Final Project
The goal for the final project is for you to learn about some piece of number theory that we didn’t talk about in class.
Instructions
Form a group of about 2–4 and choose a topic that’s related to course material but that we did not cover. There are many possibilities! You might look through [Nee] for some inspiration (eg, 1.IV, 2.VIII, 3.I.2, 3.VI–IX, 5.IX–XI, 6.I–III, 7.II–VII, 10–12…). You could look into the Riemann zeta function. You could look into the Riemann mapping theorem and Schwarz-Christoffel mappings. You could look into an application of complex analysis to a field of your choosing (the sections in [Nee] listed above include some sections on applications to physics). You don’t have to choose something I’ve listed here — try looking around yourself a bit! Just make sure that your topic involves a “substantial” application of the ideas we’ve discussed.
During week 3, you’ll be asked to submit a proposal. All you have to do for this is tell me who you’ll be working with and what you’re planning on doing. Submit it through gradescope as a group submission by following these instructions.
Write up a document in which you give a brief exposition of the topic. It should be written in LaTeX. The length is flexible (somewhere in the whereabouts of 3 pages might be reasonable). Make sure to give clear definitions of any new terms. If there’s a theorem involved whose proof is too long or hard, you can omit the proof and just provide the statement. Write in a way that a fellow classmate would be able to understand what you’ve written, and make sure to cite your sources. Submit the document through gradescope as a group submission by following these instructions.
Prepare an informal and brief (10ish minutes) presentation about your topic for your class. It can take any format you like (slides, chalk talk, etc). Just make sure everyone in your group is involved in presenting.
Grading
Your project will be graded out of 20 points, as follows.
- (10 points) Mathematical content. For full credit, make sure that there’s some substantial mathematical content to whatever you do.
- (5 points) Exposition. For full credit, write up your exposition clearly and precisely, in a way that’s easy to follow. Make sure to cite your references too.
- (5 points) Presentation. For full credit, your presentation should clearly express the main ideas of what you studied.