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1、TimothyGowersMATHEMATleSAVeryShortIntroductionOXFORDUNIVERSITYPRESSOXFORDUNIVERSITYPRESSGreatClarendonStreet,Oxfordox26npOxfordUniversityPressisadepartmentoftheUniversityofOxford.ItfurtherstheUniversity'sobjectiveofe_lIenceinresearch,scholarship,andeducatio
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3、registeredtrademarkofOxfordUniversityPressintheUKandincertainothercountrîesPublishedintheUnitedStatesbyOxfordUniversityPressInc.,NewYork©TimothyGowers2002ThemoralrightsoftheauthorhavebeenassertedDatabaserightOxfordUniversityPress(makerlFirstpublishedasaVery
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6、quirerBritishLibraryCataloguinginPublicationDataDataavailableLibraryofCongressCataloginginPublicationDataDataavaiJableISBN978-0-19-285361-514161820191715'IYPesetbyRefineCatchLld,Bungay,SuffolkPrintedinGreatBritainbyAsbfordColourPressLld,Gosport,HampshireCon
7、tentsPrefaceixListofdiagramsxiii1Models12Numbersandabstraction173Proofs354Limitsandinfinity565Dimension706Geometry867Estimatesandapproximations1128Sornefrequentlyaskedquestions126Furtherreading139Index141PrefaceEarlyinthe20thcentury,thegreatmathematicianDav
8、idHilbertnoticedthatanumberofimportantmathematicaJargumentswerestructurallysimilar.Infact,herealizedthatatanappropriatelevelofgeneralitytheycouldberegardedasthesame.Thisobservation,andotherslikeit,gave
