Math 7751. Algebra-I.

Algebra-I. Math 7751. Fall 2020.

2-3:15 pm (US Eastern), online.

Instructor: Mikhail Ershov
e-mail: ershov at virginia dot edu
Office hours: 2 hrs 30 min TBA and by APPOINTMENT
Course webpage: http://people.virginia.edu/~mve2x/7751_Fall2020

Main Text: Abstract Algebra, David Dummit and Richard Foote, 3rd edition.

Course content:

Math 7751 is the first half of the standard graduate algebra sequence (the second half is Math 7752). We will study primarily ring theory, group theory and group representation theory (in this order). I plan to spend approximately equal amounts of time on each of the 3 parts. If we go substantially slower than expected in the first 2 parts, I may replace representation theory by another topic.

For the ring theory part, I plan to cover the majority of topics in Chapters 7-9 of Dummit and Foote (DF). For the group theory part, we will very briefly review Chapters 1-3 (which mostly contain standard undergraduate material) and then cover selected topics from Chapters 4-6. I do not plan to follow a specific book for the representation theory part, but a good reference which does not assume advanced algebra background is Representation Theory of Finite Groups: An Introductory Approach by Benjamin Steinberg.

Prerequisites:

Undergraduate courses in linear algebra and abstract algebra comparable in level to UVA 4651 and 4652, respectively. Linear algebra material will not be seriously used until the last third of the course. A linear algebra assessment exam will be posted during the week before the fall semester and will be due on Thu, Aug 27. If you feel that your linear algebra preparation is not sufficient, you are strongly encouraged to attend MATH 4651 Advanced Linear Algebra (which meets MWF 1-1:50pm) and/or review the main linear algebra topics during the first half of the semester.

Exams and homework:

There will be weekly homework and three exams (two midterms and the final). The format of the exams has not been finalized yet, but the current plan is that the first midterm will be 50% in class and 50% take-home, the second midterm will be 100% take-home and the final will be 50% take-home and 50% oral.

Exams

First midterm exam: Tue, September 29th.
Second midterm exam: Thu, November 5th.
Final exam: Tue, December 8th, 9am-12pm.

The time and date for the final exam are determined by the registrar and cannot be changed. The dates of the midterm exams are tentative at this point and may be slightly changed. In case of a take-home exam date means the due date.

Evaluation:

Final exam: 30%
Midterm exams: 20% each
Homework: 30%

Homework

Homework will be assigned weekly and will usually be due on a fixed day of the week (TBD later)
Homework should be submitted as a SINGLE PDF file. If the size of your HW file is more than 1MB, you must upload the file on Collab (the current plan is to use the FileDrop tool, but this may be changed later). Files less than 1MB can also be submitted as email attachments.
No late homework will be accepted. However, the lowest homework score will be dropped.
GRADING: it may not be possible to grade all homework problems.

Collaboration policy.

On homework: you are welcome (and even encouraged) to work on homework together, but you must write up solutions independently, in your own words. In particular, you should not be consulting others during the process of writing down your solution.
On exams: you may not discuss exam problems with others.

Announcements

Major announcements will be made in class and also posted on the course webpage. Some other announcements may only be made by e-mail, so check your e-mail account regularly.

Add/drop/withdrawal dates:

Tuesday, September 8 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Tuesday, October 13 -- Last day to DROP a course (deletion from the transcript)
Tuesday, October 20 -- Last day to withdraw from a course

SDAC

All students with special needs requiring accommodations should present the appropriate paperwork from the Student Disability Access Center (SDAC). It is the student's responsibility to present this paperwork in a timely fashion and follow up with the instructor about the accommodations being offered. Accommodations for test-taking (e.g., extended time) should be arranged at least 5 business days before an exam.