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1、ATransitiontoAdvancedMathematicsThispageintentionallyleftblankATransitiontoAdvancedMathematicsASurveyCourseWilliamJohnstonAlexM.McAllister320093OxfordUniversityPress,Inc.,publishesworksthatfurtherOxfordUniversity’sobjectiveofexcellenceinresearch,scholarship,andedu
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3、landThailandTurkeyUkraineVietnamCopyright©2009byOxfordUniversityPress,Inc.PublishedbyOxfordUniversityPress,Inc.198MadisonAvenue,NewYork,NewYork10016www.oup.comOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublicationmaybereproduc
4、ed,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofOxfordUniversityPress.LibraryofCongressCataloging-in-PublicationDataJohnston,William,1960–Atransitiontoadvancedmathe
5、matics:asurveycourse/WilliamJohnston,AlexM.McAllister.p.cm.Includesbibliographicalreferencesandindex.ISBN978-0-19-531076-41.Mathematics—Textbooks.I.McAllister,AlexM.II.Title.QA37.3.J652009510—dc222009009644987654321PrintedintheUnitedStatesofAmericaonacid-freepaper
6、ForourteachersandourstudentsThispageintentionallyleftblankPrefaceATransitiontoAdvancedMathematics:ASurveyCoursepromotesthegoalsofa“transition”courseinmathematics,helpingtoleadstudentsfromcoursesinthecalculussequencetotheoreticalupper-levelmathematicscourses.Thetex
7、tsimultaneouslypromotesthegoalsofa“survey”course,describingtheintriguingquestionsandinsightsfundamentaltomanydiverseareasofmathematics.Itsonlyprerequisiteissinglevariablecalculus,andtherearemanychapters,suchaschapters1,2,3,and6,thatdonotevenrequirecalculus.Ahallma
8、rkofthebookisitsflexibility—aninstructormaychoosetousethetextinavarietyofways.Thestandardadoptionwouldbeforatransitioncourse,butthistextcouldalsobeusedin
