Optionally, you may complete a final project in lieu of writing the final exam. The project consists of two parts: (i) a talk, and (ii) a short paper covering the same material. The talk should be a presentation on a topic related to the content of the course; some potential topics are listed below. Your talk should be both accessible and interesting to your fellow classmates; in particular, it should not assume background beyone what is in the course, and should provide some new content. The written report should be on the same topic, and include any import details you are unable to fit in your presentation.
Your presentation may be given alone, or with up to three other students. The total length of the talk should be 10 minutes per group member, plus 10 minutes (so 20 minutes for a solo talk, 50 for a group of four). Each member of your group should lead the presentation for roughly an equal portion of this time.
The technical level of your presentation should be comparable to lecture: your classmates should be able to follow along for its entirety. It should also be well rehearsed, and in particular neither too long nor too short. You do not need to provide a proof of every result you mention, but you should (each) explicitly prove at least one non-trivial result, and give a brief indication of the idea behind any proof you omit. It is a very good idea to practice presenting in front of someone else who can give you feedback before your official presentation.
Your presentation must include a visual component. This may be prepared slides (beamer, powerpoint, ...), live-writing on a tablet or with a document camera, or something else reasonable.
The written report should be typed (preferably in $\LaTeX$, but any software which can accommodate mathematical formulae is acceptable), and should be 1-5 pages single spaced with 11-12 point font and 1 inch margins (explicitly this is 1-5, not 4-5; you should not feel the need to pad if you have said everything you feel needs to be said). The report should be a stand-alone work in the sense that it discusses any preliminary ideas or concepts which have not been covered in lecture, as well as providing all relevant definitions and proofs, even those which you omitted from your presentation. One of your peers should be able to read it and understand the ideas as well as if they had attended your presentation. You are welcome and encouraged to include additional examples of related concepts or other interesting things you were unable to say due to time constraints. The report should cover at least the content of your presentation; moreover, you should include some expository text both to aid the flow of the report and to help supply intuition. Your report should not be simply a list of definitions, theorems, and proofs (although it should contain those).
Even if you choose to work with others, you must write your own report independently.
The following deadlines are in effect if you choose to give a presentation:
Presentation scheduling will be addressed once I know how may presentations there are to schedule. My intent is to scheduling everything during the exam period and the final lecture, though if many people want to give presentations scheduling during additional times may become necessary. (Last term, many people asked to present during RRR week; some such arrangement might be possible again this term. Although I might make this option available, I will not schedule anyone who does not explicitly ask for it during RRR week.)
Since it is not fun to deliver a talk to an empty audience, if you elect to give a talk, you will also be expected to attend the presentations of your peers; you are also free to invite your friends to your own talk.
The final report is due on Monday May 10th at 11:59 PM, and should be emailed to me directly.
If you wish you may give a talk for fun or for practice, but count the final exam towards your grade instead. It may be an opportunity to explore a fun topic, or get feedback on or practice with presentations. In this case your should make it clear to me that this is your intent when you pick your topic. Scheduling preference will be given to those presenting for credit, however.
Below are listed some sample topics, but you are also free to propose your own. Some of these have an obvious "main theorem" while others are more about a concept, which should be introduced along with some properties and discussion of what makes the concept interesting.
You will be graded on several aspects of the presentation. The rubrics by which you will be graded are available:
Your final grade in the course will then be computed by the following scheme:
| Homework | Midterm | Final exam | Final presentation | |
|---|---|---|---|---|
| Scheme talk: | 30% | 30% | 0% | 40% |