Welcome to Math 3094: Coxeter Groups, this Fall 2018! Today is
Thursday, March 13, 2025.
Actual Schedule
See also UConn Calendar for Fall 2018 for important deadlines and other dates.
Office hours
Final Exam (Dec 10 – 16)
Overleaf document is due Friday December 14 at noon (but you may continue to make changes until Sunday, December 16 at noon) Take-home exam: Clone my Overleaf Template.
- Final Exam PDF, tex
- I may add more hints (after getting questions from students) and include more details, so please check my template link again before you share your final draft.
- Please share your Overleaf document via my UConn email.
List of Homework:
Week 15 (Dec 3 – 7)
- Tue Due (Handwritten HW) Let me know on Piazza if anything is unclear.
- Read Lemma 1.12 once (on page 22) - I will explain it in class.
- Show that the relation defined in the proof of Lemma 1.12 (page 22) is indeed a partial ordering.
Def: A relation is a partial ordering < on R^n iff, for all x,y,z in R^n we have
- (reflexive) x < x for all x in R^n
- (antisymmetry) x < y and y < x implies x = y
- (transitivity) x < y and y < z implies x < z
- Show that (34)(23)(12) is an element in W^I for S={(12),(23),(34)}, I={(23),(34)} using the same methods shown in class for showing that 1 and (12) and (23)(12) are in W^I.
- TH Due Handwritten HW
Past: Week 14 ( Nov 26 – 30)
- Tue Due
- While taking notes, spend 1 - 2 hours reading Section 1.8 and Section 1.9 of Humphreys (it’s fine if you don’t completely understand - we’ll go over them in class). You might need to look back to Section 1.7 and earlier to look up terms like Deletion Condition, etc.
- For the equalities/ other facts given in these sections, try to come up with examples in S3=A2 and S4=A3.
- TH Due Section 1.8 Humphreys (page 16) Exercise 1 and Exercise 2 (Handwritten is OK). Give informal justification for each exercise. Set aside about 1 hour.
Past: Week 13 (Thanksgiving recess Nov 18 – 24)
Past: Week 12 (Nov 12 – 16)
- TH (I said in class that this was due on Tue, but I think TH would be better) Due Week 12 HW (Handwritten is OK) Please submit in class (if handwritten) or share via Overleaf
Past: Week 11 (Nov 5 – 9)
- Tue
- TH
- Due (the parts that say LaTeX only) Week 11 Handwritten and Problem Set HW. Please invite me to your Overleaf project by email.
- If you didn’t forgot to bring Week 11 HW or Week 10 HW on Tue, you can submit on TH
Past: Week 10 (Oct 29 – Nov 2)
Past:Week 9 (Oct 22 – 26)
Past: Week 8 (Oct 15 – 19)
- Tue
- Due Correction to Week 4 Problem Set. Please invite me by entering my email (even though you’ve already put your link on HuskyCT).
- Due The exam will be all proofs. (If there are definitions that you don’t remember that I don’t put on the exam paper, you can ask me during the exam.) You can write also as many definitions as you want on a one-sided sheet of US paper size (or A3 size). Please submit in class (by Tuesday) or on HuskyCT (by the end of the day on Wednesday) and I will bring/print them for you on exam day. I can print in color.
- TH
Week 7 (Oct 8 – 12)
Week 6 (Oct 1 – 5)
- Tue
- TH
- Suggested HW: work on assignments due next week
Week 4 (Sep 17 – 22)
- Tue Continue Sec 1.1 [BB]
- TH Group homomorphism; prove that two groups are the same.
- Due in class (or HuskyCT Overleaf link or PDF scan), Week 4 computation HW, handwritten submission is OK. Please let me know if you need more time.
- Due (moved to Tuesday next week, September 25) Week 4 Problem Set All the problems from previous problem you did not complete, plus a few new problems. LaTeX submission only. Share Overleaf edit link on HuskyCT. If you are using Overleaf v2, please invite me as a collaborator with edit permission.
Week 3 (Sep 10 – 15)
- Tue
- Quiz on definition of reflexive, symmetric, and transitive properties, and compositing permutations (type A and type B).
- TH Start Sec 1.1 [BB]
- Quiz write down the definition of a group
Week 2 (Sep 3 – 7)
(Monday, September 3 Labor Day)
- Tue
- Due SageMath HW (not graded): Learn to use SageMath to compute permutations for 1 hour or until you understand the examples.
- TH
- Due (Computation) HW 2 handwritten work is accepted. Submit in class or on HuskyCT/Piazza
- Due on Saturday, Sept 8, 5pm Week 2 Problem Set LaTeX submission only. Share Overleaf link on HuskyCT.
Week 1 (Aug 27 – 31)
- Tue Introduction and Induction review activity version A, version B, and version C
- TH
- Due HW 1: Survey and LaTeX practice, HW 1 template before the beginning of class. To submit, click on the share button, copy the Read & Edit Link (so that I can write a comment directly on the file or help you investigate error messages), and paste the link on HuskyCT.
- Due Take notes (either handwritten or LaTeX) while watching Ardila Video 1: intro to type A Coxeter group
- You can play it up to 2x speed or at a slower pace.
- Make a list of all new vocab words and concepts you hear (or words you have forgotten). There should be many concepts that are new to you.
- For at least 1 hour, attempt to look up some of these vocab words/concepts (search the algebra textbook algebra textbook Judson’s Abstract Algebra or wikipedia) and write down the definitions/ explanations. If you couldn’t find them anywhere on the internet, write a note stating so.
- Make a list of questions about these new concepts.w
Handed out: