discrete mathematics - yale

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1、DiscreteMathematicsLectureNotes,YaleUniversity,Spring1999L.Lov´aszandK.VesztergombiPartsoftheselecturenotesarebasedonL.Lovasz–J.Pelik´an–K.Vesztergombi:Kombinatorika´(Tank¨onyvkiad´o,Budapest,1972);Chapter14isbasedonasectioninL.Lovasz–M.D.Plummer:Matchingtheory´(Elsevier,Amsterdam,1979)12Conte

2、nts1Introduction52Letuscount!72.1Aparty......................................72.2Setsandthelike.................................92.3Thenumberofsubsets..............................122.4Sequences.....................................162.5Permutations...................................173Inductio

3、n213.1Thesumofoddnumbers............................213.2Subsetcountingrevisited............................233.3Countingregions.................................244Countingsubsets274.1Thenumberoforderedsubsets.........................274.2Thenumberofsubsetsofagivensize.....................284.

4、3TheBinomialTheorem.............................294.4Distributingpresents...............................304.5Anagrams.....................................324.6Distributingmoney................................335Pascal’sTriangle355.1IdentitiesinthePascalTriangle.........................355.2Abi

5、rd’seyeviewatthePascalTriangle....................386Fibonaccinumbers456.1Fibonacci’sexercise................................456.2Lotsofidentities.................................466.3AformulafortheFibonaccinumbers......................477Combinatorialprobability517.1Eventsandprobabilities....

6、.........................517.2Independentrepetitionofanexperiment....................527.3TheLawofLargeNumbers...........................538Integers,divisors,andprimes558.1Divisibilityofintegers..............................558.2Primesandtheirhistory.............................568.3Factorizat

7、ionintoprimes............................588.4Onthesetofprimes...............................598.5Fermat’s“Little”Theorem...........................638.6TheEuclideanAlgorithm............................648.7Testingforprimality..........