Math 4301 - Honours Seminar on Galois Theory

• Assignment 1 (Due: Jan 20)
  • Chapter 1 - 2, 5, 6, 7, 11*, 13 *Challenge Question
  • Chapter 2 - 1, 4, 7, 10, 11, 14
  • Chapter 3 - 1a, 2a, 4, 7, 8adf, 17
• Assignment 2 (Due: Jan 25)
  • Chapter 4 - 2, 4, 7, 8, 10
• Assignment 3 (Due: Feb 1)
  • Chapter 5 -- 1, 2ace, 3, 4ac, 5, 9 [Hint for 5: If m = at^2 + bt + c, show alpha = sqrt(b^2 -4ac)]
• Assignment 4 (Due: Feb 3)
  • Chapter 6 -- 1abce, 3, 4, 6, 8, 13, 14, 17 (not h)
• Assignment 5 (Due: Feb 8)
  • Chapter 7 -- 1b, 7, 14, 17
  • Prove Lemma 7.3 for the case of two circles meeting.
• Assignment 6 (Due: Feb 22)
  • Chapter 8 -- 1, 12abcd
  • Prove the containment of sets in equation (8.2) on page 93
  • Prove:
    • Let L:K be a field and extension, and f(t) \in K[t]. If z \in L is a root of f(t), and if \alpha is any K-automorphism of L, prove that \alpha(z) is also a root of f(t).
  • Compute the Galois Group for the following extensions:
    1. Q(\sqrt{p}):Q for any prime p
    2. Q(i,\sqrt{5}):Q
    3. Q(5^{1/3}):Q
    4. Q(w):Q where w is the complex root of t^3 - 1
• Assignment 7 (Due: March 8)
  • Chapter 9 -- 1, 2, 3ac, 5bcde, 7, 9
• Assignment 8 (Due: March 10)
  • Chapter 10 -- 2, 3, 5
• Assignment 9 (Due: March 17)
  • Chapter 11 -- 2acd, 3acd, 4ac, 6, 7
• Assignment 10 (Due: March 22)
  • Chapter 12 -- 1, 2, 4*, 6
• Assignment 11 (Due: March 24)
  • Chapter 13 -- 1ab, 2ab, 3ab, 4ab, 5ab, 6ab, 11 (Hint: there are 16), 12
• Assignment 12 (Due: March 29)
  • Chapter 14 -- 1, 2, 6 (Hint: What groups have order 15?) 10, 13abcd
• Assignment 13 (Due: March 31)
  • Chapter 15 -- 1, 2, 6, 7, 10, 12 (skip f)

Here is a copy of corrections for Stewart's Book:

• Corrections to Stewart (March 1, 2005)

The following links might also be helpful:

• Ken Ribet's anonymous comments page for his Galois Course (Spring 2004 at Berkeley).
• George M. Bergman's email answer page for his Galois Course (Spring 2005 at Berkeley).

Important Dates

• Jan. 4, 2005 -- Classes Begin
• Feb. 8, 2005 -- Final date for course withdrawal with academic penalty.
• Feb. 14-18, 2005 -- Reading Week (No class)
• April 4, 2005 -- Classes End

Any course handouts will also be posted to the web. They will be posted as PDF document

• Course Description Handout The handout which describes the course.
• (Tentative) Schedule

Adam Van Tuyl
URL: http://flash.lakeheadu.ca/~avantuyl/coures/2005_winter_math4301.html
avantuyl@sleet.lakeheadu.ca