离散数学

出版时间：2006-11  出版社：机械工业  作者：多西  页数：664  
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内容概要

本书凝聚了作者多年的研究成果和实践经验，是一本优秀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。

作者简介

作者：(美)多西

书籍目录

PREFACETO THE STUDENT1 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 Readings2 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 Readings3 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 Readings4 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 Readings5 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 Readings6 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 Readings8 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 ReadingsA AN INTRODUCTION TO LOGICAND PROOF  A.1 Statements and Connectives  A.2 Logical Equivalence  A.3 Methods of Proof    Historical Notes    Supplementary Exercises    Suggested ReadingsB MATRICES  Historical NotesC THE ALGORITHMS INTHIS BOOKBIBLIOGRAPHY ANSWERS TO ODD-NUMBERED EXERCISESPHOTO CREDITSINDEX

用户评论 (总计2条)

•   一本优秀的离散数学入门教材
•   这本书的内容相对简单，其优点是在一本离散数学书中尽可能地体现算法的思想，这种思想是非常重要的。建议低年级本科生阅读。