Instructor: Dr Manjil P. Saikia
Contact: [email protected] (please only use this email address to send me emails related to this course)
Lecture Time & Place: Mondays & Fridays 1600 to 1715 (Room XXX, SAS)
Office Hours: XXX
Attendance Policy: Attendance is mandatory, check the institute’s attendance policy on AURIS (please note, we have a new policy from last semester). If you are low on attendance then you should talk to me (at least 3 weeks before the end-semester examination).
Course Details
This course is a sequel to MAT631 Algebraic Combinatorics, but we will recall some of the basic objects studied in that course when the time comes. The goal of the present course is to understand the representations of the Symmetric Group. Along the way, we will look at some beautiful combinatorics (and a decent amount of algebra).
Reading Materials
Textbook: We plan to cover the following books:
- The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions, Bruce E. Sagan, 2nd. ed., Springer, 2001.
- Symmetric Functions, Schubert Polynomials and Degeneracy Loci, Laurent Manivel, American Mathematical Society, 2001.
In addition, I will use material from other sources which I will list below as the course progresses.
Grading
- Assignments: There will be biweekly assignments. This will contribute 30% to the total score.
- Project: Students will have to read and write a summary of a research paper of contemporary interest involving some of the material discussed in the course. This will contribute 20% to their total score and will be done before the end-semester examination.
- Presentation: Students will have to give a presentation (approximately 45 minutes to an hour) on the project topic assigned to them. This will contribute 20% to their total score and will be done before the end-semester examination.
- End-Semester Examination: There will be a 180-minute written examination, this will contribute 30% to the total score.
To get an A grade, you must score atleast 80% overall. However, this doesn’t automatically guarantee an A.
Lectures
W 06/01: Introduction to the course, basics of abstract algebra
Problem Sets
- The problem set will be updated over the semester. I will announce in the class or via email when I post a set here.
- You should only submit the designated problem(s) but are encouraged to try the rest as well.
- To get the most out of this course, you are expected to spend at least thrice the amount of lecture hours on your own.
Submissions
- Due time: 11:59 am of each due date
- Must be typed in LaTeX and submitted as PDF or printed
- Begin each solution on a new page
- State your sources at the top of each problem (even if you worked independently)
Late Policy
- Penalty: Late submissions will be penalized by 25% per each late day
- Extensions: There will be no extensions given
Collaborations
- You are encouraged to first work on the problems independently before seeking collaboration.
- Meaningful collaboration is allowed and is encouraged for this course.
- You must write up your solutions.
Acknowledging collaborators and sources
It is required to acknowledge your sources (even if you worked independently).
- At the beginning of the submission for each problem, write Collaborators and sources: followed by a list of collaborators and sources consulted (people, books, papers, websites, software, etc.), or write none if you did not use any such resources.
- Failure to acknowledge will result in an automatic 20% penalty per problem.
- Acceptable uses of resources include: looking up a standard theorem/formula/technique; using Wolfram Alpha/Mathematica/Python for a calculation (no need to mention lectures)
- Unacceptable uses of resources include: directly looking up the problem online or in the research literature for a solution. (Once you have solved a problem, it is fine to seek and learn alternate solutions.)
Intentional violations of the above policies may be considered academic dishonesty/misconduct.
(Thanks to Professor Yufei Zhao for his extensive course policy page, from which I have created my policies.)