I would advise against trying to typeset lectures live, at least
for my courses. I structure my lectures as an abstract detective
work: start with a motivating problem or example, experiment with
it, distill the key ideas, formalize them into definitions, deduce
consequences (theorems, new problems). I expect my students to be
active participants at each step. Paper notes work well for this,
because they are both low overheard and sufficiently free-form.
From my experience, students that typeset or try to write overly
formal notes during class miss that crucial live narrative of my
lectures; that makes me sad because I spend a ton of effort in
this story-building.
I do think proper typesetting is a great idea afterwards, during
its own dedicated phase; it is like the report-building stage of
the detective work, where findings are revisited and structured so
the detective can reflect on the case, compare it with others and
have a reference for the future.
For anyone interested in my very opinionated patterns for latex
typesetting in Vim, I have a github page with vim templates [0] and
some demos at reddit [1].
I had been an avid latex note taker since my college days though I used Emacs Org Mode. I consider writing your own notes in the form of a well-typeset book extremely rewarding as it kind of forces you to distill concepts better. For instance, I would actively seek out additional historical origins of a formulae or an associated anecdote or analogy for helping others to better understand the concept. My motivation largely was to write in a way such that it would help others understand better.
This exercise inspired me to build my own learning platform from scratch that generates a latex-generated books at the end of course completion. The idea is to have interactive conversations while learning and at the end the personalized book is generated for you. You can see an example of personalized Python book here: https://tinyurl.com/3xfsunj9
You can see that the conversations between learner and Primer highlighted as red sprinkled throughout the book.
The learner doesn't need to write any equations or code examples as it is generated for them. They can further customize the notebook by adding notes or questions using prompts.[1]
Right now there are two free courses on the platform[2], and 5 more would be added by the end of the month. But the goal is create self-paced computer science degree.
Your classes sound amazing. In my experience though, seldom a professor or a TA tries that hard to prepare an engaging lesson.
And certainly, it'd be a shame to be busy "live-latexing" notes for your class, but I think in the vast majority of classes, for someone really adept at it, it might work.
My research lately is quite meta, and involved in breaking down the various ways in which dissemination of knowledge can be structured. Mind if I borrow this analogy and test it out on some students? Something about it resonated.
I took notes on my courses in LaTeX, and I didn't find it detrimental. If anything, it was way faster to write and understand them later. And it is easier to write whatever you need to keep track of the lecture and then modify it later (or during the lecture) than to have some paper notes where you need to first complete them and then organize them.
Not to mention that it's far easier to collaborate with LaTeX notes than paper. For example, we split the courses between friends so only one took LaTeX notes, the rest paid attention or took quick annotations on paper to later complete the notes.
For complex notation I had a keyboard distribution with symbols available (e.g., α is alt-a, ∩ is alt + shift + i, ∈ is alt + shift + [) and also made commands to abbreviate, which made it faster than writing (and more consistent). The pace depended on the lecture, but I had no issues keeping up with the teachers speaking/writing pace. If the class was being too complex and I couldn't understand and write in my own words, I just went into "memory dump mode" and wrote whatever and then understood and reformatted it later.
For diagrams I had several options. Simple ones were easy enough to do with Tikz (maybe I didn't get it perfectly on the first try but good enough to fix later), diagrams that had a repeated structure were done with commands, and then for the ones that I couldn't do on the fly I just either wrote the description in text and did them later, or did a drawing in a notebook/phone/took a picture and then replicated it later with Tikz. I could also take diagrams from the web and paste the image.
If you want examples, we actually had all our note PDFs in a shared Dropbox folder [1] (in Spanish, though). Not all of them are mine, but there are a good bunch of them where I'm the main author. I'm specially proud of some notes, like the differential geometry course [2] or topology [3] with a good amount of diagrams (for a math course).
I do think proper typesetting is a great idea afterwards, during its own dedicated phase; it is like the report-building stage of the detective work, where findings are revisited and structured so the detective can reflect on the case, compare it with others and have a reference for the future.
For anyone interested in my very opinionated patterns for latex typesetting in Vim, I have a github page with vim templates [0] and some demos at reddit [1].
[0] https://github.com/ykonstant1/dotfiles
[1] https://www.reddit.com/r/unixporn/comments/jtjol5/cinnamon_l...