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1、CONCRETEMATHEMATICSDedicatedtoLeonhardEuler(1707-l783)CONCRETEMATHEMATICSDedicatedtoLeonhardEuler(1707-l783)CONCRETEMATHEMATICSRonaldL.GrahamAT&TBellLaboratoriesDonaldE.KnuthStanfordUniversityOrenPatashnikStanfordUniversityAADDISON-WESLEYPUBLISHINGCOMPANYReading,MassachusettsMenloPark,
2、CaliforniaNewYorkDonMills,OntarioWokingham,EnglandAmsterdamBonnSydneySingaporeTokyoMadridSanJuanLibraryofCongressCataloging-in-PublicationDataGraham,RonaldLewis,1935-Concretemathematics:afoundationforcomputerscience/Ron-aldL.Graham,DonaldE.Knuth,OrenPatashnik.xiii,625p.24cm.Bibliograph
3、y:p.578Includesindex.ISBNo-201-14236-81.Mathematics--1961-2.Electronicdataprocessing--Mathematics.I.Knuth,DonaldErvin,1938-.II.Patashnik,Oren,1954-.III.Title.QA39.2.C7331988510--dc1988-3779CIPSixthprinting,withcorrections,October1990Copyright@1989byAddison-WesleyPublishingCompanyAllrig
4、htsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted,inanyformorbyanymeans,electronic,mechani-cal,photocopying,recording,orotherwise,withoutthepriorwrittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.PublishedsimultaneouslyinCanada.FGHI
5、JK-HA-943210Preface“Aodience,level,THISBOOKISBASEDonacourseofthesamenamethathasbeentaughtandtreatment-annuallyatStanfordUniversitysince1970.Aboutfiftystudentshavetakenitadescriptionofeachyear-juniorsandseniors,butmostlygraduatestudents-andalumnisuchmattersiswhatprefacesareoftheseclasse
6、shavebeguntospawnsimilarcourseselsewhere.Thusthetimesupposedtobeseemsripetopresentthematerialtoawideraudience(includingsophomores).about.”ItwasadarkandstormydecadewhenConcreteMathematicswasborn.-P.R.Halmos11421Long-heldvalueswereconstantlybeingquestionedduringthoseturbulentyears;colleg
7、ecampuseswerehotbedsofcontroversy.Thecollegecurriculumitselfwaschallenged,andmathematicsdidnotescapescrutiny.JohnHam-mersleyhadjustwrittenathought-provokingarticle“Ontheenfeeblementofmathematicalskillsby‘ModernMathematics’andbysimilarsoftintellectualtrashinschoolsanduniversities”[145
