327
6.4 Applications of the Algorithm337
6.5 The Hungarian Method346
Historical Notes354
Supplementary Exercises355
Computer Projects357
Suggested Readings357
7 NETWORK FLOWS358
7.1 Flows and Cuts358
7.2 A Flow Augmentation Algorithm369
7.3 The Max-Flow Min-CutTheorem382
7.4 Flows and Matchings389
Historical Notes397
Supplementary Exercises397
Computer Projects400
Suggested Readings401
8 COUNTING TECHNIQUES402
8.1 Pascal's Triangle and the Binomial Theorem402
8.2 Three Fundamental Principles406
8.3 Permutations and Combinations416
8.4 Arrangements and Selections with Repetitions421
8.5 Probability428
8.6 The Principle of Inclusion-Exclusion434
8.7 Generating Permutations and r-Combinations445
Historical Notes452
Supplementary Exercises453
Computer Projects456
Suggested Readings457
9 RECURRENCE RELATIONS AND GENERATING FUNCTIONS458
9.1 Recurrence Relations458
9.2 The Method of Iteration470
9.3 Linear Difference Equations with Constant Coefficients482
9.4 Analyzing the Efficiency of Algorithms with Recurrence Relations494
9.5 Counting with Generating Functions506
9.6 The Algebra of Generating Functions513
Historical Notes523
Supplementary Exercises524
Computer Projects527
Suggested Readings528
10 COMBINATORIAL CIRCUITS AND FINITE STATE MACHINES529
10.1 Logical Gates529
10.2 Creating Combinatorial Circuits538
10.3 Karnaugh Maps546
10.4 Finite State Machines560
Historical Notes569
Supplementary Exercises570
Computer Projects573
Suggested Readings573
A AN INTRODUCTION TO LOGICAND PROOF574
A.1 Statements and Connectives574
A.2 Logical Equivalence583
A.3 Methods of Proof587
Historical Notes593
Supplementary Exercises594
Suggested Readings596
B MATRICES597
Historical Notes604
C THE ALGORITHMS IN THIS BOOK607
BIBLIOGRAPHY613
ANSWERSTO ODD-NUMBERED EXERCISES618
PHOTO CREDITS658
INDEX659