Math 55 a Honors Abstract Algebra

Math 55a Honors Abstract Algebra Algebra Fall 2015 Place: Science Center 222 Time: Tuesdays, Tuesdays, Thursdays 2:30 p.m. - 4 p.m. INSTRUCTOR: Proessor !" !"#$Tong #$Tong S%" (e-mail: s%"&#ath'har(ar)'e)" ) O%ce Ho"rs: T"es)a*s+ Th"rs)a*s+ 11 a'#' $ 12:,0 -'#'+ Sc%ence Center 511 COURS. ASSISTANTS:

Cal(%n /eng e$#a%l: /eng  e$#a%l: cal(%n)eng&college'har(ar)'e)" Sect%on: Fr%)a* 2 $ , -'#'+ Sc%ence Center ,10 O%ce Ho"rs: S"n)a* , $  -'#'+ Mathe#at%cs /e-art#ent /e-art#ent 3o"nge 4%ra# S"n)ar e$#a%l: (%ra#s"n)ar&college'har(ar)'e)" Sect%on: Th"rs)a*  $ 5 -'#'+ Sc%ence Center 221 O%ce Ho"rs: Ho"rs: Sat"r)a* , $  -'#'+ 3e(erett 3e(erett /%n%ng Hall S*llab"s: Th%s %s the %rst ter# o Math 55 6h%ch %s a one$*ear co"rse' Tho"gh the co"rse t%tle o Math 55a %s 7Honors Abstract Algebra7 an) that o Math 55b %s 7Honors Real an) Co#-le8 Anal*s%s7+ the )%(%s%on o the to-%cs bet6een Math 55a an) Math 55b %s not that str%ct' There 6%ll be #ater%al %n both algebra an) anal*s%s %n both Math 55a an) Math 55b' No te8tboos 6%ll be "se) or Math 55a 55a an) Math 55b' Instea)+ lect"re notes 6%ll be -oste) on th%s co"rse 6ebs%te' INTRO/UCION TO TH. COURS. FINA3 9RA/. COMPUTATION COMPUTATION AN/ TOPICS P3ANN./ TO . CO4.R./ IN TH. COURS. 3.CTUR. NOT.S: Peano;s F%(e A8%o#s Part 1 HOM. > %le % le 3aTe> FI3. AN/ FI3.  AN/ P/F FI3. OF FI3. OF T.MP3AT. FOR Te> ing  HOM.
Please e$#a%l *o"r ho#e6or to Cal(%n /eng e$#a%l: cal(%n)eng&college'har(ar)'e)" an) 4%ra# S"n)ar e$#a%l: (%ra#s"n)ar&college'har(ar)'e)" 3.CTUR. NOT.S: F"n)a#ental Theore# o Algebra ro# Mean 4al"e Pro-ert* o  Rat%onal F"nct%on O"ts%)e the ?ero$Set o Its /eno#%nator  3.CTUR. NOT.S: Peano;s F%(e A8%o#s Co#-lete HOM. > %le % le 3.CTUR. NOT.S: Fro# Sol(%ng C"b%c an) "art%c .B"at%ons to Intro)"ct%on o 9ro"-s Part 1

HOM. %le Or%g%nal Pa-er o ose-h 3o"%s 3agrange o 1DD0 on the #etho) o -art%al s*##etr* to sol(e -ol*no#%al eB"at%ons ' 3%near transor#at%ons o three (ar%ables on -'E an) o"r (ar%ables on -'@ o the -oste) lect"re notes Fro# Sol(%ng C"b%c an) "art%c .B"at%ons to the Intro)"ct%on o 9ro"-s;; are o"n) on -'221 an) -'2EG res-ect%(el* o the 1DD0 -a-er o 3agrange' 3.CTUR. NOT.S: Fro# Sol(%ng C"b%c an) "art%c .B"at%ons to Intro)"ct%on o 9ro"-s Co#-lete HOM. %le 3.CTUR. NOT.S: Re(%e6 o as%c Matr%8 Theor* HOM. %le 3.CTUR. NOT.S: Tensor Pro)"ct an) .8ter%or Pro)"ct Ater Re(%e6 o as%c 4ector S-ace Theor* Part 1 HOM. %le 3.CTUR. NOT.S: Tensor Pro)"ct an) .8ter%or Pro)"ct Ater Re(%e6 o as%c 4ector S-ace Theor* Parts 1 an) 2 HOM. %le HOM. %le 3.CTUR. NOT.S: Tensor Pro)"ct an) .8ter%or Pro)"ct Ater Re(%e6 o as%c 4ector S-ace Theor* Parts 1+ 2+ an) , HOM. %le 3.CTUR. NOT.S: Matr%8 Nor#al For# b* Techn%B"e o .le#entar* Ro6 an) Col"#n O-erat%ons o(er a R%ng Part 1 HOM. %le 3.CTUR. NOT.S: Matr%8 Nor#al For# b* Techn%B"e o .le#entar* Ro6 an) Col"#n O-erat%ons o(er a R%ng Parts 1 an) 2 3.CTUR. NOT.S: Matr%8 Nor#al For# b* Techn%B"e o .le#entar* Ro6 an) Col"#n O-erat%ons o(er a R%ng Parts 1+ 2+ an) , HOM. %le 3.CTUR. NOT.S: Matr%8 Nor#al For# b* Techn%B"e o .le#entar* Ro6 an) Col"#n O-erat%ons o(er a R%ng Parts 1+ 2+ ,+ an) 

In$Class M%)$Ter# Test on No(e#ber ,+ 2015 T"es)a* 3.CTUR. NOT.S: 9alo%s Theor* Part 1 HOM. %le HOM. %le 3.CTUR. NOT.S: 9alo%s Theor* Parts 1 an) 2 3.CTUR. NOT.S: 9alo%s Theor* Parts 1+ 2+ an) , HOM. %le 3.CTUR. NOT.S: 9alo%s Theor* Parts 1+ 2+ ,+ an)  HOM. %le 3.CTUR. NOT.S: 9alo%s Theor* Parts 1+ 2+ ,+ + an) 5 HOM. %le SO3UTIONS OF PRO3.MS IN MI/$T.RM T.ST OF NO4.RM.R ,+ 2015 3.CTUR. NOT.S: Constr"ct%on o Reg"lar Pol*gon o 1D S%)es b* Stra%ght .)ge an) Co#-ass HOM. %le 9a"ss;s Or%g%nal Proo o the Constr"ct%b%l%t* o the Reg"lar Pol*gon o 1D S%)es b* Stra%ght .)ge an) Co#-ass 9%(en %n h%s oo Disquisitiones Arithmeticae 3.CTUR. NOT.S: 3eschet /eo#-os%t%on HOM. %le HOM. %le 3.CTUR. NOT.S: Co#-os%t%on o S-ace Rotat%ons+ "atern%ons an) S-ec%al Un%tar* 9ro"- o /egree T6o Part 1 Onl* HOM. %le HOM. %le HOM. %le 3.CTUR. NOT.S: Sch"r;s 3e##a+ Re-resentat%on o F%n%te 9ro"-s an) !o"ng /%agra#s Co#-lete

TA=.$HOM. FINA3: )"e 11:5G -'#' /ece#ber 10+ 2015 3aTe> %le