Math 120: Groups and Rings

In Fall 2015 I taught Math 120 at Stanford University. The course assistant was Niccolò Ronchetti. For questions about the material and class discussions, we used the Math 120 Piazza page. Office hours: Church Monday 4–5:30 and Thursday 4–5 in 383-Y; Ronchetti Tuesday 6–7:30 and Friday 6–7:30 in 381-M.


The take-home midterm exam, and the take-home final exam.
[Note to teachers: both exams were on the easy side, quite possibly too easy for a take-home exam. Q5 on the final could be "brute-forced" in terms of entries of C, which made it easier than intended.]

Material covered:

WIM paper topics:
1) alternating group An is simple for n≥5, or
2) Banach–Tarski paradox.

For alternating group: definition of An is 3.5, definition of simple group is on p102, simplicity of A5 is Theorem 4.3.12, simplicity for general n is 4.6 (there are other proofs, you can use another argument if you like).
Source for Banach–Tarski: Brief exposition by Terry Tao, also sketch of the proof on Wikipedia.

The full syllabus for the course is available here.

Textbook: Dummit and Foote, Abstract Algebra (3rd ed), required.

Further resources: