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1、CONCRETEMATHEMATICSDedicatedtoLeonhardEuler(1707-l783)CONCRETEMATHEMATICSDedicatedtoLeonhardEuler(1707-l783)CONCRETEMATHEMATICSRonaldL.GrahamAT&TBellLaboratoriesDonaldE.KnuthStanfordUniversityOrenPatashnikStanfordUniversityAADDISON-WESLEYPUBLISHINGCOMPANYReadin
2、g,MassachusettsMenloPark,CaliforniaNewYorkDonMills,OntarioWokingham,EnglandAmsterdamBonnSydneySingaporeTokyoMadridSanJuanLibraryofCongressCataloging-in-PublicationDataGraham,RonaldLewis,1935-Concretemathematics:afoundationforcomputerscience/Ron-aldL.Graham,Dona
3、ldE.Knuth,OrenPatashnik.xiii,625p.24cm.Bibliography: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,withc
4、orrections,October1990Copyright@1989byAddison-WesleyPublishingCompanyAllrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystemortransmitted,inanyformorbyanymeans,electronic,mechani-cal,photocopying,recording,orotherwise,withoutthepriorwr
5、ittenpermissionofthepublisher.PrintedintheUnitedStatesofAmerica.PublishedsimultaneouslyinCanada.FGHIJK-HA-943210Preface“Aodience,level,THISBOOKISBASEDonacourseofthesamenamethathasbeentaughtandtreatment-annuallyatStanfordUniversitysince1970.Aboutfiftystudentshav
6、etakenitadescriptionofeachyear-juniorsandseniors,butmostlygraduatestudents-andalumnisuchmattersiswhatprefacesareoftheseclasseshavebeguntospawnsimilarcourseselsewhere.Thusthetimesupposedtobeseemsripetopresentthematerialtoawideraudience(includingsophomores).about
7、.”ItwasadarkandstormydecadewhenConcreteMathematicswasborn.-P.R.Halmos11421Long-heldvalueswereconstantlybeingquestionedduringthoseturbulentyears;collegecampuseswerehotbedsofcontroversy.Thecollegecurriculumitselfwaschallenged,andmathematicsdidnotescapescrutiny.Jo
8、hnHam-mersleyhadjustwrittenathought-provokingarticle“Ontheenfeeblementofmathematicalskillsby‘ModernMathematics’andbysimilarsoftintellectualtrashinschoolsanduniversities”[145
