MATH 121 - Galois Theory (Winter 2023)

| General Information | Homework | Lecture Notes | Other Resources |

Galois theory is a subtle, yet beautiful subject which characterizes solutions to polynomial equations through connections between groups and fields. It was the brainchild of a troubled teenager, Évariste Galois, grieving his father's death and his college rejection, who was repeatedly arrested for his political activism. Galois sadly died in a duel, and his work wasn't fully appreciated until many decades later, but has since become an essential part of mathematics, with connections to advanced topics in number theory, algebraic geometry, and elsewhere.

General Information

LectureMWF 9:30am-10:20am
Building 200, Rm 205
TextbookDavid Dummit & Richard Foote
Abstract Algebra, 3rd Edition
(primarily chapters 13 and 14)
InstructorAndy Hardt
Office: Building 380, Rm 382C
Email: hardt@stanford.edu
Office Hours: MWF 10:30am-11:30am
Course AssistantYuefeng Song
Office: Building 380, Rm 381L
Email: songyf@stanford.edu
Office Hours: M 1:00pm-3:00pm, TuTh 9:00am-10:00am
More Details Canvas page | Syllabus | (for Gradescope link, see Canvas)

Homework

Homework assignments are weekly, due at noon on Tuesdays via Gradescope. All problems are from Dummit and Foote, unless stated otherwise. Using LaTeX for your homework is encouraged (and good practice!), but not required.

Lecture Notes

Schedule

Midterm Exam: Wednesday, February 8th – 7:00PM – 9:00PM (Room 200-205)
Final Exam: Thursday, March 23rd – 8:30AM – 11:30AM (Room 200-205)

Background and Other Resources

Background

Most of the necessary background for this course was covered in Math 120: Groups and Rings. Having a working knowledge of topics from that course will be invaluable in this one. All relevant material can be found in earlier sections of Dummit & Foote. We will cover/review some of the most important ideas, but here are some particularly relevant topics:

Other Galois Theory Resources

Bonus Links

Relevant to Galois theory, and (perhaps) fun. Feel free to send me anything interesting you run across.