Math 4657. Bilinear Forms and Group Representations.

Syllabus for Math 5657 (Bilinear Forms and Group Representations), Fall 2021

TuTh 2-3:15 pm, Cabell 187.

Instructor: Mikhail Ershov
Office: Kerchof 302
e-mail: ershov at virginia dot edu
Office hours: 2 hrs 30 min TBA and by APPOINTMENT
Course webpage: https://m-ershov.github.io/5657_Fall2021/

Reading

Required text Representation Theory of Finite Groups: An Introductory Approach, 2012th edition, by Benjamin Steinberg.
Here are other recommended books on representation theory:
- Linear Representations of Finite Groups by Jean-Pierre Serre,
- Representations and Characters of Groups by Gordon James and Martin Liebeck.
- Representation Theory of Finite Groups by Martin Burrow.

Prerequisites

The minimal prerequisites for this class are Math 3351 Elementary Linear Algebra and Math 3354 Survey of Algebra. An ideal background involves advanced versions of these classes, Math 4651 Advanced Linear Algebra and Math 4652 Introduction to Abstract Algebra. If you have not taken 4651 and/or 4652, you can still take 5657, but you should be prepared to learn some background material on your own. Also you should expect that the pace in 5657 will be much faster than what you experienced at 3000 level.

Evaluation

The course grade will be based on homework, two midterms and the final, with weights distributed as follows:

homework: 30%
midterms: 20% each
final: 30%

Exams

The format of the exams (in class, take-home or combined) has not been finalized at this point and will be announced later. The midterm dates given below are tentative and may be changed later. The date and time of the final exam is determined by the registrar and cannot be changed (in the case of a take-home final it will be due on that date).

First midterm exam: Thu, Sep 30th
Second midterm exam: Thu, Nov 4nd
Final exam: Sat, Dec 11th, 9am-12pm

Make-up policy

Make-ups or extensions (for take-home exams) will be given only under extreme circumstances (such as serious illness). Except for emergencies, you must obtain my permission for a make-up (resp. extension) before the exam (resp. due date).
If you miss an in-class exam or fail to submit a take-home exam by the due date without a compelling reason, you will be assigned the score of 0 on that exam.
University regulations specifically prohibit early make-ups.

Homework

Homework will be assigned weekly (the due day will be announced later).
All homeworks should submitted electronically (detailed instructions will be given later)
No late homework will be accepted. However, two lowest homework scores 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 take-home exams: you MAY NOT discuss problems with other people or use any resources (including web) except for the class textbook and your class notes. You may ask me questions about the exam problems, but normally I will only provide very brief hints.

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 7 -- Last day to ADD a course, elect the audit option, change the grading option (grade or CR/NC), or establish an independent study
Wednesday, September 8 -- Last day to DROP a course (deletion from the transcript)
Tuesday, October 26 -- 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.