1. Due Tue. 10/24: Shift Operators and Circulant Matrices

Homework 1 (LaTeX).
2. Due Tue. 10/31: Characters

Homework 2 (LaTeX).
3. Due Tue. 11/7: Random Walks

Homework 3 (LaTeX).
Note: You may work on and submit this assignment with up to two classmates. Just make sure all of your names are on the submission.
4. Due Tue. 11/14: DFTs

Homework 4 (LaTeX).
Note: You may work on and submit this assignment with up to two classmates. Just make sure all of your names are on the submission.
5. Due Tue. 11/21: Idempotents

Homework 5 (LaTeX).
Note: You may work on and submit this assignment with up to two classmates. Just make sure all of your names are on the submission.
6. Due Wed. 12/13: Final Paper
Write a 46 page paper on something related to finite Fourier analysis that is of interest to you. Your paper can be completely expository in nature, it can focus solely on original research you have done, or it can be some combination of expository and original work. Your paper should (1) be wellmotivated, (2) go beyond the foundational material we have encountered in class, (3) include references, images, tables, etc., when appropriate, and (4) be written so that your classmates can easily read and understand it.
This assignment is designed to free you up to delve deeply into a topic that you personally find intriguing. There will be no additional homework for the rest of the course so that you can spend a good amount of quality time researching ideas and writing your paper. You will want to start your paper early, though, and you will be expected to meet with me at least once outside of class for about 20 minutes to discuss the progress you are making on your paper. I will say more about these meetings in class.
In case you are struggling to find a topic for you paper, here are some topics you might enjoy exploring: the Uncertainty Principle, image processing, signal processing, random walks on groups, fast polynomial multiplication, fast matrix multiplication, Rader's FFT, Bluestein's FFT, decimationinfrequency FFTs, the Chirp Ztransform, FFTs for finite groups, adapted bases, harmonic analysis on continuous groups, and connections to fields such as chemistry, physics, and computer science.
A PDF copy of your paper is due via email at 5:00 PM on Wednesday, December 13.