Welcome to Math 3094: Coxeter Groups, this Fall 2018! Today is
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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: