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內容簡介

　　本書是作者在多年教授離散數(shù)學所獲得的經(jīng)驗基礎上寫出的，其目的是為學生提供準確而可讀的教材，使離散數(shù)學的概念和技術得以清晰地介紹和演示。向愛懷疑的學生們展示離散數(shù)學的實用性。為計算機科學專業(yè)的學生提供一切必需的數(shù)學基礎。使數(shù)學專業(yè)的學生理解數(shù)學概念的重要性以及這些概念為什么對應用而言是重要的。為教師（指導者）設計一個靈活而全面的教學工具。本教材的內容包括了邏輯、代數(shù)、圖論、組合數(shù)學和計算理論的基礎知識，講解生動而直觀，可作為1至2個學期離散數(shù)學入門課的教材，適用于包括數(shù)學專業(yè)、計算機科學專業(yè)、工程專業(yè)在內的許多專業(yè)的學生。

作者簡介

暫缺《離散數(shù)學及其應用（英文版）》作者簡介

圖書目錄

     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