Syllabus - Representation Theory - Spring 2023
MATH 742 - 001
General Information
- Course webpage
- https://duncan.math.sc.edu/s23/math742
Instructor
- Name
- Alexander Duncan
- duncan@math.sc.edu
- Office
- Leconte 448
- Office Hours
-
Tuesday 9:00 AM - 10:00 AM
Wednesday 10:30 AM - 11:30 AM
Thursday 1:30 PM - 2:30 PM
Meeting Times
- Lecture
- Tuesday, Thursday 10:05 AM-11:20 AM
Leconte 315
Bulletin Information
- Description
- Representation and character theory of finite groups (especially the symmetric group) and/or the general linear group, Young tableaux, the Littlewood Richardson rule, and Schur Functors.
- Prerequisites
- MATH 702
- W Deadline
- January 17
- WF Deadline
- March 27
Textbook
There is no required textbook for the course.
Learning outcomes
After successful completion of this course, you will be able to:
- compute the character tables of finite groups.
- extract group and representation theoretic information from character tables.
- classify representations of the general linear group and symmetric group.
- prove theorems about representation theory over arbitrary fields.
Assessment
There are two completely distinct grading schemes: either regular assignments or a written report. The report option is only available to students that have passed their comprehensive exams. There will be more problems on the assignments than are required to get 100% in the course. It is expected that you will think about all the problems, but only write up full solutions to a subset of them. Writing up full solutions to every single problem is not expected (and is probably not a good use of your time).
Assignments
There will be written assignments roughly every two weeks. It is your responsibility to check regularly for new assignments. Late assignments will not be graded. You are encouraged to work in groups, but you are required to write up every assignment yourself and to use your own words. Your assignments must be written up in LaTeX and submitted via email as a PDF.
Each assignment will be scored out of 100 points, although more than 100 points may be available. Your raw numerical grade will be obtained by taking the average score of all assignments, weighted evenly. Some portion of scores in excess of 100 points may be used towards this average at the instructor's discretion at the end of the course. Your final letter grade will be determined from your raw numerical grade as follows:
You are guaranteed, at least, the letter grade indicated by the following table:
| A | B+ | B | C+ | C | D+ | D |
|---|---|---|---|---|---|---|
| 80 | 70 | 60 | 50 | 40 | 30 | 20 |
The table may be revised later (to your benefit) at the instructor's discretion.
Written Report
If you have obtained candidacy, instead of assignments you may submit a written report (say 10-15 pages) on a topic in representation theory. For example, you may write about an application of the techniques learned in the class, a report on a research paper in the area, or an exposition of a more advanced topic. The subject matter and source materials should be decided in consultation with the instructor. This report is due by the last day of class. This option is only available to PhD Candidates (i.e. those that have passed their comprehensive exams).
Course Policies
Attendance and Missed Work
No attendance policy will be enforced. However, it is not reasonable to expect to learn the material without regularly attending classes. Students are solely responsible for material or announcements missed due to missed classes without a documented excuse.
Late or missing work may only be graded for documented excuses as listed in the Graduate Bulletin. In the case of a religious holiday or participation in a university-authorized activity, please notify the instructor within the first two weeks of class. The Graduate Student Ombuds may review appropriate documentation for absences due to medical conditions or illness, death or severe illness of an immediate/dependent family member, military duty, or legal obligation.
Academic Integrity
You are expected to practice the highest possible standards of academic integrity. Any deviation from this expectation will result in a minimum academic penalty of a zero in the relevant assessment, and may result in additional disciplinary measures.
Other Resources
Office of Student Disability Services
Any student with a documented disability should contact the Student Disability Resource Center to make arrangements for appropriate accommodations.