| Adjustments due to the pandemic |
As you know, this will not be an ordinary semester.
Throughout this syllabus, you will see ways that this course is being adjusted because of the Covid pandemic. I will do my best to make this a good learning experience despite the changes.
I will need you to communicate with me about your needs and how the adjustments are affecting you.
Please read this syllabus addendum relating specifically to Covid adjustments. Although this is standard language that has been prepared by the university, it is very important, and is considered part of the syllabus for the course. |
| Fundamental principles | I will try to conduct this class according to the principles expressed in Ardila's Axioms (and the logical consequences of these axioms) and will expect all students in the class to try to do the same. I welcome feedback about how well I am doing, and I encourage students to talk to me if their experience (in my class or elsewhere) is not consistent with these axioms. |
| Course Description | This course will develop the theory of Coxeter groups. The beauty of Coxeter groups lies in the rich interplay between geometry, combinatorics and order/lattice theory. Most proofs about Coxeter groups exploit a combination of methods. The methods that play a role include the combinatorics of words, the geometry of arrangements of reflecting hyperplanes (or the geometry of root systems), order/lattice theory and linear algebra. We will begin our study with geometry, closely mixed with order/lattice theory, and progress towards an understanding of the combinatorics of finite Coxeter groups. With the geometric intuition in mind, we will proceed to study the more combinatorial aspects of (not necessarily finite) Coxeter groups. |
| Prerequisites | Abstract algebra (groups in particular) and some low-level linear algebra. Previous experience with combinatorics will be helpful, but will not be assumed. In particular, I will assume no previous experience with the combinatorics of words or with order/lattice theory. |
| Credit load | 3 credits |
| Instructor | Nathan Reading |
| Office | SAS 4118 During Covid times, I will rarely if ever be in this office. |
| Telephone | 919-515-3261. This is an office desk phone that does not accept text messages. During Covid times, I will rarely if ever be near this phone. Email is a much better way to reach me than phone. |
| reading AT math DOT ncsu DOT edu | |
| Course website and Moodle | https://nreadin.math.ncsu.edu/coxeter. You will be responsible for material on this site. You will be notified by email (possibly through the Moodle Announcments Forum) or in class when new information is posted on the site (except for regularly occurring changes like posting of assignments and solutions). There is also a Moodle page for this course, which you can find in the usual way through Wolfware. We will use the Announcements Forum and the Gradebook. The Moodle page is also where you will find the link to Zoom meetings for class and office hours, and the links to whiteboard images and recorded lectures. |
| Class email list | You will be responsible for information emailed to your ncsu account. Some course emails will come through the Moodle Announcements Forum, and so will be archived on the Moodle page. You should check your ncsu email account roughly every day. |
| Class Sessions | Tuesdays and Thursdays, 8:30 to 9:45 in Park Shops 210. I plan to have all class sessions available in three ways: Sychronously in Park Shops 210, synchronously through Zoom, and asynchronously through recorded Zoom sessions. UPDATE: Given the current Covid situation and the preferences of class members, we will forego the in-person aspect of the class and do Zoom only. This decision may be revisited later. I strongly prefer that you attend either in person or via Zoom (with your camera on), but I have no preference between these two options. I will try to make the recorded classes as helpful as possible, but I think synchronous attendance will be better for your learning. Attendance in the class is considered mandatory. I will take roll every day in the classroom and on Zoom. If, instead, you watch a recorded lecture, you should immediately email me a statement like "I watched the [LECTURE DATE] Lecture on [DATE WATCHED]." I will be using an online whiteboard. The whiteboard will be projected in the class, but I will make the previous whiteboard "panels" available online in real time. If you attend in Park Shops 210, you will probably find it helpful to bring a device that can connect to the internet, to access earlier boards. If you attend through Zoom, you may want to look at earlier boards in a separate browser window. The Zoom meeting link, recorded lectures, and whiteboard images are available through the Moodle page. If at some point during the semester I am ill or quarantined, I will continue teaching if I can, but only through the synchronous and asynchronous online methods. |
| Every challenge is an opportunity | One good side-effect of the online component of the course is that copies of the whiteboards for every lecture will be available to you. Consider changing your class strategy accordingly: There will be no need to transcribe everything you see on the board. Instead, engage your entire brain in the mathematics, and write down only the insights that you have, or things that I say, that are not on the board. |
| Office hours |
Tuesdays and Thursdays, 10:00-10:45*, Wednesdays 11:30-12:30, or by appointment. *On Tuesdays and Thursdays, I will stay after class and move right into office hours, but I will end the meeting before 10:45 if people leave before then. Showing up near the end of that office hour is fine, but if you plan to do that, please let me know ahead of time. |
| Text |
There will be one required text for the course and one optional text. Required: Bjorner and Brenti, Combinatorics of Coxeter groups Optional: Humphreys, Coxeter groups and reflection groups. These are both excellent books and should be on your desk if you want to work seriously with Coxeter groups. The required text covers the topics that we will focus on. The optional text develops the theory of Coxeter groups more fully and will particularly useful for the student who wants a more complete geometric treatment. There are also many other good books out there which cover Coxeter groups from different points of view. At some points during the course, I will work from some book chapters that I wrote. These will be provided to you in electronic form. I ask that you not distribute them. |
| Material Covered | Tentatively, we will cover Bjorner and Brenti Chapters 1-3 and parts of 4. Depending on time, we will supplement this with parts of Chapters 7 and 8 and possibly a very small amount of material from Humphreys. I will give you more details about what parts of my book chapters we will cover. |
| Pictures | Occasionally, I may post some pictures here. |
| Homework |
Homework assignments will be assigned and collected over the course of the semester.
You are encouraged to collaborate on solving the assigned problems as long as everyone in the group gains a thorough understanding of the solution.
Furthermore, each student must write up the solution in their own words based on their own understanding. Here are the homework assignments. Here are some Comments and answers on homework assignments. |
| Grading | Your course grade will be determined by your attendance and your performance on the assignments. |
| Final Exam | This class has a final exam scheduled for Wednesday, December 13, 8:00-11:00.
The final exam will be a take-home exam.
This take-home will look just like the other assignments, will be about as long as the other assignments and will contribute exactly as much to your final grade as each of the other assignments. However, it is a take-home final exam. Here is the final. |
| N.C. State Polices, Regulations, and Rules |
Students are responsible for reviewing the NC State University Policies, Rules, and Regulations (PRRs) which pertain to their course rights and responsibilities, including those referenced both below and above in this syllabus: Equal Opportunity and Non-Discrimination Policy Statement with additional references at https://oied.ncsu.edu/divweb/policies/ Code of Student Conduct. |
| Policy on Attendance and Make-ups | Attending every lecture (in its entirety) is considered part of the course requirement. No provisions will be made for students to make up missed work or tests except as spelled out in the University's attendance regulation available at http://policies.ncsu.edu/regulation/reg-02-20-03 . Covid note: I understand that these are unusual times. If you are having trouble attending, please talk to me. |
| Policy on Incompletes | Incompletes are not offered except in cases where special circumstances (such as outlined in the attendance regulation mentioned above) make it impossible for a student to complete the course. Even in these special circumstances, incompletes will not be offered unless the student was in a position to pass the class before the special circumstance arose. In particular, incompletes cannot be used as a way to "bail out" when a student feels that they cannot pass the course or feels they cannot do all the work they put off until the end of the semester. |
| Statement on privacy | Students may be required to disclose personally identifiable information to other students in the course, via digital tools, such as email or web-postings, where relevant to the course. Examples include online discussions of class topics, and posting of student coursework. All students are expected to respect the privacy of each other by not sharing or using such information outside the course. |
| Statement for students with disabilities | Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with the Disability Resource Office at Holmes Hall, Suite 304, 2751 Cates Avenue, Campus Box 7509, 919-515-7653. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (NCSU REG02.20.01). |
| Academic Integrity | Students are expected to conform to standards of academic integrity as described in the Code of Student Conduct, which can be found in the Code of Student Conduct. The student, by signing or writing their name on a homework assignment or test, affirms that they have neither given nor received unauthorized aid. (See "Homework Assignments" above for guidelines on acceptable collaboration on homework.) |
| NCSU Counseling center | The Counseling Center offers confidential counseling to NC State students experiencing personal, academic or vocational problems. Check out counseling.dasa.ncsu.edu. |
| Help for students in distress | Although the counseling center is a great help, sometimes it's hard to recognize when we need help. So we need to look out for each other too. Occasionally, you may come across a fellow student whose behavior worries you. You can and should report worrisome behavior to the NC State Cares website: https://prevention.dasa.ncsu.edu/nc-state-cares/about/. You can report anonymously, but if you share your contact information, they can follow-up with you personally. |