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1、SolvingMathematicalProblemsThispageintentionallyleftblankSolvingMathematicalProblemsAPersonalPerspectiveTerenceTaoDepartmentofMathematics,UCLA,LosAngeles,CA9009513GreatClarendonStreet,OxfordOX26DPOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversity’sobjectiveofexcel
2、lenceinresearch,scholarship,andeducationbypublishingworldwideinOxfordNewYorkAucklandCapeTownDaresSalaamHongKongKarachiKualaLumpurMadridMelbourneMexicoCityNairobiNewDelhiShanghaiTaipeiTorontoWithofficesinArgentinaAustriaBrazilChileCzechRepublicFranceGreeceGuatemalaHungaryItalyJapanPolandPortugalS
3、ingaporeSouthKoreaSwitzerlandThailandTurkeyUkraineVietnamOxfordisaregisteredtrademarkofOxfordUniversityPressintheUKandincertainothercountriesPublishedintheUnitedStatesbyOxfordUniversityPressInc.,NewYork©TerenceTao,2006ThemoralrightsoftheauthorhavebeenassertedDatabaserightOxfordUniversityPress(m
4、aker)Firstpublished2006Allrightsreserved.Nopartofthispublicationmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,withoutthepriorpermissioninwritingofOxfordUniversityPress,orasexpresslypermittedbylaw,orundertermsagreedwiththeappropriatereprographicsrightsorganization.
5、EnquiriesconcerningreproductionoutsidethescopeoftheaboveshouldbesenttotheRightsDepartment,OxfordUniversityPress,attheaddressaboveYoumustnotcirculatethisbookinanyotherbindingorcoverandyoumustimposethesameconditiononanyacquirerBritishLibraryCataloguinginPublicationDataDataavailableLibraryofCongre
6、ssCataloginginPublicationDataDataavailableTypesetbyNewgenImagingSystems(P)Ltd.,Chennai,IndiaPrintedinGreatBritainonacid-freepaperbyBiddlesLtd.,King’sLynn,NorfolkISBN0–19–920561–2978–0–19–920561–5ISBN0–19–920560–4978–0–19–920560–8(Pbk.)10987654321Dedicatedtoallmymentors,whotaughtmethemeaning(and
7、joy)ofmathematics.ThispageintentionallyleftblankContentsPrefacetothefirsteditionviiiPrefacetothesecondeditionxi1Strategiesinproblemsolving12Examplesinnumbertheory93Examplesinalgebraandanalysis354Euclideangeometry495Analyticgeometry
