You are expected to read and comment on some readings prior to attending class. We will use an online forum called Perusall for posting your comments. You should always post at least one comment, ideally more. Your comments should be posted by 7pm Eastern time the day before lecture. The instructions I post on Perusall will indicate what I'd like you to focus on as you do your reading. Typically, there will be a few pages of required reading corresponding to the course lecture notes, and then longer extracts from the textbooks that are optional reading to be used according to your interest and needs.
Here are some examples of things to think about when reading and commenting:
What would you like us to spend more time on in our class meetings?
What points did you find most interesting? most confusing?
What are the key notions and concepts introduced (in both high-level and technical terms)? Why are particular choices made in the definitions? What would happen if things were defined differently?
What are the main results? How would you describe the conceptual messages underlying the formal mathematical statements?
Why are the results interesting (or not)? How could they possibly be improved?
What are the possible connections or relevance to anything else you have seen (outside this course)?
If we ask you to understand a theorem statement or a proof, do you understand it at both a high level and technical level? How would you explain it at both levels?
What interesting questions does the material bring to mind (not just the explicitly stated open problems)?
How would you draw a picture to illustrate what's happening in a particular construction?
Note that Perusall allows you to post comments anonymously, meaning that other students in the class won't see your name attached to the comment (but the teaching staff will). If you don't feel comfortable making a particular comment on Perusall at all, you can also post on Piazza as a private message to the course staff.
The point of having you read and comment in advance is to make our class meetings as effective and interactive as possible. We can avoid spending time on material that is easier for you all to learn on your own, and focus our attention on the aspects that you all found more confusing and/or interesting. In addition, rather than always lecturing, I will often ask one of you to recall a concept, definition, or proof idea, and ask questions like those listed above. The goal is for class to feel like a collaborative effort to understand and explore the material, so expressing your confusions is just as important a contribution as giving a correct explanation. I hope that everyone will become an active and comfortable participant and by the end of the course, you will all feel well-equipped to learn a subject like this on your own.
We will also use the Ed platform for discussions that are not specific to the readings, for example about problem sets, projects, etc. One of the highlights during the Fall 2020 Zoom-only offering of the course was the continuous discussion happening in the Zoom chat during lecture; I encourage you all to use Ed for the same, in addition to participating orally by raising your hand.