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

Handouts and links

• Syllabus
• Boardwork from days I teach on a tablet
• Zoom link for any online office hours, classes, etc.

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)
• Problem Set 6 (due Wednesday 10/23 Friday 10/25 at 10pm)
• Problem Set 7 (due Friday 11/1 at 10pm)
• Problem Set 8 (due Wednesday 11/20 at 10pm)
• Problem Set 9 (due Wednesday 12/4 Friday 12/6 at 10pm)
• Problem Set 10 (due Wednesday 12/11 at 10pm)

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.

• Midterm exam (due Wednesday 11/13 at 10pm)

• Final exam (due Friday 12/20 at midnight)