Math 594, Winter 2012. Algebra II

 My office is 4859 East Hall, and my office hours are Tuesdays 2-5pm (and also by appointment).
The class meets on Mondays, Wednesdays and Fridays, 2pm-3pm, in room 3096 of East Hall.

The grader for the course is Jeff Meyer.
 
Syllabus in PDF
Exams
Midterm problems in PDF
Midterm solutions in PDF

The final exam is scheduled for Monday, April 16, 6-9pm, 1360 East Hall
Homeworks
Homework 1 (due Friday, January 13, at the beginning of class) in PDF
Suggestions for Homework 1 in PDF
Solutions for Homework 1 in PDF

Homework 2 (due Friday, January 20, at the beginning of class) in PDF
Suggestions for Homework 2 in PDF
Solutions for Homework 2 in PDF

Homework 3 (due Friday, January 27, at the beginning of class) in PDF
Suggestions for Homework 3 in PDF
Solutions for Homework 3 in PDF

Homework 4 (due Friday, February 3, at the beginning of class) in PDF
Suggestions for Homework 4 in PDF
Solutions for Homework 4 in PDF

Homework 5 (due Friday, February 10, at the beginning of class) in PDF
Solutions for Homework 5 in PDF

Homework 6 (due Friday, February 17, at the beginning of class) in PDF
Solutions for Homework 6 in PDF

Homework 7 (due Monday, March 5, at the beginning of class) in PDF
Solutions for Homework 7 in PDF

Homework 8 (due Friday, March 16, at the beginning of class) in PDF

Homework 9 (due Friday, March 23, at the beginning of class) in PDF

Homework 10 (due Friday, March 30, at the beginning of class) in PDF

Homework 11 (due Friday, April 6, at the beginning of class) in PDF

Homework 12  (due Friday, April 13, at the beginning of class) in PDF
Approximate course contents (arranged by week)
  1. Sylow theorems for finite groups (week of January 4 and 6)
     
  2. Finite p-groups, applications of the Sylow theorems (week of January 9)
    Notes for the January 9 lecture in PDF
     
  3. Nilpotent, solvable and simple groups (week of January 18 and 20)
     
  4. Permutation groups (week of January 23)
     
  5. Representations of finite groups; Wedderburn theory (week of January 30)
     
  6. Wrap-up of Wedderburn theory; complex characters of finite groups (week of February 6)
     
  7. Proofs of the main results of character theory for finite groups (week of February 13)
     
  8. Proof of Burnside's p^a q^b theorem; induced representations (week of February 20)
     
  9. Spring break: week of February 27
     
  10. Field extensions (week of March 5)
     
  11. Main theorem of Galois theory (week of March 12)
     
  12. Normal and separable extensions; some applications of Galois theory (week of March 19)
     
  13. Extensions of modules and group cohomology (week of March 26)
     
  14. Applications of group cohomology (week of April 2)
     
  15. Brauer groups of fields; examples (week of April 9)
     
  16. Brauer groups of local fields (April 16)