Math 494, Winter 2013. Honors Algebra II

My office is 4859 East Hall, and my office hours are 3-6pm on Thursdays.
The class meets on Mondays, Wednesdays and Fridays, 2pm-3pm, in room 4088 of East Hall.


Syllabus in PDF

Some notes on Galois theory in PDF


Exams


Midterm: Friday, March 15, 6-8pm (4088 East Hall).

Final exam: TBA.



Homeworks

Homework will usually be assigned each week on Friday, and will be due the following Friday at the start of class.
The homework assignments are an integral part of the learning experience. No late homework will be accepted.

Homework 1 (due Friday, January 18, at the beginning of class) in PDF
Solutions for Homework 1 in PDF
Ho
mework 2 (due Friday, January 25, at the beginning of class) in PDF
Solutions for Homework 2 in PDF
Homework 3 (due Friday, February 1, at the beginning of class) in PDF
Solutions for Homework 3 in PDF
Homework 4 (due Friday, February 8, at the beginning of class) in PDF
Solu
tions for Homework 4 in PDF
Homework 5 (due Friday, February 15, at the beginning of class) in PDF
Solutions for Homework 5 in PDF
Homework 6 (due Friday, March 1, at the beginning of class):
    Problems 1.1, 1.2, 1.3, 1.6, 1.7, 1.8, 1.9, 1.10, 1.15, 1.16, 1.17, 1.18
    from the first chapter of "Undergraduate Commutative Algebra" by Reid
Solutions for Homework 6 in PDF
Homework 7 (due Friday, March 15, at the beginning of class) in PDF
Solutions for Homework 7 in PDF
Homework 8 (due Friday, March 22, at the beginning of class):
    Problems 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.11
    from the third chapter of "Undergraduate Commutative Algebra" by Reid
Solutions for Homework 8 in PDF
Homework 9 (due Friday, March 29, at the beginning of class) in PDF
Solutions for Homework 9 in PDF
Homework 10 (due Friday, April 5, at the beginning of class) in PDF
Solutions for Homework 10 in PDF
Homework 11 (due Friday, April 12, at the beginning of class) in PDF
Solutions for Homework 11 in PDF
Homework 12 (due Friday, April 19, at the beginning of class) in PDF
Solutions for Homework 12 in PDF



Approximate course contents (arranged by week)

  1. Review of rings and fields (January 9 and 11).
     
  2. Field extensions and Galois groups (week of January 14).
     
  3. Basic properties of field homomorphisms (January 23 and 25).
     
  4. Main theorems of Galois theory: proofs (week of January 28)
     
  5. Cyclotomic polynomials and applications (week of February 4)
     
  6. Solvability by radicals (week of February 11)
     
  7. Introduction to commutative algebra (week of February 18)
     
  8. Spec Z and Spec Z[x] (week of February 25)
     
  9. Spring break (week of March 4)
     
  10. Nakayama's lemma and applications (week of March 11)
     
  11. Finiteness conditions in commutative algebra (week of March 18)
     
  12. Noether normalization and integral extensions (week of March 25)
     
  13. The Nullstellensatz (week of April 1)
     
  14. More on affine algebraic varieties (week of April 8)
     
  15. Localization in commutative algebra (week of April 15)