| 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.
|Lecture||MWF 9:30am-10:20am |
Building 200, Rm 205
|Textbook||David Dummit & Richard Foote|
Abstract Algebra, 3rd Edition
(primarily chapters 13 and 14)
|Instructor||Andy Hardt |
Office: Building 380, Rm 382C
Office Hours: MWF 10:30am-11:30am
|Course Assistant||Yuefeng Song |
Office: Building 380, Rm 381L
Office Hours: M 1:00pm-3:00pm, TuTh 9:00am-10:00am
|More Details||Canvas page | Syllabus | (for Gradescope link, see Canvas)|
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.
This project entails computing the Galois correspondence and associated data for different polynomials. Due via Gradescope on Friday, March 3rd, 2023 at noon.
Midterm Exam: Wednesday, February 8th – 7:00PM – 9:00PM (Room 200-205)
Final Exam: Thursday, March 23rd – 8:30AM – 11:30AM (Room 200-205)
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:
Relevant to Galois theory, and (perhaps) fun. Feel free to send me anything interesting you run across.