The grades include writing a final paper. This will be an expository article of no less than five and no more than ten pages that you’ll prepare on a topic related to material in the course and your own interests. Here’s how it will work:
When there are six weeks (or so) left in the term, I’ll talk about a possible topic with you. I’ll try to match topics to students based on their own interests, and will give you pointers to the literature. Here are some possibilities.
You will research these topics outside of class and start to prepare a draft. You can ask me for advice if you need help. As an example of what kind of writing I have in mind, you can consult my TWIGS talks. These papers are on the short side, since the talks were only an hour. You could pretend that you have two hours to give a lecture, and write up notes from that.
A draft of your paper should be completed within three weeks (a deadline will be given later), which you will submit to me. I will read these drafts and make comments.
You’ll get the draft back as soon as possible, hopefully with lots of comments, which you should not take personally. You will address the comments and prepare a new draft. I will give you even more nitpicky and annoying comments, and so forth. It might take a few iterations. Then you will prepare and submit a final version.
Any kind of writing is challenging, and writing mathematics poses its own challenges. It’s rare for a graduate student to get detailed feedback on writing before his or her thesis, but I feel that such feedback would have been extremely helpful to me. This should be a good opportunity for you to get some. Also, students in the past have been enthusiastic about this writing assignment, even though it’s a lot of work and is not without a certain amount of pain.
For more information about writing and mathematical writing in particular, you can consult the following:
Mathematical writing, by Don Knuth, Tracy Larrabee, and Paul M. Roberts.
Tips for authors by James Milne.
Goss’s writeup of J.-P. Serre’s Hints on mathematical style.
MIT has a writing requirement for its undergraduates, and Steve Kleiman has prepared an excellent introduction to writing short mathematical papers.