离散数学（英文版.第5版）|经典原版书库|美 Lawrence E.Spence Charles Vanden Eynd|机械工业出版社

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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

PREFACE.iii 
TOTHESTUDENTviii 
1ANINTRODUCTIONTOCOMBINATORIALPROBLEMSAND 
TECHNIQUES1 
1.1TheTimetoCompleteaProject 
1.2AMatchingProblem10 
1.3AKnapsackProblem16 
1.4AlgorithmsandTheirEfficiency23 
HistoricalNotes35 
SupplementaryExercises37 
ComputerProjects39 
SuggestedReadings40 
2SETS,RELATIONS,ANDFUNCTIONS41 
2.1SetOperations41 
2.2EquivalenceRelations47 
2.3PartialOrderingRelations54 
2.4Functions65 
2.5MathematicalInduction76 
2.6Applications84 
HistoricalNotes93 
SupplementaryExercises95 
ComputerProjects98 
SuggestedReadings98 
3CODINGTHEORY99 
3.1Congruence100 
3.2TheEuclideanAlgorithm106 
3.3TheRSAMethod113 
3.4Error-DetectingandError-CorrectingCodes122 
3.5MatrixCodes132 
3.6MatrixCodesthatCorrectAllSingle-DigitErrors140 
HistoricalNotes147 
SupplementaryExercises149 
ComputerProjects152 
SuggestedReadings153 
4GRAPHS154 
4.1GraphsandTheirRepresentations154 
4.2PathsandCircuits164 
4.3ShortestPathsandDistance181 
4.4ColoringaGraph193 
4.5DirectedGraphsandMultigraphs202 
HistoricalNotes219 
SupplementaryExercises220 
ComputerProjects226 
SuggestedReadings227 
5TREES228 
5.1PropertiesofTrees228 
5.2SpanningTrees238 
5.3Depth-FirstSearch253 
5.4RootedTrees266 
5.5BinaryTreesandTraversals274 
5.6OptimalBinaryTreesandBinarySearchTrees287 
HistoricalNotes306 
SupplementaryExercises308 
ComputerProjects311 
SuggestedReadings312 
6MATCHING313 
6.1SystemsofDistinctRepresentatives313 
6.2MatchingsinGraphs319 
6.3AMatchingAIgorithm327 
6.4ApplicationsoftheAlgorithm..337 
6.5TheHungarianMethod346 
HistoricalNotes354 
SupplementaryExercises355 
ComputerProjects357 
SuggestedReadings357 
7NETWORKFLOWS358 
7.1FlowsandCuts358 
7.2AFlowAugmentationAlgorithm369 
7.3TheMax-FlowMin-CutTheorem382 
7.4FlowsandMatchings389 
HistoricalNotes397 
SupplementaryExercises397 
ComputerProjects400 
SuggestedReadings401 
8COUNTINGTECHNIQUES402 
8.1Pascal'sTriangleandtheBinomialTheorem402 
8.2ThreeFundamentalPrinciples406 
8.3PermutationsandCombinations416 
8.4ArrangementsandSelectionswithRepetitions421 
8.5Probability428 
8.6ThePrincipleofInclusion-Exclusion434 
8.7GeneratingPermutationsandr-Combinations445 
HistoricalNotes452 
SupplementaryExercises453 
ComputerProjects456 
SuggestedReadings457 
9RECURRENCERELATIONSANDGENERATINGFUNCTIONS458 
9.1RecurrenceRelations458 
9.2TheMethodofIteration470 
9.3LinearDifferenceEquationswithConstantCoefficients482 
9.4AnalyzingtheEfficiencyofAlgorithmswithRecurrence 
Relations494 
9.5CountingwithGeneratingFunctions506 
9.6TheAlgebraofGeneratingFunctions513 
HistoricalNotes523 
SupplementaryExercises524 
ComputerProjects527 
SuggestedReadings528 
10COMBINATORIALCIRCUITSANDFINITESTATEMACHINES529 
10.1LogicalGates529 
10.2CreatingCombinatorialCircuits538 
10.3KarnaughMaps546 
10.4FiniteStateMachines560 
HistoricalNotes569 
SupplementaryExercises570 
ComputerProjects573 
SuggestedReadings573 
AANINTRODUCTIONTOLOGICANDPROOF574 
A.1StatementsandConnectives574 
A.2LogicalEquivalence583 
A.3MethodsofProof587 
HistoricalNotes593 
SupplementaryExercises594 
SuggestedReadings596 
BMATRICES597 
HistoricalNotes604 
CTHEALGORITHMSINTHISBOOK607 
BIBLIOGRAPHY613 
ANSWERSTOODD-NUMBEREDEXERCISES618 
PHOTOCREDITS658 
INDEX...659

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