離散數(shù)學(xué)

內(nèi)容概要

本書凝聚了作者多年的研究成果和實(shí)踐經(jīng)驗(yàn)，是一本優(yōu)秀的離散數(shù)學(xué)入門教材。本書充分考慮到初學(xué)者的需要，內(nèi)容、例題、習(xí)題都經(jīng)過精心的挑選和組織，講解細(xì)致，循序漸進(jìn)，實(shí)例貼近日常生活或計(jì)算機(jī)應(yīng)用。本書注重算法，且算法描述獨(dú)立于某種具體的編程語言。教師可根據(jù)學(xué)生的層次和興趣來靈活拓展和組織講解內(nèi)容。    本書可作為計(jì)算機(jī)專業(yè)或其他相關(guān)專業(yè)的離散數(shù)學(xué)教材或教學(xué)參考書，也可作為自學(xué)者的參考用書。

作者簡(jiǎn)介

作者：(美)多西

書籍目錄

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

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