| Fundamental principles |
I will try to conduct this class according to the principles expressed in Ardila's Axioms particularly "Every student deserves to be treated with dignity and respect [by their teacher and their classmates]." 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 |
| Telephone | 919-515-3261. This is an office desk phone that does not accept text messages. 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 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 mostly just use the Moodle Gradebook. |
| Class email list | You will be responsible for information emailed to your ncsu account. You should check your ncsu email account roughly every day. |
| Class Sessions | Mondays and Wednessdays, 8:45 to 10:00 in 2102 SAS Hall. Attendance in the class is considered mandatory. But if you are sick or have other reasons to miss class, please let me know. |
| Office hours |
Mondays and Wednesdays, 10:10-11:00, or by appointment. You can follow me to my office after class if you are interested in office hours. Or it's fine to come later. |
| Text | There will be three main sources for the course. All three are available for free online, either from the library or on my website. Links are provided here. Björner and Brenti, Combinatorics of Coxeter groups. Humphreys, Coxeter groups and reflection groups. Reading, Chapters 9-10 of Lattice Theory: Special Topics and Applications, Volume 2. The Björner and Brenti book covers the topics that we will focus on. The Humphreys book develops the theory of Coxeter groups more fully and will particularly useful for the student who wants a more complete geometric treatment. The other source is some book chapters that I wrote. There are also many other good books out there which cover Coxeter groups from different points of view. |
| 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 Monday, May 4, 8:30-11:00. 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. |
| 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 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 that 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.)
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| NCSU Counseling center |
As a student you may experience a range of personal issues that can impede learning, such as strained relationships, increased anxiety, alcohol/drug concerns, feeling down, difficulty concentrating and/or lack of motivation. These concerns or stressful events may lead to diminished academic performance and may impact your ability to participate in daily activities. It is very important that you have a support system and that you ask for help when you are struggling. The Counseling Center at NC State offers confidential services for full time NC State students, including same-day emergency services and telehealth counseling services. 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. |