I am the algebra prelim tutor for winter 2022!
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.