Textbook Grading Homework Assignments Course Schedule Notes Back to Main Page

Office: Zoom link on Canvas

Email: efuchs at math dot ucdavis dot edu

Office hours: MWF 10AM-10:50AM

TA: Matt Litman (mclitman at ucdavis dot edu)

Discussion: Tuesdays 2:10-3PM, TBA

TA Office hours: Thursdays 11AM-12PM (see Zoom link on Canvas)

The 250 series is meant to equip the graduate student with a thorough background in Algebra, in particular in preparation for the preliminary exam. For 250A, this will include, very roughly, various standard important theorems on groups, fields, and Galois theory.

The assumption is that students taking this course have a solid background in undergraduate algebra. Another assumption is that students will read about the basic notions in the text, and digest these notions, as well as those covered in class, through weekly homework assignments. Being able to read up on topics independently is an important skill every graduate student should work to develop. There is a lot of material to cover, and so class time will be devoted only to main theorems and applications thereof: for example, definitions which you should either have seen in undergraduate algebra or could easily grasp by reading the book will not be covered during class time. On the other hand, we will cover some material in class that is either not emphasized in the book or deferred to an exercise.

To make it easier for you to prepare for the lectures, I will post in advance a weekly list of concepts we will cover in class, as well as notions that I will assume you know throughout each lecture on this website.

This course will be taught remotely. The structure of the course will be as follows:

- I will be posting pre-recorded lectures of about 30 minutes in length on Canvas. The videos will be posted as VoiceThreads, and we will go over how you will be able to interact with these videos on the first day of class during class time on Zoom.
- During class time, I will be holding Zoom homework sessions where I will be putting you into breakout rooms to work on specific problems. We will do homework collaboratively and attending these sessions is highly recommended, although not required. Think of these sessions as a chance to form bonds with your fellow graduate students as well.
- Additional office hours can be requested over email.
- The midterm and final will be take-home.

There is no required text for this class. Some books you may consider learning from alongside the lectures are below. If you are to purchase a new book, I would purchase Dummit and Foote.

*Algebra*by Artin*Algebra*by Birkhoff and MacLane*Abstract Algebra*by Dummit and Foote- J.S. Milne's notes on group theory and Galois theory on this website

Grades will be based on weekly homework assignments (40%), one midterm (25%) taken remotely on Monday, November 9th 9-11AM, and one final (35%). Most homeworks (unless otherwise noted) will be due on Fridays on Canvas (submitted online) at 2PM. Collaboration on the homework is encouraged, but please do cite any sources which helped you to complete the assignment. ** No late homeworks will be accepted!**

- Cyclic Groups by Arthur Ogus
- Simplicity of A_n by George Bergman
- Simplicity of PSL_2(R)
- On the number of Sylow subgroups of a finite group by Marshall Hall.
- G. Bergman's notes on a PID which is not a Euclidean Domain
- Notes on geometric constructions

- 9/30-10/2: Lectures 1-3 (posted on Canvas): Isomorphism theorems, exact sequences, composition series. This week's suggestions on what to know before class are here.

Some or all solutions will be posted on our course page on Canvas once homeworks are handed in.

- Homework 0: send me an email telling me a little about yourself: who you are, what kind of math you like/don't like (be honest, I won't be offended), what your hopes and worries are for this course, and so on.
- Homework 1 due on Friday, 10/9.