Math 200C - Algebra (Spring 2022)
- Lecture times and location: pre-recorded, posted below
- Instructor: Steven Sam email
- Instructor office hours: Zoom, Tuesdays, Thursdays 12:30PM-1:30PM (if there is enough demand, I will add more)
- TA: Alexander Mathers email
- TA office hours: Zoom, Mondays, Wednesdays 3-4PM
- Discord server: link (we'll use this to discuss the class)
About the course
There are no exams in this course; your grade is entirely determined by homework.
Sections 2-5 of the notes below are the material that will be represented in the 200C portion of the algebra qualifying exam.
The material in Section 1 is used throughout 2-5 but I do not plan to test specifically on that material (though any overlap with 200AB could appear in that part).
About the content
We will cover some basic topics in commutative algebra: localization, integral extensions, chain conditions, dimension theory, completion
Much of the material is drawn from Atiyah and Macdonald's text with some things taken from Eisenbud's Commutative Algebra.
Atiyah-Macdonald is a nice concise introduction to the basic ideas and the structure of the course is loosely based on it.
Eisenbud is harder for a beginner, but for further study there are a lot of important topics covered there, so it is worth getting used to.
It also includes a lot of motivation and examples from other subjects which can be helpful to look through.
Interesting and short examples and computations are hard to come by at this level, so most of that will be covered in homework.
Homework will be due roughly every 1.5 weeks. Please upload your submissions to Gradescope by the date specified.
My notes for the course
- Notes (last updated 4/28/22)
We will go by weeks rather than individual lectures. I will break up videos based on logical stopping places rather than set time limits.
Each week corresponds to roughly 5-7 pages of the course notes (how much I cover in an in-person lecture).
Unfortunately there may be small mistakes in the videos. I list them in the video description.
The videos cover the same material as the typed notes above. If you prefer reading over watching a lecture, you will not miss out on any content by sticking with the notes.
Atiyah-Macdonald contains more results and examples than I cover, so it is recommended to look through it for additional context.
- Week 1 (Mar 28)
- Notes: Sections 1, 2.1-2.2
- Atiyah-Macdonald: Chapter 3
- Instead of Lecture 1, please read Section 1 from the notes, which is a combination of review from 200AB and miscellaneous definitions we'll use.
- Videos: Lecture 2, Lecture 3
- Notes from lectures: Lecture 2, Lecture 3
- Week 2 (Apr 4)
- Week 3 (Apr 11)
- Week 4 (Apr 18)
- Week 5 (Apr 25)
- Week 6 (May 2)
- Week 7 (May 9)