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1、MathematicsasProblemSolvingSecondEditionAlexanderSoiferMathematicsasProblemSolvingSecondEditionAlexanderSoiferCollegeofLetters,ArtsandSciencesUniversityofColoradoatColoradoSprings1420AustinBluffsParkwayColoradoSprings,CO80918USAasoifer@uccs.eduISBN:978-0-387-74646-3e-ISBN:978-0-387-74647
2、-0DOI:10.1007/978-0-387-74647-0LibraryofCongressControlNumber:2009921736MathematicsSubjectClassification(2000):00-XX,00A05,00A07,00A08,00A35,97A20,05CXX,05C15,05C55,05-XX©AlexanderSoifer2009Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewrittenpermissionofthe
3、publisher(SpringerScience+BusinessMedia,LLC,233SpringStreet,NewYork,NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Useinconnectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilarmethodologynowknownorh
4、ereafterdevelopedisforbidden.Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyarenotidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubjecttoproprietaryrights.CoverdesignedbyMaryBurgessPrintedonacid-freepaperspringer.comToM
5、arkandJuliaSoiferFrontispiecereproducesthefrontcoveroftheoriginaledition.ItwasdesignedbymylaterfatherYuriSoifer,whowasagreatartist.WillRobinson,whoproducedadocumentaryabouthimfortheColoradoSpringsaffiliateofABC,calledhim“anartistoftheheart.”ForhisfirstAmericanone-manshowattheUniversityofCo
6、loradoinJune–July1981,Yurisketchedhisautobiography:Iwasbornin1907inthelittlevillageStrizhevkaintheUkraine.Fromtheageofthree,IwastaughtattheCheder(elementaryschoolbyasyna-gogue),andsincethattimeIhavebeenpainting.Attheageoften,IenteredFeinsteinsJewishHighSchoolinthecityofVinniza.Theartteac
7、her,AbramMarkovichCherkassky,agraduateoftheAcademyofFineArtsatSt.Peters-burg,lookedatmybookofsketchesofprayingJews,andconsequentlytaughtmeforsixyears,untilhisdepartureforKiev.Cherkasskywasmyfirstandmostimportantteacher.Henotonlycritiquedmyworkandexplainedvari-oustechniques
