離散數(shù)學(xué)（英文版第5版）

PREFACE
TO THE STUDENT  
1 AN INTRODUCTION TO COMBINATORIAL PROBLEMS AND TECHNIQUES 1
1.1The Time to Complete a Project 2
1.2 A Matching Problem 10
1.3 A Knapsack Problem 16
1.4 Algorithms and Their Efficiency 23
    Historical Notes 35
    Supplementary Exercises 37
    Computer Projects 39
    Suggested Readings 40
2  SETS, RELATIONS, AND FUNCTIONS  41
2.1 Set Operations 41
2.2 Equivalence Relations 47
2.3 Partial Ordering Relations 54
2.4 Functions 65
2.5 Mathematical Induction 76
2.6 Applications 84
    Historical Notes 93
    Supplementary Exercises 95
    Computer Projects 98
    Suggested Readings 98
3 CODING THEORY 99
3.1 Congruence 100
3.2 The Euclidean Algorithm 106
3.3 The RSA Method 113
3.4 Error-Detecting and Error-Correcting Codes 122
3.5 Matrix Codes 132
3.6 Matrix Codes that Correct All Single-Digit Errors 140
    Historical Notes 147
    Supplementary Exercises 149
    Computer Projects 152
    Suggested Readings 153
4 GRAPHS 154
4.1 Graphs andTheir Representations 154
4.2 Paths and Circuits 164
4.3 Shortest Paths and Distance 181
4.4 Coloring a Graph 193
4.5 Directed Graphs and Multigraphs 202
    Historical Notes 219
    Supplementary Exercises 220
    Computer Projects 226
    Suggested Readings 227
5 TREES 228
5.1 Properties of Trees 228
5.2 Spanning Trees 238
5.3 Depth-First Search 253
5.4 Rooted Trees 26
5.5 Binary Trees and Traversals 274
5.6 Optimal Binary Trees and Binary Search Trees 287
    Historical Notes 306
    Supplementary Exercises 308
    Computer Projects 311
    Suggested Readings 312
6 MATCHING 313
6.1 Systems of Distinct Representatives 313
6.2 Matchings in Graphs 319
6.3 A MatchingAIgorithm 327
6.4 Applications of the Algorithm .. 337
6.5 The Hungarian Method 346
    Historical Notes 354
    Supplementary Exercises 355
    Computer Projects 357
    Suggested Readings 357
7 NETWORK FLOWS 358
7.1 Flows and  358
7.2 A Flow Augmentation Algorithm 369
7.3 The Max-Flow Min-CutTheorem 382
7.4 Flows and Matchings 389
    Historical Notes 397
    Supplementary Exercises 397
    Computer Projects 400
    Suggested Readings 401
8 COUNTING TECHNIQUES 402
8.1 Pascal's Trianglecand the Binomial Theorem 402
8.2 Three Fundamental Principles 4067
8.3 Permutations and Combinations 416
8.4 Arrangements and Selections with Repetitions 421
8.5 Probability 428
8.6 The Principle of Inclusion-Exclusion 434
8.7 Generating Permutations and r-Combinations 445
    Historical Notes 452
    Supplementary Exercises 453
    Computer Projects 456
    Suggested Readings 457
9 RECURRENCE RELATIONS AND GENERATING FUNCTIONS 458
9.1 Recurrence Relations 458
9.2 The Method of Iteration 470
9.3 Linear Difference Equations with Constant Coefficients 482
9.4 Analyzing the Efficiency of Algorithmscwith Recurrences  
Relations 494
9.5 Counting with Generating Functions 506
9.6 The Algebra of Generating Functions 513
    Historical Notes 523
    Supplementary Exercises 524
    Computer Projects 527
    Suggested Readings 528
10 COMBINATORIAL CIRCUITS AND FINITE STATE MACHINES 529
10.1 Logical Gates 529
10.2 Creating Combinatorial Circuits 538
10.3 Karnaugh Maps 546
10.4 Finite State Machines 560
     Historical Notes 569
     Supplementary Exercises 570
     Computer Projects 573
     Suggested Readings 573
A AN INTRODUCTION TO LOGIC AND PROOF 574
A.1 Statements and Connectives 574
A.2 Logical Equivalence 583
A.3 Methods of Proof 587
    Historical Notes 593
    Supplementary Exercises 594
    Suggested Readings 596
B MATRICES 597
    Historical Notes 604
C THE ALGORITHMS IN THIS BOOK 607
BIBLIOGRAPHY 613
ANSWERS TO ODD-NUMBERED EXERCISES 618
PHOTO CREDITS 658
INDEX  659