1) find a topic for your in-class presentation (plan for 25-30 minutes).
Next week I'd like to start scheduling the presentations and approving the chosen topics. (The presentations themselves will start in a couple of weeks). Bonus points for going in the first week. I would like to see each presentation outside of class a few days before it is given in class. I will schedule some times to do that. Other students are welcome to watch these practice talks too.
There are some suggested topics on the course web page.
2) Start thinking about a topic for your final paper. This can be related to your presentation.
The paper will be due at the beginning of final exam period for the term. Within a few weeks I'd like to have approved a topic for each person or group. I encourage you to have a draft ready earlier than that, so I can read it and give you feedback for the final version. A group of people can write a paper together, in which case each person should contribute 6-10 pages worth, and I should know who contributed what. If some sections are worked on by more than one person, that's okay, but one person should be responsible for each section. (That section will be what they are graded on.)
3) Proofs groups. I put some problems and advice for the proofs groups up at:
Please schedule a regular time and place in the beginning of each week to meet with your group. I suggest that each person in the group choose a different problem to think about and present to the group at the group meeting. The presentation can be at the board, with grilling by the group members until all group members understand, or it can be written, in which case a couple of the other group members should read the written part and give feedback about what's clear and what's not. In this case (written proofs) the exchange can take place outside the meeting (e.g. by email) too.
I will find a time and place towards the end of each week for the groups to mix and present to each other highlights of what they did that week. Probably, I will ask people to split into pairs (two people from different study groups) and have each person present to the other (orally) something that someone else in their study group presented to them (either orally or in writing) earlier in the week.