Math 7752. Algebra-II.

Algebra-II. Math 7752. Spring 2021.

TuTh 11-12:15 pm (US Eastern), online via zoom .

Instructor: Mikhail Ershov
e-mail: ershov at virginia dot edu
Office hours (tentative): Wed 8-9:15pm, Thu 2-3:15pm and by APPOINTMENT

Main Text:

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

Prerequisites:

Math 7751 and an undergraduate course in linear algebra comparable in level to UVA 4651.

Course content

In the first part of the semester (about 4 weeks) we will continue studying modules (picking up where we left off in Algebra-I) and some of their applications. I will assume familiarity with the content of Sections 11.1-11.4 as this material is discussed in standard undergraduate linear algebra and Sections 10.1-10.4 which were mostly covered at the end of Algebra-I in Fall 20. Next we will study fields and Galois theory (also 5-6 weeks). The material we will cover is mostly discussed in Chapters 13-14 of Dummit and Foote, though the order of my exposition will be quite different. I plan to finish with a brief introduction to either commutative algebra (parts of Chapter 15 of Dummit and Foote) or representation theory (parts of Chapters 18 and/or 19 of Dummit and Foote).

Exams and homework:

There will be weekly homework and three exams (two midterms and the final). The format of the exams will be determined later; the current plan is that both midterms will be take-home while the final will be "in-class" (proctored over zoom).

Exams

First midterm exam: Fri, March 12th
Second midterm exam: Fri, April 16th
Final exam: Sat, May 15th, 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.
Please STAPLE your homework.
No late homework will be accepted. However, the lowest homework score will be dropped. The second lowest homework score will also be dropped provided that score is over 60%

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.

Class meetings

I will normally start the zoom session for the class meetings around 10:50am (10 minutes before the start of the class). Whenever possible, please join the meeting by 10:58am. You are also strongly encouraged to keep your video on during the class meetings. This would make it much easier for me to see whether you are following the presentation and help keep the class meetings more interactive.

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, February 16 -- Last day to ADD a class, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Tuesday, March 23 -- Last day to DROP a class (deletion from the transcript)
Tuesday, April 6 -- Last day to withdraw from a class

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.