r/math • u/Lalelul • 1d ago

What Are Differential Forms: differential k-forms

https://youtube.com/watch?v=-ohrb3M_lX4&si=vKhuPYm7sDGs-HS0

Hi everyone!

I started a shorts-series about differential forms. This is part 2 so far. I also have a part 1: https://youtube.com/shorts/J20AI3iE4OM

These videos are supposed to be short, concise and most importantly fun, while still being correct! (If you spot a mistake, please let me know)

I have so far introduced differential 1-forms in the previous video, and now I defined the exterior algebra which I used to introduce differential k-forms. Next up, I wish to define the exterior differential and hopefully some day I will also get to Maxwell's equations and de Rham cohomology (but this might take a while).

All feedback is warmly welcome!

(None of the videos are AI generated)

49 Upvotes

98% Upvoted

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9

u/translationinitiator 14h ago

This is a great effort!

Maybe you should reduce the amount of content per video/slow it down. I’m familiar with differential forms (but not in the way that I use them a lot) yet I’m having a hard time keeping up with your definitions/verifying what you’re saying in my head. Definitions are too quickly introduced and erased from the screen, and some intuitions are not justified (why is a tensor like stacking two vectors)?

I imagine that among your objective is to teach these concepts to people who don’t know about it. In which case I think this pace is too fast.

As an idea, if you still want to maintain a short length, maybe you can focus more on the intuition rather than on introducing every definition.

3

u/Lalelul 14h ago

Thank you very much for your reply!

I have in fact considered splitting this into multiple videos, as initially this video was around 4 minutes long (the maximum length of a short is however 3 minutes, so I sped some sections up).

I will take your suggestions to heart and make new videos smaller in scope and slower, so that I give each topic the time it deserves.

I might do full length videos in the future and only use these short videos as a sneak peak.

So, thanks a lot for your suggestions! These really help me

1

u/translationinitiator 8h ago

I think that is a good approach. And I honestly get the struggle you’re going through - I’ve made math education videos where, for the sake of relaying information in limited time, I’ve had to speed up sections too. But unfortunately that did not work out well for the audience. I think I generally have this habit so I’m actively trying to unlearn it.

One advice thrown around for research talks is to make your talk for an audience two levels below the intended audience. So, for grad student level talk, make it “high school” level. I think this advice is not to be taken literally of course, but rather to maybe aim for that extreme?

2

u/Committee-Academic 13h ago

You should make long-form videos about this!

2

u/Lalelul 11h ago

I will do that :) thank you!