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:CrankingOutClassicsAnyeditorinvolvedwithpublishinginmathematicsforanylengthoftimeisfamiliarwiththephenomena—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.
