复旦大学 赵一鸣 离散数学 一

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1、DiscretemathematicsDiscretei.e.nocontinuousSettheory,Combinatorics,Graphs,ModernAlgebra(Abstractalgebra,Algebraicstructures),Logic,classicprobability,numbertheory,AutomataandFormalLanguages,Computabilityanddecidabilityetc.Beforethe18thcentury,Discrete，quantityandspacea

2、stronomy,physicsExample:planetaryorbital,Newton'sLawsinThreeDimensionscontinuousmathematics:calculus,EquationsofMathematicalPhysics,FunctionsofRealVariable,FunctionsofcomplexVariableDiscrete?stagnancyinthethirtiesofthetwentiethcentury,TuringMachinesFiniteDiscreteDataSt

3、ructuresandAlgorithmDesignDatabaseCompilersDesignandAnalysisofAlgorithmsComputerNetworksSoftwareinformationsecurityandcryptographythetheoryofcomputationNewgenerationcomputersSettheory,IntroductoryCombinatorics,Graphs,Algebtaicstructures,Logic.Thisterm:Settheory,Introdu

4、ctoryCombinatorics,Graphs,Algebtaicstructures(Group,Ring，Field).Nextterm:Algebtaicstructures(LatticesandBooleanAlgebras),Logic每周一交作业，作业成绩占总成绩的10%；平时不定期的进行小测验，占总成绩的20%；期中考试成绩占总成绩的20%；期终考试成绩占总成绩的50%1.离散数学及其应用（英文版·第5版）作者：KennethH.Rosen著出版社：机械工业出版社2.组合数学（英文版·第4版）——经典原版书库作者

5、：（美）布鲁迪（Brualdi,R.A.）著出版社：机械工业出版社3,离散数学暨组合数学（英文影印版）DiscreteMathematicswithCombinatoricsJamesA.Anderson,UniversityofSouthCarolina,Spartanburg大学计算机教育国外著名教材系列（影印版）清华大学出版社ⅠIntroductiontoSetTheoryTheobjectsofstudyofSetTheoryaresets.Assetsarefundamentalobjectsthatcanbeusedto

6、defineallotherconceptsinmathematics.GeorgCantor(1845--1918)isaGermanmathematician.Cantor's1874paper,"OnaCharacteristicPropertyofAllRealAlgebraicNumbers",marksthebirthofsettheory.paradoxtwentiethcenturyaxiomaticsettheorynaivesettheoryConceptRelation,function,cardinalnum

7、berparadoxChapter1BasicConceptsofSets1.1SetsandSubsetsWhatareSets?AcollectionofdifferentobjectsiscalledasetS,ATheindividualobjectsinthiscollectionarecalledtheelementsofthesetWewrite“tA”tosaythattisanelementofA,andWewrite“tA”tosaythattisnotanelementofAExample:Thesetof

8、allintegers,Z.Then3Z,-8Z,6.5ZThesesets,eachdenotedusingaboldfaceletter,playanimportantroleindiscretemathematics:N=