How the Course Is Going 1

John Baez · April 2018

Here are some thoughts on how the course is going so far. I'd like to hear your thoughts too!

I've registered about 250 people so far. Of these, only a small fraction are doing exercises, solving puzzles and joining discussions. I'd love to get more participation, but on the other hand I'm plenty busy keeping up with the conversations already!

I really need you folks to start discussions like this, where you state one of the Exercises in the book. Then other people can add solutions and discuss them. I can't keep doing all this work. I think my job should be to comment on the solutions.

Let me talk about the pace of the course.

I plan to finish giving lectures around September 25th. Since there are are 7 chapters, that's about 25 days per chapter. The later chapters are harder so maybe they deserve more time. On the other hand, maybe it pays to start slow. I'll aim to finish lectures on Chapter 1 between April 11th and 18th.

One student, Matthew Johnson, had some concerns about the pace of the course:

Hi John,

I really appreciate you running the Applied Category Theory course. It is an incredible opportunity! Thank you!

I also want to let you know that I am finding the pace of the course to be a little too fast at this point. With so many active participants I am just barely able to keep up with the reading and am not finding much time to work the exercises on my own. I know one of the other participants personally and he is also feeling like it’s been hard to keep up.

In my cases this experience is partly because I work full time and also have a 3 year old to keep up with. I’m not necessarily asking you to change anything. I just thought you might like to know that the at least some of us are having trouble with the pace. I intend to get the most I can out of the course in the time I have available regardless!

I replied:

Thanks for letting me know. Since I have until September 25th to cover 7 chapters, I'd been imagining about 3 weeks per chapter. However, there's no need for anyone to work at a certain pace. I'm not planning to close down the website or stop people from asking questions after September 25; I'll just need to quit giving "lectures".

So, it's fine to "lag behind". If you do, and if I manage to lead the course successfully, most of the puzzles and exercises will have worked-out answers online by the time you get to them. But that's not a bad thing - it means you'll be able to check your answers.

There's also no need to keep up with all the comments being generated by the students. Right now they (and I) are exploring various issues in Chapter 1, just wrapping their heads around them.

I think it would be better to discuss these issues publicly, on the forum, so people can compare their experiences. Do you mind if I copy your message and my reply over there?

And he said yes. He also said:

I am hoping to participate in the discussion along the way as I think I would learn the most that way. That said, I’ll try not to feel too bad if much of the discussion moves ahead - as you point out I can always check my answers against what has been posted already.

I understand all of the material that has been presented thus far, I just haven’t been able to work most of the exercises yet which will deepen and strengthen that’s understanding and probably lead to some questions! In fact, I have already run across a few questions which had already had answers in the discussion when I checked! This was great to see.

I study independently which works well for me much of the time but can be frustrating when I think I understand something correctly but am not fully confident in my understanding. I can already tell that this course will be a great avenue for removing that kind of doubt.

I would like to hear from the rest of you, too. Needless to say I can't make everyone happy, and suggestions that require me to do more work are likely to be met with a comment like "That sounds like a great idea! Why don't you organize some students to do it!" Nonetheless I want to get some sense of how things are going. Right now the course is just starting, so it's hard to tell. I'll be posting articles like this periodically to see how you feel as things develop.

Dan Schmidt · April 2018

I'm doing all the exercises (through 1.80 so far) although I haven't talked about them here. They are excellent for ensuring that I understand the material before moving on but I think that they may be too numerous and too simple (in general) to clog up the forums with a single post for each. (I'd be happy to be wrong!)

The discussions are of such a varied level that it can be difficult to jump into them. Often things will go off on an (interesting!) tangent that assumes some additional background knowledge to participate in. So I've been relatively quiet so far, but I am working assiduously through the book and plan to continue to keep up.

I'd love to see more discussions that start with "I don't quite understand topic X yet", which would both give me a reason to jump in more (trying to explain things is a great way of learning them) and demonstrate to everyone that it's okay to struggle with the material a bit.

Vishal Lama · April 2018

My family is in the middle of moving to our new house, and so, that leaves me with very little time to participate in the discussions, right now. In about a week, I will be participating much more frequently and vigorously!

I think the pace of the course is just fine thus far. I do think the pace should be somewhat slow in the beginning. This will ensure that a significant majority of participants are firmly grounded in the basics, which in turn will allow us to go through the later advanced material at a relatively fast pace, especially if we keep in mind the progression of difficulty of material as mentioned by the authors in the Preface (page iv.)

John Baez · April 2018

Dan wrote:

I'm doing all the exercises (through 1.80 so far) although I haven't talked about them here. They are excellent for ensuring that I understand the material before moving on but I think that they may be too numerous and too simple (in general) to clog up the forums with a single post for each. (I'd be happy to be wrong!)

Elsewhere are are having a debate about whether to have these exercises be posts or put them on the Azimuth Wiki. The two exercises so far have been fairly worthwhile as posts, in part because they're covering topics that I haven't hit in the lectures. And in fact my lectures will always cover just a fraction of the stuff in the book... while expanding on the topics I find most important.

I'd love to see more discussions that start with "I don't quite understand topic X yet", which would both give me a reason to jump in more (trying to explain things is a great way of learning them) and demonstrate to everyone that it's okay to struggle with the material a bit.

I would love to see more like that too! Can you start a few? I suspect everyone is afraid to admit ignorance.

Maybe I need to start some discussions like this myself. But then the students may run home and say "Mom! My teacher doesn't know what he's doing!"

Dan Oneata · April 2018

Hello! I've added the statements of a few more exercises from the first chapter (4, 5, 12); I will add more in the following days. Regarding the course, I have enjoyed your lecture notes as they are short, clear and insightful – thank you! I also try to keep up with the forum discussions: they are very instructive, but it takes some time to internalize everything. I went through some of the puzzles you posted, but I just didn't post my solutions, as there were already good answers.

Nathan Pellegrin · April 2018

Between my job and family I will not have the time to work through all exercises with the level of attention that each deserves; add to that the fact that I tend to be a slow reader generally (especially in math) and you get a student in the slow lane. While the course will likely move faster than I can keep up with that is absolutely fine and i don't expect the course to slow down for me and I am used to that! For me it is absolutely the explore/exploit tradeoff - I will scan the book and comments knowing that I will not have enough time to engage all questions at the level I would like, so I look for those exercises and/or comment threads that seem to be in the sweet spot for yielding the most learning with a deeper dive.

John Baez · April 2018

That sounds good, Nathan.

As I mentioned, the website is not going away on September 25th, nor am I - at least, not voluntarily. So, if you have questions in a year from now, I should still be around to answer them - and I hope others will be around too.

If I like this enough, I may do another course next summer. But one year at a time! We're just getting started; I may get burnt out.

Vladislav Papayan · April 2018

John, thank you very much for the opportunity to join the course. In my view, it has been, sofar an incredibly useful investment of my time. The subject, the book, the quality of instruction and discussion, and your enthusiasm and energy exceeded my expectations, by a lot.

I am moving through the material very slow, compared to others. However, I do not find myself overwhelmed and forced to move forward, without grasping the material. The asynchronous nature of the forums, make it a bit more natural to stay behind, I guess :-).

For example, I just finished exercises just up till Chapter 1, exersize 3, and touched on some of your 'just-for-fun' problems (although, clearly, without much success).

It also really helped me read contributions/explanations by other students.

For example, I had difficult time understanding (and coming up with examples) of asymmetry property. But when somebody mentioned that it removes cycles -- all became clear, and so on.

So this 'mini-crowd-sourced' contribution of examples, clarifications, questions, etc -- to the studying pace is incredibly useful model to learn with, in my view.

If I may,I do have some suggestions/asks that I think would make consuming the material and participating easier.

A ) It would help if there would be a single page/cheat sheet of how to write formulas/charts and embed images into the posting (may be is there, but I just did not find it).) I tend to click on the gear-button to view other people's source and copy what I can,but that does not seem to work for many things.

B ) It may make your view of students progress more complete, if there is a way for you to poll (say, twice a week) your student audience, on where they are in terms of puzzles, lectures, etc. This way you get summary numbers and will help you to gauge your audience's progress. Not sure if Azimuth forum is already enabled with polling feature, or if external sites need to be used.

C) I personally would prefer to see puzzle area separated from the lecture area. (this way I can skip other student's answers, to form my own tries first..)

D) I do not know, that I clearly understand the distinction between Chapter and Lecture topics. It seems like lectures are 'within chapters'. But that's my own interpretation, not sure if that's correct.

It seems that I read your lecture, prior to me reading the chapter material in the book. In other words, I use 'online' material first, and then the book. Not sure if that's what's expected or not, but if you have in mind a particular sequence (or sequences) that you would like your students to follow, perhaps make that expectation explicit -- would help.

E) we do not have 'lab works', so to speak. But I see there a few folks who already have experience or experimenting with thigs like Coq (or Z3, my preference) provers. Perhaps, allowing to spawn like lab works where students can (if they choose to collaborate) on something in that area, and the present it to the larger group -- would add some additional value. I realize,that this is outside of the course's pace, but perhaps adding a way for students to have smaller groups of cooperation, would enrich the learning experience further.

Scott Finnie · April 2018

Adding my thanks too John: for your energy and patience as much as the simple understandability of your lectures & comments. The pace is at the upper end for me. I'm with Nathan in having limited time and being a slow reader of maths. I am, however, hugely enjoying it. It can be a little difficult to follow, with multiple active discussions on several topics$^{1}$. But that's a necessary consequence of differential pace. A picture might be useful to help navigate; something like this?

course structure

It's not complete, but already getting quite complicated. And the vertices could be hyperlinked direct to the relevant sections. This is the sort of thing that participants could perhaps contribute$^{2}$ - which would help with your time commitment.

$^{1}$ which means, I think, the topics form a poset (but not an order). Rationale: there are parallel topics but no loops - so reflexivity, transitivity and antisymmetry hold - but trichitomy doesn't.

$^{2}$ this particular diagram is generated using graphviz. The source is on github if anyone wants to help complete it.

Bob Haugen · April 2018

I may be the slowest student, but like some others, I get a lot out of the answers from other students. I particularly appreciate students like Scott Finnie who provide diagrams of real-world examples. They help me understand the mathematical abstractions.

The asynchronous nature of the class is necessary for me as for many many others. And likewse, how the class evolves from the interactions of the participants. I expect if we mapped the interactions between the students, John Baez, and the poset of topics diagrammed above, that we would see categorically amazing living structure emerge. (No, I don't know how to do that...)

But overall, I love this opportunity to learn category theory in this setting, from this teacher, with this set of students.

Michael Hong · April 2018

A ) It would help if there would be a single page/cheat sheet of how to write formulas/charts and embed images into the posting (may be is there, but I just did not find it).) I tend to click on the gear-button to view other people's source and copy what I can,but that does not seem to work for many things.

I agree with Vladislav Papayan. Very frustrating...

Fredrick Eisele · April 2018

As near as I can tell you recently switched to VanillaForums . It appears that many of the features are not enabled https://docs.vanillaforums.com/help/addons/advanced-editor/ I find myself spending way to much time trying to figure out how to post a comment. Forum - Guide seems like the right place to put this information.

I have updated that page with the items I would like to know how to do.

Jared Summers · April 2018

Re Pace: I think the pace is fine, especially if it'll work out to approximately 25 days per chapter. My primary issue (with commenting) is that most of my puzzle/exercise solutions are already presented and I have no immediate insights to give. That's not really a problem, it's good to see that I'm on track with everyone else.

Additionally, I'm slightly behind on the lectures (though I've read every one and their comments), because I've restarted the chapter. I read through chapter one fairly quickly with a quick attempt at each exercise (mentally or in the margins of my printout). I've restarted and am doing each exercise thoroughly and properly on paper, along with making notes about definitions and other things.

Re Comments: I will make a more deliberate effort to comment, but an issue there is I spend much of my time "on mobile". And dealing with the formatting of the math on mobile is a pain. So I read the book, check the forum, work some exercises. Make sure I'm on track more often than sitting down at the computer to write comments. I will try to set aside time every other evening to make comments, though. And (as noted above) I usually find the same answers I'd provide in the comments already, or the same insights. Like on the Just For Fun 1, Michael Hong had made the same binary tree note that I was going to but with additional information. Other than an, "I saw that too!", I had little to add.

Overall, I'm enjoying this course. Category theory is making more sense to me, though I'm still not at a point where I feel I could apply it. I'm optimistic I'll have more insights and a greater ability to study it and its applications in greater depth as this course progresses.

Michael Hurley · April 2018

at the moment it is a bit fast for me, but I am content to trail along at my own pace and not slow the whole group down. In addition to spending more time doing the exercises, I need to deeply familiarize myself with some of the jargon in order to get an intuition about the material. But that is coming along, so no complaints.

John Baez · April 2018

Vladimir wrote:

) It would help if there would be a single page/cheat sheet of how to write formulas/charts and embed images into the posting (may be is there, but I just did not find it).) I tend to click on the gear-button to view other people's source and copy what I can,but that does not seem to work for many things.

I urge all you students to start creating such a cheat sheet. Add material to Forum - Guide! We've got 200 people here, including at least 100 computer scientists and programmers, so it should be quick work. I'll just give a few high-level hints.

Writing math

The Azimuth Forum uses MathJax to display equations. MathJaX is a version of LaTeX designed for use on the web, limited in its power compared to full LaTeX. If you don't know LaTeX, you can't do math in the 21st century! No other method is as good at creating equations such as this one from the book:

$$ d(U,V) :=\sup_{u\in U}\inf_{v\in V}d(u,v) \qquad\qquad \mathcal{X}(U,V) :=\bigwedge_{u\in U}\bigvee_{v\in V}\mathcal{X}(u,v). $$ It takes a while to learn LaTeX: everyone serious about math must go through the pain of this. Here is a quick intro:

MathJax basic tutorial.

Unfortunately, a couple things on this tutorial don't apply here! Most importantly, as I mentioned on the welcome page:

For "displayed" equations, centered on the page, use double dollar signs: $$E = \sqrt{m^2 + p^2}$$ produces this: $$E = \sqrt{m^2 + p^2}$$

For "inline" equations, mixed in with your text, use this method: \$E = \sqrt{m^2 + p^2}\$ produces this: $E = \sqrt{m^2 + p^2}$.

Formatting

Unlike full-fledged LaTeX, MathJaX does not handle formatting outside equations. The Azimuth Forum runs on Vanilla, but not all the fancy features of Vanilla have been activated here.

To create italics, boldface, quoted passages numbered or itemized lists, subject headers, and the like, use Markdown. To include images you can also use HTML: for example,

<img src = "http://math.ucr.edu/home/baez/mathematical/7_sketches/exercise_1.2.png">

creates this:

This image is stored in my own personal website. If someone wants to create a Github site or other method for storing images to be used in this course, please go ahead and let us know about it!

Questions

If you don't know how to do something, and someone else does, the quickest solution is often to click on the little gear at upper right of each comment, and choose "View Source". Then you can see how they did it.

Every imaginable question about LaTeX has already been asked and answered here:

TeX - LaTeX Stack Exchange.

If you have specific technical questions about MathJax or Vanilla or Markdown, or other aspects of how the Azimuth Forum works, start a discussion in category Technical. Since we have a lot of experts on computer science here, someone here can probably answer your question.

Dave Tanzer set up the forum, and he's paying for it. But he doesn't have much time to manage it, or answer questions - nor do I. So please restrain your desire to perfect the environment and focus on learning math. If one of you wants to help run the forum, and has time to do it in a consistent way throughout the course, please volunteer!

Jacob MacDonald · April 2018

Unlike many of the folks here I don't have many commitments to explain my slow pace. So far just working on getting back into the rhythm of studying instead of skimming. It's fascinating material though so I plan on keeping up with the lectures and dropping in to ask questions and contribute what insights I can gather.

John Baez · April 2018

Jacob - sounds good! There's no rush to learn things here. I'm glad at least one person on the planet isn't claiming to be "too busy" to do things quickly.

John Baez · April 2018

Vladislav wrote:

It seems that I read your lecture, prior to reading the chapter material in the book. In other words, I use 'online' material first, and then the book. Not sure if that's what's expected or not, but if you have in mind a particular sequence (or sequences) that you would like your students to follow, perhaps make that expectation explicit -- would help.

Whatever you want to do is fine! I am trying to write the lectures in such a way that you can follow them without reading the book. And of course, the book was written in such a way that you can follow it without reading my lectures. I hope that having both available, and also giving people the ability to try Puzzles and discuss topics with each other in the Chapter posts, gives people many different ways to learn the material.

There is definitely a lot of material in the book that won't be in my lectures - especially all the Exercises, which contain a lot of good information. So, you can think of my lectures as a distilled version of the book that's strongly biased toward my own tastes.

If there's too much information to absorb all of it, I think it'll be easiest to just make sure you understand the Lectures. If you want to become an expert, you need to read the book.

Artur Grzesiak · April 2018

I find the course and community very inspiring and would like to say thank you for this rare opportunity. The material is extremely interesting. But to be honest I find a bit hard / overwhelming to participate actively and even follow all discussions.

The biggest limitation for me seems to be the medium / forum in which the course takes place. One problem is that within threads all comments are totally ordered - new comments go always to the end. I think having some form of partial order would be very helpful - ability to [recursively] comment on a particular comment. Maybe with more granularity of main threads it will get better. Another potentially helpful thing could be adding some order by voting on comments - so more helpful stuff would be more visible.

Again these are limitations of the platform itself and definitely I am going to follow the course and hopefully participate more.

Dan Schmidt · April 2018

Just a note to encourage people to do all the exercises. They are "simple" enough that if you can't do them, you probably don't totally understand the material, so they're a useful check. They also act as nice speed bumps to slow you down a bit, for people like me who tend to read too fast, nodding as they go, and then suddenly realize that they're lost. And you can check your answers against other people's responses here!

Ilmu Kalm · April 2018

Artur #18 I would be the counter-example because I prefer the forum this way.

Voting on posts detracts a lot from the quality of discussion in my opinion since people start being too self aware.

Regarding whether the forum is totally ordered on partially ordered it is actually the latter where each thread is totally ordered but if a thread grows out of hand it is always possible to move the discussion off into a new thread dedicated to that subject.

If we were 'internet scale' like reddit or something then these suggestions would be more justified but since there's only around 200 people registered and maybe half active there's no need.

Fredrick Eisele · April 2018

I am creating my drawings as google-drawings. "Publish"ing them produces a url which can be included in the discussion.

e.g.

Michael Hong · April 2018

Frederick Eisele

Thanks for the great info!

John Baez · April 2018

I wouldn't want people to vote on comments. I've gotten people signing up for the course saying they're glad to find an environment where they can learn stuff without the fear of looking stupid. I think voting on comments makes people focus on what other people think of them.

Some of other proposed improvements to the software sound good. Unfortunately I don't have time to look into them: I'm completely busy explaining math and correcting my own mistakes!

So, I think those improvements will come about iff some of you start talking to David Tanzer on the Technical thread, and impress him and me as being sufficiently reasonable, responsible, and technically competent to be given responsibility for improving the forum software. Such a person would need to seek consensus for changes before making them.

The kind of feedback that's easier for me to take advantage of concerns the subject matter and how the course is taught: the balance between math and applications, the pace of the course, how to bring more people into making comments, etc.

Andrew Ardill · April 2018

Still reading through the backlog here, and have almost finished chapter 1 and exercises.

One thing that has come to mind is that it would be nice to have a link between each lecture/set of puzzles. So a reading order, and for each post a link to the previous and next thing to read. Would that be easy to do without adding too much overhead?

The main reason for this is that looking at the default board view it's not necessarily obvious what I should look at next. Many people won't be able to read every conversation either, and if you're not able to follow as the conversation goes (say you're away for a week or more) then being able to jump back in to where you left off would be nice.

An alternative would be an index, perhaps on the wiki page or stickied to the top of the board, and it would probably be nice to have both!

John Baez · April 2018

Andrew Ardill - it would add some extra work to make these links each time. Perhaps a less tiring solution is for me to add links saying

[Applied Category Theory - Course](http://www.azimuthproject.org/azimuth/show/Applied+Category+Theory#Course)

Try going there:

Applied Category Theory - Course.

This page on the Azimuth Wiki will give you the information you want, at least if we update this page often enough! Please help out - we could use links to all the "exercises".

Valter Sorana · April 2018

@AndrewArdill: you may find this page useful: http://www.azimuthproject.org/azimuth/show/Applied Category Theory

Vladislav Papayan · April 2018

@AndrewArdill #24.

WRT exercise numbering. There is a scheme that is being used.

(1) There are book exercises.
(2) There are puzzles authored by John.
(3) There are puzzle's authored by students.
(4) There are 'fun problems'.

Items in ( 1 ), get their own discussion thread. These threads are named by Chapter Number, and then Exercise number.

Item (2) are created and discussed within the Lecture thread they belong to. Puzzles are exercises that are not part of the book. They are initiated by John within his lecture notes, or by students within the same lecture topic. John's puzzles just numbered by a number, while puzzle's authored by student's noted by student's initials.

Item (3) discussed within lecture threads (just like ( 2 )).

Item (4) get their own thread.

There are probably some, unintended deviations, especially when we just started the course. But is seems like the above scheme is maintained.

When folks make mistakes/misses in their exersize answers, they either change them or add to the answer by noting what was wrong -- so that others do not run into same mistakes...

BTW, on a separate topic, I am glad that we do not have comment voting/rating.

JimStuttard · April 2018

I've bookmarked or am reading the fantastic set of incredibly diverse but spot-on links people have posted in the discussions: a good 7 months reading already I guess. Is it a good idea to add a bibliography to the ACT wiki resources page with pure and applied sections or course and misc or summat? Then folks can add appropriately at will.

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How the Course Is Going 1

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