upuntilrecently,riemanniangeometryandbasictopologywerenotincluded,evenbydepartmentsorfacultiesofmathematics,ascompulsorysubjectsinauniversity-levelmathematicaleducation.thestandardcoursesintheclassicaldifferentialgeometryofcurvesandsurfaceswhichweregiveninstead(andstillaregiveninsomeplaces)havecomegraduallytobeviewedasanachronisms.however,therehasbeenhithertonounanimousagreementastoexactlyhowsuchcoursesshouldbebroughtuptodate,thatistosay,whichpartsofmoderngeometryshouldberegardedasabsolutelyessentialtoamodernmathematicaleducation,andwhatmightbetheappropriatelevelofabstractnessoftheirexposition.
|