Math 410: Galois Theory (Fall 2024)

Galois Theory is the study of symmetry in the solutions to polynomial equations. In its modern formulation, it describes a beatiful correspondence between field extensions and certain symmetry groups. We will develop this theory starting from a basic knowledge of groups, rings, and fields. One of our main goals will be to prove that there is no general version of the quadratic formula for a polynomial of degree five or more. Along the way, we will also show that a circular cake can be divided into 17 (but not 7) equal slices using only a straight-edged knife.

Time and location

  • Monday, Wednesday, and Friday, 2:00-2:50am (SMUD 204)

Help hours

  • My office hours in SMUD 401 are:
    • Tuesday 9:15-10:45
    • Wednesday 9:15-10:45
    • Friday 10:30-11:30

Problem Sets

  • Homework is submitted via Gradescope; our course code is G386G6.
  • Problem Set 1 (due Friday 9/13 at 10pm)
  • Problem Set 2 (due Friday 9/20 at 10pm)
  • Problem Set 3 (due Wednesday 9/25 at 10pm)
  • Problem Set 4 (due Wednesday 10/2 at 10pm)
  • Problem Set 5 (due Wednesday 10/9 at 10pm)
  • (Due to the break, we will skip one Wednesday, with Problem Set 6 due on Wednesday 10/23)

Exams

There will be a take-home midterm exam, likely in the first week of November, and a take-home final exam due during finals period. More details will be announced later.