Elementary Number Theory, 2nd Edition (Dover Books on Mathematics)

Elementary Number Theory, 2nd Edition (Dover Books on Mathematics)
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作者:
出版社: Dover Publications
2008-09
版次: 1
ISBN: 9780486469317
定价: 127.70
装帧: 平装
开本: 其他
纸张: 其他
页数: 249页
正文语种: 英语
  • Idealforafirstcourseinnumbertheory,thislively,engagingtextrequiresonlyafamiliaritywithelementaryalgebraandthepropertiesofrealnumbers.AuthorUnderwoodDudley,whohaswrittenaseriesofpopularmathematicsbooks,maintainsthatthebestwaytolearnmathematicsisbysolvingproblems.Inkeepingwiththisphilosophy,thetextincludesnearly1,000exercisesandproblems?somecomputationalandsomeclassical,manyoriginal,andsomewithcompletesolutions.
    Theopeningchaptersoffersoundexplanationsofthebasicsofelementarynumbertheoryanddevelopthefundamentalpropertiesofintegersandcongruences.SubsequentchapterspresentproofsofFermat'sandWilson'stheorems,introducenumbertheoreticfunctions,andexplorethequadraticreciprocitytheorem.Threeindependentsectionsfollow,withexaminationsoftherepresentationofnumbers,diophantineequations,andprimes.Thetextconcludeswith260additionalproblems,threehelpfulappendixes,andanswerstoselectedexercisesandproblems. UnderwoodDudleyisProfessorEmeritusofMathematicsatDePauwUniversity.UnderwoodDudley:CrankingOutClassics
    Anyeditorinvolvedwithpublishinginmathematicsforanylengthoftimeisfamiliarwiththephenomena—thereceipt,usuallyviasnailmail,ofgenerallyhandwritten,andgenerallyinterminable,really,reallyinterminable,thesesonsomebizarreandunprovablepoint—theseshoping,tryingagainstallhope,demandinginfact,toprovetheunprovable,torewritesomefundamentalpartofmathematics,ofteninmyexperiencetodemonstrateforonefinaltimethat,forexample,Einsteindidn'tknowwhathewastalkingabout—inshort,theworkofamathematicalcrank!UnderwoodDudley(Woodytoeveryoneinthemathworld),ProfessorEmeritus,DepauwUniversity,providedaninestimableservicetoallmatheditorsintheuniversebydemonstratingthattheyarenotaloneintheirexperience.HisuniqueandwonderfulbookMathematicalCranks(TheMathematicsAssociationofAmerica,1992)isareadablefeast,especiallyforthosewhohavebeenonthereceivingendofmathematicalcrankmail.We'reallinWoody'sdebtforhavingassembledthiscollectionoffailedsquaredcircles,angletrisections,andmuch,muchmore.However,chroniclingthecranks—asenjoyableasitmayhavebeentotherestofus—ishardlyacareer,Woodyhaswrittenmanyotherbooksaswell.Andanyreaderwhowantstocheckoutatotallyuncranky,reader-andstudent-friendly,time-testedbasictextinElementaryNumberTheorycouldhardlydobetterthantolookattheDovereditionofWoody'sbookbythatname,whichstarteditscareerwithFreemanin1969andwhichDoverwaspleasedtoreprintin2008.
  • 内容简介:
    Idealforafirstcourseinnumbertheory,thislively,engagingtextrequiresonlyafamiliaritywithelementaryalgebraandthepropertiesofrealnumbers.AuthorUnderwoodDudley,whohaswrittenaseriesofpopularmathematicsbooks,maintainsthatthebestwaytolearnmathematicsisbysolvingproblems.Inkeepingwiththisphilosophy,thetextincludesnearly1,000exercisesandproblems?somecomputationalandsomeclassical,manyoriginal,andsomewithcompletesolutions.
    Theopeningchaptersoffersoundexplanationsofthebasicsofelementarynumbertheoryanddevelopthefundamentalpropertiesofintegersandcongruences.SubsequentchapterspresentproofsofFermat'sandWilson'stheorems,introducenumbertheoreticfunctions,andexplorethequadraticreciprocitytheorem.Threeindependentsectionsfollow,withexaminationsoftherepresentationofnumbers,diophantineequations,andprimes.Thetextconcludeswith260additionalproblems,threehelpfulappendixes,andanswerstoselectedexercisesandproblems.
  • 作者简介:
    UnderwoodDudleyisProfessorEmeritusofMathematicsatDePauwUniversity.UnderwoodDudley:CrankingOutClassics
    Anyeditorinvolvedwithpublishinginmathematicsforanylengthoftimeisfamiliarwiththephenomena—thereceipt,usuallyviasnailmail,ofgenerallyhandwritten,andgenerallyinterminable,really,reallyinterminable,thesesonsomebizarreandunprovablepoint—theseshoping,tryingagainstallhope,demandinginfact,toprovetheunprovable,torewritesomefundamentalpartofmathematics,ofteninmyexperiencetodemonstrateforonefinaltimethat,forexample,Einsteindidn'tknowwhathewastalkingabout—inshort,theworkofamathematicalcrank!UnderwoodDudley(Woodytoeveryoneinthemathworld),ProfessorEmeritus,DepauwUniversity,providedaninestimableservicetoallmatheditorsintheuniversebydemonstratingthattheyarenotaloneintheirexperience.HisuniqueandwonderfulbookMathematicalCranks(TheMathematicsAssociationofAmerica,1992)isareadablefeast,especiallyforthosewhohavebeenonthereceivingendofmathematicalcrankmail.We'reallinWoody'sdebtforhavingassembledthiscollectionoffailedsquaredcircles,angletrisections,andmuch,muchmore.However,chroniclingthecranks—asenjoyableasitmayhavebeentotherestofus—ishardlyacareer,Woodyhaswrittenmanyotherbooksaswell.Andanyreaderwhowantstocheckoutatotallyuncranky,reader-andstudent-friendly,time-testedbasictextinElementaryNumberTheorycouldhardlydobetterthantolookattheDovereditionofWoody'sbookbythatname,whichstarteditscareerwithFreemanin1969andwhichDoverwaspleasedtoreprintin2008.
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