This course is going to be online this semester, so we're going to do things a little differently than in the past. Recent instructors have emphasized the communication aspect and have required a number of oral presentations from each student over the course of the semester. I don't think that is practical under the circumstances, so here is what I would like to do: I want to give you some experience dealing with research, so every other Wednesday, starting with Jan 13, I'm going to pose a problem that will be more difficult than you are used to, but which some of you can make progress on and maybe even solve. I'd like you to write up a solution or attempted solution, warts and all, and submit that two weeks after the problem is sent out. I'm going to grade that on effort and clarity of presentation. In the off weeks I will post hints.

In parallel with the biweekly mini-research questions, I want you to think about a math topic that you can write a 12 page paper on. You can make this an expository paper, proving you understand some subject in math that perhaps you did not previously. This paper would be supported by references from the literature and graded on clarity of presentation. Or you can team up with another professor and help them with their research or ask them to guide you doing your own research. The standard for grading would be the same, but I would like to see this option rather than the expository one. To keep the level of difficulty appropriate, I would like you to settle on a topic and run it by me in week three, then give me a status report during week six, another status report during week ten, a first draft by week twelve, and a final draft during week sixteen. Final grade will be 75% final paper and 25% biweekly "research problems".