离散数学及其应用（英文版）

　　本书是作者在多年教授离散数学所获得的经验基础上写出的，其目的是为学生提供准确而可读的教材，使离散数学的概念和技术得以清晰地介绍和演示。向爱怀疑的学生们展示离散数学的实用性。为计算机科学专业的学生提供一切必需的数学基础。使数学专业的学生理解数学概念的重要性以及这些概念为什么对应用而言是重要的。为教师（指导者）设计一个灵活而全面的教学工具。本教材的内容包括了逻辑、代数、图论、组合数学和计算理论的基础知识，讲解生动而直观，可作为1至2个学期离散数学入门课的教材，适用于包括数学专业、计算机科学专业、工程专业在内的许多专业的学生。

暂缺《离散数学及其应用（英文版）》作者简介

     CONTENTS
   Preface ix
   The Companion Web Site xix
   TotheStudent xxi
   1
   The Foundations: Logic, Sets, and Functions
    1.1Logic
    1.2Propositional Equivalences
    1.3Predicates and Quantifiers
    1.4Sets
    1.5Set Operations
    1.6Functions
    1.7Sequences and Summations
    1.8The Growth of Functions
    Key Tenns and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   2
   The Fundamentals: Algorithms, the Integers, and Matrices
    2.1Algorithms
    2.2ComplexityofAlgorithms
    2.3The Integers and Division
    2.4Integers and Algorithms
    2.5Applications of Number Theory
    2.6Matrices
    Key Terms and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Exploratiuns
    Writing Projects
   3
   Mathematical Reasoning
    3.1MethodsofProof
    3.2Mathematical Induction
    3.3Recursive Definitions
    3.4Recursive Algorithms
    3.5Program Correctness
    Key Tenns and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   4
   Counting
    4.1The Basics of Counting
    4.2The Pigeonhole Principle
    4.3Pennutations and Combinations
    4.4Discrete Probability
    4.5Probability Theory
    4.6Generalized Pennutations and Combinations
    4.7Generating Pennutations and Combinations
    Key Terms and Concepts
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   5
   Advanced Counting Techniques
    5.1Recurrence Relations
    5.2Solving Recurrcnce Relarions
    5.3Divide-and-Conquer Relations
    5.4Generating Functions
    5.5Inclusion-Exclusion
    5.6Applications of Inclusion-Exclusion
    Key Terms and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   6
   Relations
    6.lRelations and Their Properties
    6.2n-ary Relations and Their Applications
    6.3Representing Relations
    6.4ClosurcsofRelations
    6.5Equivalence Relations
    6.6Partial Orderings
    Key Terms and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Prqjects
   7
   Graphs
    7.1Introduction to Graphs
    7.2Graph Tenninology
    7.3Representing Graphs and Graph Isomorphism
    7.4Connectivity
    7.5Euler and Hamilton Paths
    7.6Shortest Path Problems
    7.7Planar Graphs
    7.8Graph Coloring
    Key Terms and Results :
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   8
   Trees
    8.l Introduction to Trees
    8.2 Applications ofTrees
    8.3 Tree Traversal
    8.4 Trees and Sorting
    8.5 Spanning Trees
    8.6 Minimum Spanning Trees
    Key Terms and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   9
   Boolean Algebra
    9.1Boolean Functions
    9.2Representing Boolean Functions
    9.3Logic Gates
    9.4MinimizationofCircuits
    Key Terms and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   10
   Modeling Computation
    10.1Languages and Grammars
    10.2Finite-State Machines with Output
    10.3Finite-State Machines with No Output
    10.4Language Recognition
    10.5Turing Machines
    Key Tenns and Results
    Review Questions
    Supplementary Exercises
    Computer Projects
    Computations and Explorations
    Writing Projects
   Appendixes A-l
    A.1Exponential and Logarithmic Functions
    A.2Pseudocode
   Suggested Readings B-l
   Index of Biographies 1-1
   Index 1-3
   LISTOFSYMBOLS L-l