This page is intended as a resource for the PhD students at UConn taking the algebra prelim.
I am the algebra prelim tutor for winter 2022!
A good first place to start studying is UConn’s past algebra prelims. Another good resource is Jeremy Teitelbaum’s course webage.
Although the course text that is always recommended for this prelim and used in class is Dummit and Foote, I have found it extremely helpful to read through Keith Conrad’s expository papers on various related prelim topics. For example, if you are struggling with semi-direct products (which are on the prelim syllabus), Keith has this great paper that you can read in order to get a better understanding of what is going on.
For general information on how to study for prelims, you can read this blog post.
Here are the notes from the tutoring sessions:
- Session one, notes (Jan. 2021 prelim)
- Session two, notes1 (Aug. 2020 prelim), notes2 (Jan. 2020 prelim)
- Session three, notes (Aug. 2019 prelim)
- Session four, notes (Jan. 2019 prelim)
- Session five, notes (Aug. 2018 prelim)
- Session six, notes1 (Jan. 2018 prelim), notes2 (Aug. 2017 prelim)
Here are some random notes of things that were helpful for me when I was studying:
- General (brief) overview. This has most, but not all, important definitions and theorems.
- Theorems with group actions on finite groups. It is good and helpful to know the proofs of these, or at least to memorize the main tools used in the proofs.
- Ring theory. This has a lot of useful theorems and proofs, some of which have appeared on past prelims, but this is not exhaustive of all the ring theory material.
- Linear algebra problems. This has linear algebra problems/solutions from past homeworks and exams from when I took the course.