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1、HowToSolveItANewAspectofMathematicalMgthoa!G.POLYAStanfordU,niversitySECONDEDITIONPrincetonUniversityPressPrinceton,NewJerseyCupyrightigggbyPrincetonUniversityPressCopyright@renewed1973byPrincetonUniversityPressFromthePrefacetotheFirstPrintingSecondE
2、ditionCopyright@I1957byG.PolyaAllRightsReservedAgreatdiscoverysolvesagreatproblembutthereisagrainofdiscoveryinthesolutionofanyproblem.YourL.C.Card:79-I60544problemmaybemodest;butifitchallengesyourcuria-ISBN0-69I-02356-1,(paperbackedn.)jtyandbringsint
3、oplayyourinventivefaculties,andifISBN0-69I-08097-6(hardcoveredn.)yousolveitbyyourownmeans,youmayexperiencethetensionandenjoythetriumphofdiscovery.Suchexperi-encesatasusceptibleagemaycreateatasteformentalFirstPrincetonPaperbackPrinting,197Iworkandleav
4、etheirimprintonmindandcharacterforalifetime.-SecondPrinting,1973Thus,ateacherofmathematicshasagreatcpportu-nity.Ifhefillshisallottedtimewithdrillinghisstudentsinroutineoperationshekillstheirinterest,hamperstheirintel1ectualdevelopment,andmisuseshisap
5、por-tunity.ButifhechallengesthecuriosityofhisstudentsThisbookissoldsubjecttotheconditionthatbysettingthemproblemsproportionatetotheirknowl-itshallnot,bywayoftrade,belent,resold,edge,andhelpsthemtosolvetheirproblemswithstimu-hiredout,orotherwisedispos
6、edofwitlloutlatingquestions,hemaygivethematastefor,andsomethepublisher'sconsent,inanyformofbindmeansof,independentthinking.ingorcoverotherthanthatinwhichitisAlsoastudentwhosecollegecurriculumindudessomepublished,mathematicshasasingularopportunity.Thi
7、sopportu-nityislost,ofcourse,ifheregardsmathematicsasasubjectinwhichhehastoearnsomdsomuchaeditandwhichheshouIdforgetafterthefinalexaminationasquicklyaspossible.TheopportunitymaybelostevenPrintedintheUnitedStatesofAmericaifthestudenthassomenaturaltale
8、ntfoxmathematicsbyprincetonUniversitypress,princeton,NewJersevbemusehe,aseverybodyelse,mustdiscoverhistalentsandtastes;hecannotknowthathelikesraspberrypieifhehasnevertastedraspberrypie.Hemaymanagetofindout,however,thatamathematicsproblemmaybeasmuchfu
