离散数学(英文版.第5版)

本书凝聚了作者多年的研究成果和实践经验，是一本很好的离散数学入门教材。本书充分考虑到初学者的需要，内容、例题、习题都经过精心的挑选和组织，讲解细致，循序渐进，实例贴近日常生活或计算机应用。本书注重算法，且算法描述独立于某种具体的编程语言。教师可根据学生的层次和兴趣来灵活拓展和组织讲解内容。
    本书可作为计算机专业或其他相关专业的离散数学教材或教学参考书，也可作为自学者的参考用书。

PREFACE
TO THE STUDENT
1 AN INTRODUCTION TO COMBINATORIAL PROBLEMS AND TECHNIQUES
  1.1 TheTime to Complete a Project
  1.2 A Matching Problem
  1.3 A Knapsack Problem
  1.4 Algorithms andTheir Efficiency
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
2 SETS, RELATIONS, AND FUNCTIONS
  2.1 Set Operations
  2.2 Equivalence Relations
  2.3 Partial Ordering Relations
  2.4 Functions
  2.5 Mathematical Induction
  2.6 Applications
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
3 CODING THEORY
  3.1 Congruence
  3.2 The Euclidean Algorithm
  3.3 The RSA Method
  3.4 Error-Detecting and Error-Correcting Codes
  3.5 Matrix Codes
  3.6 Matrix Codes that Correct All Single-Digit Errors
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
4 GRAPHS
  4.1 Graphs andTheir Representations
  4.2 Paths and Circuits
  4.3 Shortest Paths and Distance
  4.4 Coloringa Graph
  4.5 Directed Graphs and Multigraphs
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
5 TREES
  5.1 Properties of Trees
  5.2 Spanning Trees
  5.3 Depth-First Search
  5.4 Rooted Trees
  5.5 Binary Trees and Traversals
  5.6 Optimal Binary Trees and Binary Search Trees
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
6 MATCHING
  6.1 Systems of Distinct Representatives
  6.2 Matchings in Graphs
  6.3 A Matching Algorithm
  6.4 Applications of the Algorithm
  6.5 The Hungarian Method
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
7 NETWORK FLOWS
  7.1 Flows and Cuts
  7.2 A Flow Augmentation Algorithm
  7.3 The Max-Flow Min-CutTheorem
  7.4 Flows and Matchings
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
8 COUNTING TECHNIQUES
  8.1 Pascal's Triangle and the Binomial Theorem
  8.2 Three Fundamental Principles
  8.3 Permutations and Combinations
  8.4 Arrangements and Selections with Repetitions
  8.5 Probability
  8.6 The Principle of Inclusion-Exclusion
  8.7 Generating Permutations and r-Combinations
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
9 RECURRENCE RELATIONS AND GENERATING FUNCTIONS
  9.1 Recurrence Relations
  9.2 The Method of Iteration
  9.3 Linear Difference Equations with Constant Coefficients
  9.4 Analyzing the Efficiency of Algorithms with Recurrence Relations
  9.5 Counting with Generating Functions
  9.6 TheAIgebra of Generating Functions
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
10 COMBINATORIAL CIRCUITS AND FINITE STATE MACHINES
  10.1 Logical Gates
  10.2 Creating Combinatorial Circuits
  10.3 Karnaugh Maps
  10.4 Finite State Machines
    Historical Notes
    Supplementary Exercises
    Computer Projects
    Suggested Readings
A AN INTRODUCTION TO LOGICAND PROOF
  A.1 Statements and Connectives
  A.2 Logical Equivalence
  A.3 Methods of Proof
    Historical Notes
    Supplementary Exercises
    Suggested Readings
B MATRICES
  Historical Notes
C THE ALGORITHMS INTHIS BOOK
BIBLIOGRAPHY
ANSWERS TO ODD-NUMBERED EXERCISES
PHOTO CREDITS
INDEX