#### Reflection Groups & Coxeter Groups

When doing your homework, I encourage you to use the Elements of Style for Proofs as a reference. **Note:** On each homework assignment, please write (i) your name, (ii) name of course, and (iii) Daily/Weekly Homework number.

### Daily Homework

The following assignments are to be turned in at the end of the indicated class period. I reserve the right to modify the assignment if the need arises. These exercises will form the basis of the student-led presentations each day. Daily assignments will be graded on a $\checkmark$-system. During class, **you are only allowed to annotate your homework using the marker pens that I provide**.

**Daily Homework 1:**Read the syllabus and write down 5 important items.*Note:*All of the test dates only count as one item. Turn in on your own paper at the beginning of class. (Due Thursday, Jan 15)**Daily Homework 2:**Stop by my office (AMB 176) and say hello. If I’m not there, just slide note under my door saying you stopped by. (Due Friday, Jan 16 by 5PM)**Daily Homework 3:**Complete problems found here. (Due Thursday, Jan 15)**Daily Homework 4:**Complete problems found here. (Due Tuesday, Jan 20)**Daily Homework 5:**Complete problems found here. (Due Thursday, Jan 22)**Daily Homework 6:**Complete problems found here. (Due Tuesday, Jan 27)**Daily Homework 7:**Complete problems found here. (Due Thursday, Jan 28)**Daily Homework 8:**Complete problems found here. (Due Tuesday, Feb 3)**Daily Homework 9:**Complete problems found here.*Note:*You can skip the first problem. I’ll put it on the next homework assignment. (Due Thursday, Feb 5)**Daily Homework 10:**Complete problems found here. (Due Tuesday, Feb 10)**Daily Homework 11:**Complete problems found here. (Due Thursday, Feb 12)**Daily Homework 12:**Complete problems found here. (Due Tuesday, Feb 17)**Daily Homework 13:**Complete problems found here. (Due Tuesday, Feb 24)**Daily Homework 14:**Complete problems found here. (Due Thursday, Feb 26)**Daily Homework 15:**Complete problems found here. (Due Tuesday, Mar 2)**Daily Homework 16:**Complete problems found here. (Due Thursday, Mar 4)**Daily Homework 17:**Complete problems found here. (Due Tuesday, Mar 9)**Daily Homework 18:**Complete problems found here. (Due Thursday, Mar 11)**Daily Homework 19:**Complete problems found here. Check out Andrew’s model of the Coxeter system of type $A_3$ on the tetrahedron. (Due Tuesday, Mar 24)**Daily Homework 20:**Complete problems found here. (Due Thursday, Mar 26)**Daily Homework 21:**Complete problems found here. (Due Tuesday, Mar 31)**Daily Homework 22:**Complete problems found here. (Due Thursday, April 2)**Daily Homework 23:**Complete problems found here. (Due Thursday, April 9)**Daily Homework 24:**Complete problems found here. (Due Tuesday, April 14)**Daily Homework 25:**Complete problems found here. You can skip Problem 2 for now. I’ll tack it onto the next assignment. (Due Thursday, April 16)**Daily Homework 26:**Complete problems found here. (Due Tuesday, April 21)**Daily Homework 27:**Complete problems found here. (Due Tuesday, April 28)

### Weekly Homework

In addition to the Daily Homework, we will also have Weekly Homework assignments. For most of these assignments, you will be required to submit 2-3 formally written solutions/proofs. You are required to type your submission using $\LaTeX$ or Lyx (see below for more on this). I will walk you through how to do this.

**Weekly Homework 1:**Write up any two of Problems 1(a), 1(b), 2(c), 3(b) from Daily Homework 3. (Due by 5pm on Friday, Jan 23)**Weekly Homework 2:**Write up any two of Problem 4 from Daily Homework 4 or Problems 1(b)(c)(d), 3(b), 3(c)(d)(e) from Daily Homework 5. (Due by 5pm on Saturday, Jan 31)**Weekly Homework 3:**Write up any two of Problems 3 or 4 from Daily Homework 6 or Problem 1 from Daily Homework 7. (Due by 5pm on Saturday, Feb 7)**Weekly Homework 4:**Write up both parts (simple and positive) of Problem 3 from Daily Homework 8. (Due by 5pm on Saturday, Feb 14)**Weekly Homework 5:**Write up any two of Problem 1 from Daily Homework 10, Problems 1 or 2 from Daily Homework 11, or Problems 1, 2(a), or 2(b) from Daily Homework 12. (Due by 5pm on Saturday, Feb 28)**Weekly Homework 6:**Write up both Problem 2 from Daily Homework 13 and Problem 2 from Daily Homework 14. (Due by 5pm on Saturday, Mar 7)**Weekly Homework 7:**Write up both Problem 3 from Daily Homework 15 and Problem 2 from Daily Homework 16. (Due by 5pm on Friday, Mar 12)**Weekly Homework 8:**Write up both Problem 1 from Daily Homework 17 and Problem 2 from Daily Homework 18. (Due by 5pm on Saturday, Mar 28)**Weekly Homework 9:**Write up both Problem 2 from Daily Homework 19 and Problem 2 from Daily Homework 20. For the second problem, be sure to show sufficient justification. (Due by 5pm on Saturday, April 4)**Weekly Homework 10:**Write up either Problem 1 from Daily Homework 22 or Problem 1 from Daily Homework 23. (Due by 5pm on Saturday, April 18)**Weekly Homework 11:**Last one! Write up both Problem 2 from Daily Homework 24 and Problem 1 from Daily Homework 25. (Due by 5pm on Saturday, April 25)

You are required to use $\LaTeX$ or Lyx to type up your Weekly Homework assignments. To do this, I suggest that you use my LaTeX Homework Template, but you do not have to. The easiest way to get started with $\LaTeX$ is to use an online editor. I recommend using Overleaf or the Sage Math Cloud, but there are other options. The good folks over at Overleaf have preloaded my template, so to get started, all you need to do is click the link below.