Hi everyone,
I’m gradually reading through everyone’s registration, and the numbers are large enough that it’s going to take me some time to do this (and put people into groups). I’m done for tonight, and I’m through 453 of them. But I may as well take advantage of this time to also give a few thoughts before things get fully underway.
(1) One question to throw out there: when I put people into group (who aren’t already coming as a group), it makes sense for me to group people at similar levels who are in the same university, or national educational system, or geographical region. Except maybe that’s not wise —having some random people from the same university thrown together may not be ideal. I’m really not sure, and things will be pretty random, but I am open to suggestions (as long as you are open to my not taking your suggestions.)
(2) The group of you is very diverse — what you know and what you want to know varies hugely. So what to do? I know the number of participants will drop quickly once we get going, and people realize that they do not have the background to enjoy it, or the time to enjoy it. But I don’t like the idea of being unwelcoming, and I know that people unused to this sort of thinking may feel that I’m being deliberately obtuse and needlessly forbidding.
One of the most important things while learning is to know why you care. Someone else can tell you why you should care, or at least why they think you should care, but you should not take what they say on faith.
The problem with this project is that at the outset, I’ll have to assume that you already know why you care. This is bad for a first course, which is why I do not recommend this as a motivating first course in the subject. I don’t mean that you need to have taken a course in algebraic geometry per se — you just need to know enough to know why you might desperately want to learn about it. Very many of you know why you care (and your reasons are appropriately not varied). To the rest of you — I deeply apologize.
Math 216: Foundations of Algebraic Geometry 
May 21, 2020 at 12:57 am
So I guess I’d say grouping people from the same region is a very good idea (because of time zones etc) but possibly grouping people from differerent universities is a good idea as it allows a kind of ‘networking’.
With regards to your apology for being ‘unwelcoming’ I would say don’t be so hard on yourself – most people will appreciate that you ran this course in the first place, in fact doing so is by all means the opposite of being forbidding for anyone who has so much as glanced at Hartshorne’s work!
May 21, 2020 at 6:25 am
Scale requires flexibility. You could make this largely self-organizing: people walk into and out of groups, (or moderators do this upon request,) while you only set the criteria for the groups. This is less work, and also more robust and flexible. It handles people dropping out according to what someone humorously called “the law of diminishing returns”, as well as people who want to join their friends, etc.
You may have thought of a way to match expertise and motivation levels, while keeping group sizes to optimal levels. If some of these criteria are made explicit as group descriptions or rules, people can read that and re-sort themselves.
MOOCs do fine with a flat structure and possibly a common place for questions/comments. It’s hard to go wrong.
May 21, 2020 at 8:19 am
Another echo of what Will said: I know a few students from my university were considering signing up for this and I would be fine/happy working with them even though we didn’t coordinate well. People will have the option to leave or (perhaps with the help of Discord) find a new group to become a part of. I think that a cluster from the same university should probably not comprise over half of the group, however, as that would begin to feel unwelcoming to the odd students out.
May 21, 2020 at 4:04 pm
Sir, I think it would be a good decision to put students of nearly similar mathematical background in one group. Then mathematical communication among group people will be more convenient. Difficulty of topics and problems will nearly same for all group members, which will help, I think.
Thanks again for organizing this course for students all over the world.
Regards
May 21, 2020 at 6:34 pm
I second Anand V’s suggestion. Perhaps you can create the first n groups based on certain criteria and let people join them as they will; while at the same time allow the possibility, at least for the first few weeks, to create new groups. This will minimize your work and allow people to settle into a group on their own without having to conform to any prior notion of what sort of membership ought to make sense for them.
May 22, 2020 at 3:10 pm
I think the simplest way to solve problem (2) is to appoint group-of-groups leaders and let participants reach out to them directly if their group isn’t a fit.
These leaders just need to be organized and good communicators, not necessarily the most senior AG experts (who probably have less free time anyway).
Thanks!
May 23, 2020 at 7:32 pm
useful ideas sent by a participant by email:
Hi Professor Vakil – I would urge you to reconsider putting people in groups by common university, age, or geographic location. This is a course that we are taking for the sheer pleasure of learning the subject (we know it is a hard course and we are willing to work hard at it.) But my point is that meeting new people from different walks of life, different regions (and different countries, too) who all share a desire to learn this amazing subject together is going to be a big part of what keeps us motivated. It would be a pity to just mimic a standard college environment. We would be missing one of the coolest features of online group learning.
Yes, it makes sense to try to have people with roughly the same background in algebraic geometry specifically. But beyond that, mix it up a bit! I would even suggest you not worry about time zones even. After all, nighttime on the east coast is morning in Asia so we students should be able to figure it out within our group.
Thank you for all you are doing! Please take care of yourself and don’t burn out in the preparation phase of this course. I can only imagine how much work it must be to organize a course for 1000+ students.
May 23, 2020 at 7:36 pm
Some wise ideas above! I’m currently intending that only people in the group (plus group-leaders and group-leader-leaders) can see group discussion, so people feel more comfortable asking questions or making comments that they fear might be considered “stupid”. (The fear of “asking stupid questions” is something that takes practice in breaking.) But Paul’s idea of having group-of-group leaders be people who can swap people around is particularly good, because I’d like the groups in a group-of-groups to be, to first order, somewhat similar.