Transcription of Math 422/501: Groups and Fields Fall Term, 2009
1 Math422/501:GroupsandFieldsFallTerm,2009 LiorSilb (Septemb er13,2009) ~lior/teaching/0910/501_F09/ 2010/Winter_Term1/MATH501 ContactmeatMAT229B 604-827-3031 ceHoursByapp o okVarious seebelowCoursePrerequisitesMATH322Ab outthecourseThiscoursewillcovertwobasicc omp onentsofabstractalgebra: Grouptheory FieldsandGaloisTheoryTheirinitialdevelop ment(mostsigni cantly,byGalois)datetotheearly19thcentur yandlieatthero otsofmo , eldsandtheirextensions,esp (negatively)theage-oldproblemsoftrisecti ngtheangle,duplicatingthecub e,andsolvingp o oks thesuggestionsherearenotmeanttob ,anytextb o oktitled Algebra , AbstractAlgebra [1,3,4,5].
2 Similarly,anytextb o oktitled GroupTheory suchas[7,8]or GaloisTheory suchas[6,9]willb esu 'stextb o ok[2]istheo cial optional b o okforthecourse; Seeingsomefoundationsofabstractalgebra. Practicingwitheverydayto olsofthetrade. Applyingcombinatorialandalgebraicmachine ry(Sylowtheorems;theGaloiscorresp ondence).1 Whatyoucanexp ectfromme Tocomepreparedforclass:knowingwhatwewant toachieve,andhowwewillachieveit. Resp onsestoyourquestionsandconcerns:continuo uslyinclassandduringmyo cehours,withinreasonabletimebye-mailouts ideclass.
3 'sexp ectedfromyou Comepreparedtoclass,havingreadrelevantma terialanddoneproblemsets. Activelyparticipateinthecourse:readahead ofclass,thinkab outthematerial,andaskquestions. cialPoliciesLearning Mylectureswillassumethatyouhavereadsomem aterialb ecomefamiliarwiththevocabularyandnotatio ns,aswellastheideasb ehindpro ofs,whileuseful,isnotthep ove,anytextwillserveforthis. Assignedproblemsmayb ebasedonprosp ectivereadingmaterial, Markswillb emostlybasedonthecorrectness(rigor)ofyou rpro ofs, edwillreceivelittlecredit,ifany.
4 Therewillb etwelveweeklyproblemsets,tob ep eforecalculatingthehomeworkgrade. Lateassignmentswillnotb (apro ofoftheemergencyandadvancenoti cationifp ossiblewillb erequired)alateproblemsetwillb eregistered(thatis,willnotb escoredazero)ifyou nishitandhanditinaftertheemergencyhaspas sed. ,eachofyoumustwriteyoursolutionsindep (andshould)shareyourideasbutyoumaynotsha reyourwrittenwork. Itisp ossiblethatonlycertainproblemsfromaprobl emsetwillb ep ostedinanycase. Therewillb eamidtermexaminclassonWednesday,Octob er7th,aswellasa nalexamduringtheusualexamp erio d.
5 Ifyouneedsp ecialaccommo dationswhentakingwrittenexams,pleasecont acttheO Ifthemidterm(or nal)examcon ictswithareligiousobservance, The nalgradewillb ecalculatedasfollows:Problemsets:30%Midt erm:20%Finalexam:50%References[1] ,Englewo o dCli s,NJ,1991.[2] ,NewYork, ,1984.[3] ,Hob oken,NJ,thirdedition,2004.[4] ,NewYork,secondedition,1985.[5] , ,NewYork,thirdedition,2002.[6] [7] [8] , ,NewYork,fourthedition,1995.[9] ,Bo caRaton,FL,thirdedition, ;changeswillb eannouncedinclassandp duction; 16/9 Groupactions;theclassformula; 23/9 CauchyandSylowTheorems;classi 30/9 Nilp 7/10 Midterm612/10 14/10 Fieldsand 21 28/10 Normalextensions;splitting elds; 4/11 Fieldemb 11 18 2 2/12 Topictob
