You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Joe Moeller (Jun 03 2020 at 19:31):There's an idea I've been kicking around for a few weeks that I guess I should air out here and now. I would like to organize a sort of seminar to happen during this summer to be recorded and put on YouTube, where people take turns giving an excellent introduction/lesson on some topic in CT.
Joe Moeller (Jun 03 2020 at 19:33):I think it would be great to get people involved that are known for giving great explanations of things.
Joe Moeller (Jun 03 2020 at 19:33):I guess I'd have to hear interest in such an event to get the energy to put it together though.
John Baez (Jun 03 2020 at 19:34):That's a great idea. I will be glad to advertise it, and I'd be glad to give one talk, but only if other people actually run it.
It would be good to decide on a "level".
John Baez (Jun 03 2020 at 19:34):I would recommend very basic CT.
John Baez (Jun 03 2020 at 19:35):That way a lot of good people could quite easily prepare talks, and LOTS more people could benefit than if you did something at a higher level.
Joe Moeller (Jun 03 2020 at 19:35):I think there could be various levels, but definitely skewed towards basic CT
Joe Moeller (Jun 03 2020 at 19:35):Right, this is precisely what I was thinking.
John Baez (Jun 03 2020 at 19:35):I think it would work best if people of a given level could understand all the talks, not just some. It's discouraging to hit a talk that's a lot harder than the last one.
John Baez (Jun 03 2020 at 19:36):So, I'm recommending that you choose a level and choose speakers who understand the concept of explaining things to people who know X and Y but not Z or W.
Joe Moeller (Jun 03 2020 at 19:37):Yes, I guess what I meant by various levels is that I could imagine a lesson about something which is considered medium/advanced, but which starts at the basic level and works up to the advanced ideas.
John Baez (Jun 03 2020 at 19:37):You could probably get the original Catsters to contribute talks.
John Baez (Jun 03 2020 at 19:38):Anyway, I think you'll either need to run the show yourself or get a committed partner to help you run it. Either way, if you did it right you'd become "famous" in a useful way.
Alexander Kurz (Jun 03 2020 at 19:38):What about getting ambitious and try a series of CT for high-schoolers. Aimed at students who liked math at school, but did not have done university level math.
Alexander Kurz (Jun 03 2020 at 19:39):Accessible to, say, last year of high-school, but useful also to early undergraduates.
Joe Moeller (Jun 03 2020 at 19:39):That is ambitious, but maybe possible.
Joe Moeller (Jun 03 2020 at 19:40):I did include this here since we were just talking about teaching CT.
Alexander Kurz (Jun 03 2020 at 19:40):I agree, I am not sure it is possible. But imagine young maths students starting their university already knowing about category theory ... that could be a real booth ...
Jules Hedges (Jun 03 2020 at 19:41):Also remember standards in schools vary pretty widely around the world. At least where I am, most school graduates don't have a clear idea of what a set or a function is for example
Alexander Kurz (Jun 03 2020 at 19:41):Jules, I agree, we couldnt assume knowledge about sets and functions
Joe Moeller (Jun 03 2020 at 19:41):Perhaps an ideal we could shoot for is like the first third should be understandable by HS students, the middle by undergrads, and the end by grads.
Jules Hedges (Jun 03 2020 at 19:42):You can probably get some mileage by just replacing the phrase "a set of X" with "a bunch of X"
Alexander Kurz (Jun 03 2020 at 19:42):yes, we dont need to be too formal ...
Joe Moeller (Jun 03 2020 at 19:43):Right, the aim should be that a person who is trying to learn some math by watching youtube videos could learn something.
Alexander Kurz (Jun 03 2020 at 19:45):Joe, yes, a sequence would be good, but I would start with HS without committing to the other stages to do in the same summer ... alternatively we could start with grads and work backwards ...
Joe Moeller (Jun 03 2020 at 19:45):Oh, I meant within a single video.
Alexander Kurz (Jun 03 2020 at 19:46):but watching a video is not enough ... if you like the video you want something to work on as well ... could we integrate some exercises and research projects as well?
Joe Moeller (Jun 03 2020 at 19:46):Alternatively, videos could be organized by advancedness via playlists once they get to youtube.
Joe Moeller (Jun 03 2020 at 19:46):yes, that would be very cool.
Alexander Kurz (Jun 03 2020 at 19:50):I also like to make students think as if they did do research. Instead of lecturing them on a topic, start with a research problem and make them discover the maths on the journey. A problem with this is that this format does not translate well into videos, afaik.
Tomáš Gonda (Jun 03 2020 at 20:02):3blue1Brown had a cool series of videos of similar kind recently. Of course, resources available to a YT channel with ~3M subscribers are way out of reach, but there may be some things to learn there.
Alexander Kurz (Jun 03 2020 at 20:24):Yes, 3Blue1Brown is great ... but no way I could do this, not sure how much he takes to make 1 video, but I know that I dont have this amount of time. And if I tried this I would probably need 10x as much time as it takes him.
Joe Moeller (Jun 03 2020 at 20:27):This is partially why I would want to distribute the lessons across several people.
Joe Moeller (Jun 03 2020 at 20:28):I can't pay someone what they deserve to teach a university course :laughter_tears:
Joe Moeller (Jun 03 2020 at 20:28):The other part is that getting a variety of perspectives would be helpful to people learning the ropes.
John Baez (Jun 03 2020 at 20:29):I think you can get a bunch of good people to each give one stand-alone short lecture, like less than an hour, just out of the goodness of their heart.
Eigil Rischel (Jun 25 2020 at 08:35):About teaching basic CT to highschoolers: I used to help organize an annual math summer camp for (the Danish equivalent of ) high school students. A few years ago we did a basic CT course. I would have to dig a bit to find the material (which is written in Danish, anyways), but as I recall we managed to cover categories, functors, products and coproducts (and maybe some other stuff - it's been a while)
The hardest thing was probably to come up with a large stock of examples, since most of the "basic" examples we take for granted (groups, rings, linear algebra, topological things) are things people usually don't meet until university.
I think they managed to absorb quite a bit of the material. They weren't exactly median highschoolers (they had to apply to go to a math camp, and then choose the category theory course over another course), but I don't think they were exceptional, as a class, either. And I think even some of the weaker students managed to get something out of it.
(=_=) (Jun 25 2020 at 08:58):Eigil Rischel said:
I would have to dig a bit to find the material (which is written in Danish, anyways)
Sounds great! These days, Google Translate works fine for a quick skim, and I wouldn't mind a linguistic challenge.
The hardest thing was probably to come up with a large stock of examples, since most of the "basic" examples we take for granted (groups, rings, linear algebra, topological things) are things people usually don't meet until university.
I think that's probably the most valuable part of the material.
Todd Schmid (he/they) (Jul 06 2020 at 07:57):Sounds great. Where do I sign up?