Instructor:
Swastik Kopparty (swastik.kopparty@gmail.com)
Class
Time and Place: Mondays and Thursdays 12:00noon – 1:20pm, in ARC 105.
Office
Hours: Monday 3pm-4pm (Hill 432)
Textbook:
Algebra by Artin
TA:
Johannes Flake (jmf399@math.rutgers.edu)
TA
Office Hours: Wednesdays 10:20 am-11:40 am (Hill 624)
Problem
Sessions: Wednesdays 12 noon – 1:20 pm (Hill 425)
Homework
·
Homework
1, due September 21. the relevant pages from Artin Chapter 2
·
Homework
2, due October 2, the relevant pages
from Artin Chapter 2
·
Homework
3, due October 19, the relevant pages
from Artin Chapter 5
·
Homework
4, due November 16, the relevant pages
from Artin Chapter 6
·
Homework
5, due December 4, the relevant pages
from Artin Chapter 6
Lecture Schedule
·
September 7: sets
with operations, groups
·
September 11:
isomorphism, subgroups
·
September 14:
homomorphisms, cosets
·
September 18:
Lagrange’s theorem
·
September 21:
products
·
September 25:
quotient groups
·
September 28: first
isomorphism theorem
·
October 2: affine
group, rigid motions
·
October 5: finite
groups of rigid motions
·
October 9:
dihedral group
·
October 12: group
actions
·
October 16: more
group actions
·
October 19:
Fermat’s little theorem: several proofs
·
October 23: MIDTERM I
·
October 26: first
Sylow theorem
·
October 30: second
and third Sylow theorems
·
November 2:
applications of Sylow theorems
·
November 6:
semidirect products
·
November 9: free
groups
·
November 13:
classification of finite abelian groups
·
November 16:
commutators etc.
·
November 20: fun
with the symmetric group
·
TUESDAY November 21: (THURSDAY
SCHEDULE):
·
November 27: more
fun with the symmetric group
·
November 30: MIDTERM II
·
December 4:
solvable groups, nonsolvability of S5
·
December 7: representations,
characters
·
December 11:
Fourier analysis on abelian groups