ThisbookisintendedtocomplementmyElementsofAlgebra,anditissimilarlymotivatedbytheproblemofsolvingpolynomialequations.However,itisindependentofthealgebrabook,andprobablyeasier.InElementsofAlgebrawesoughtsolutionbyradicals,andthisledtotheconceptsoffieldsandgroupsandtheirfusioninthecelebratedtheoryofGalois.Inthepresentbookweseekintegersolutions,andthisleadstotheconceptsofringsandidealswhichmergeintheequallycelebratedtheoryofidealsduetoKummerandDedekind.
Thebookisbasedontwoshortcourses(about20lectureseach)givenatMonashUniversityinrecentyears;oneonelementarynumbertheoryandoneonringtheorywithapplicationstoalgebraicnumbertheory.Thustheamountofmaterialissuitableforaone-semestercourse,withsomevariationpossiblethroughomissionoftheoptionalstarredsections.Aslower~pacedcoursecouldstopattheendofChapter9,atwhichpointmostofthestandardresultshavebeencovered,fromEuclid'stheoremthatthereareinfinitelvmanyprimestoquadraticreciprocity.