Mathematical Structures for Computer Science, 6/e (Hardcover)

Judith L. Gersting

  • 出版商: W.H. Freeman and Com
  • 出版日期: 2006-07-07
  • 售價: $1,140
  • 語言: 英文
  • 頁數: 784
  • 裝訂: Hardcover
  • ISBN: 071676864X
  • ISBN-13: 9780716768647
  • 相關分類: Computer-Science
  • 已絕版
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<內容簡介>

Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of Mathematical Structures for Computer Science covers all the topics in the CC2001 suggested for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes:
1 . Importance of logical thinking
2 . Power of mathematical notation
3 . Usefulness of abstractions

<章節目錄>

CONTENTS:
      Preface
    Note to the Student
   
  1. Formal Logic
    1.1 Statements, Symbolic Representation, and Tautologies
    1.2 Propositional Logic
    1.3 Quantifiers, Predicates, and Validity
    1.4 Predicate Logic
    1.5 Logic Programming
    1.6 Proof of Correctness
   
  2. Proofs, Recursion, and Analysis of Algorithms
    2.1 Proof Techniques
    2.2 Induction
    2.3 More on Proof of Correctness
    2.4 Recursive Definitions
    2.5 Recurrence Relations
    2.6 Analysis of Algorithms
   
  3. Sets, Combinatorics, Probability, and Number Theory
    3.1 Sets
    3.2 Counting
    3.3 Principle of Inclusion and Exclusion; Pigeonhole Principle
    3.4 Permutations and Combinations
    3.5 Probability
    3.6 Binomial Theorem
    3.7 Number Theory
   
  4. Relations, Functions, and Matrices
    4.1 Relations
    4.2 Topological Sorting
    4.3 Relations and Databases
    4.4 Functions
    4.5 The Mighty Mod Function
    4.6 Matrices
   
  5. Graphs and Trees
    5.1 Graphs and their Representations
    5.2 Trees and their Representations
    5.3 Decision Trees
    5.4 Huffman Codes
   
  6. Graph Algorithms
    6.1 Directed Graphs and Binary Relations; Warshall's Algorithm
    6.2 Euler Path and Hamiltonian Circuit
    6.3 Shortest Path and Minimal Spanning Tree
    6.4 Traversal Algorithms
    6.5 Articulation Points and Computer Networks
   
  7. Boolean Algebra and Computer Logic
    7.1 Boolean Algebra Structure
    7.2 Logic Networks
    7.3 Minimization
   
  8. Modeling Arithmetic, Computation, and Languages
    8.1 Algebraic Structures
    8.2 Finite-State Machines
    8.3 Turing Machines
    8.4 Formal Languages
   
  Appendixes
    Appendix A Derivation Rules for Propositional and Predicate Logic
    Appendix B Summation Notation
    Appendix C The Logarithm Function
    Answers to Practice Problems
    Answers to Selected Exercises
    Answers to Self-Tests
    Index

 

 

商品描述(中文翻譯)

《計算機科學的數學結構》第六版涵蓋了IEEE/CS(電機電子工程師學會/計算機學會)和ACM(計算機協會)共同進行的計算機科學本科學位的基本內容。這本書涵蓋了CC2001建議的一學期密集離散結構課程的所有主題,以及建議的兩學期離散結構課程的幾乎所有主題。Gersting的書籍通過強調以下主題將原本看似零散的主題聯繫在一起:

1. 邏輯思維的重要性

2. 數學符號的力量

3. 抽象的實用性

《計算機科學的數學結構》第六版的章節目錄如下:

      前言

    給學生的說明

   

  1. 形式邏輯

    1.1 陳述、符號表示和永真式

    1.2 命題邏輯

    1.3 量詞、謂詞和有效性

    1.4 謂詞邏輯

    1.5 邏輯編程

    1.6 正確性證明

   

  2. 證明、遞歸和算法分析

    2.1 證明技巧

    2.2 歸納法

    2.3 更多關於正確性證明的內容

    2.4 遞歸定義

    2.5 遞迴關係

    2.6 算法分析

   

  3. 集合、組合學、概率和數論

    3.1 集合

    3.2 計數

    3.3 包含與排斥原理;鴿巢原理

    3.4 排列組合

    3.5 概率

    3.6 二項定理

    3.7 數論

   

  4. 關係、函數和矩陣

    4.1 關係

    4.2 拓撲排序

    4.3 關係和數據庫

    4.4 函數

    4.5 強大的模運算

    4.6 矩陣

   

  5. 圖和樹

    5.1 圖及其表示

    5.2 樹及其表示

    5.3 決策樹

    5.4 哈夫曼編碼

   

  6. 圖算法

    6.1 有向圖和二元關係;華沙爾算法

    6.2 歐拉路徑和漢密爾頓迴路

    6.3 最短路徑和最小生成樹

    6.4 遍歷算法

    6.5 關節點和計算機網絡

   

  7. 布爾代數和計算機邏輯

    7.1 布爾代數結構

    7.2 邏輯網絡

    7.3 最小化

   

  8. 數學建模、計算和語言

    8.1 代數結構

    8.2 有限狀態機

    8.3 圖靈機

    8.4 形式語言

   

  附錄

    附錄A 命題邏輯和謂詞邏輯的推導規則