How to Get to Manifolds Naturally

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Inspired by this book and this article:

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[malicksoumare]

Very good. We definitely need more vidéos about manifolds. They are just everywhere....

[goliathsteinbeisser]

I really, really appreciate you providing the PDF. It allows for much more careful study of the subject. Merci.

[GuillermoSV]

A pretty good explanation! I need the second part soon

[kamik]

Definitely would like to see more stuff on manifolds like operations on manifolds, this is one of the best explanations I've seen on youtube.

[disnecessaurorex]

So glad this got recommended to me. I'd enjoy more videos like this

[massfikri]

Exceptional audio and language quality.

[guscastilloa]

Thank you very much for your videos, it’s wonderful to learn math with you!! Lovely to address manifolds in a Saturday night 😊

[mahmoudhabib]

awesome. I did my graduation project on smooth manifolds, it's a very interesting topic to me.. please continue.. lots of support ❤❤❤❤

[RAyLV]

You guys deserve more subs! (And yes! more vids on operations on manifolds pls). Also to make it a bit more beginner friendlier, can you add examples or maybe a case base approach so the transition towards abstraction is bit more smooth?

[ליאורפ-הכ]

Thank you for the video! It’s a nice channel you are running. Just a small comment: I think it would help to have some longer pauses and speak more slowly such that someone seeing this subject for the first time would digest it more efficiently.

[MusicEngineeer]

Thanks! Yes, I'm interested in learning more about manifolds!

[jacemandt]

Hmmm...trying to understand what a manifold *is*, but when you first really start talking about manifolds, you just said "let's say we have a manifold" (3:21) and I still don't really know what it is. How is it different from just "a set in R_n" or something? I confess that I didn't really learn what a manifold is from this video.

[shutupimlearning]

More manifold content please! Maybe you guys could describe sheafs next? Or maybe isometries?

[ayandaripa]

You guys are making great videos!!!! Please carry on...

[Mahmood]

Please continue, this was very elegant and accessible.

[VCT]

Take a paper, make one fold, then do another, then another, then another.... that's how you get Mani(y)fold 😁

[scottmiller]

Pretty good. A few rough spots, but you hit the high points - I was looking for you to mention atlases and smoothness, and you got those. A minor quibble is C^k is a smooth function that is not identically zero. The last bit is why x is C^1, and not C^2; this point is almost never made clear in the definitions used.

[m.k.]

The figure 8 is an immersed submanifold of the plane, in particular it is a manifold. It is just not a proper submanifold.
Another example the Klein Bottle is a 2d manifold that does self intersect.
Also a chart doesn't map to a lower dimensional Euclidean space, it has exactly the same dimension as the manifold. In fact this is how the dimension of a manifold is defined in the first place.

[ygfddgghhbvdx]

In biology during morphogenesis how does cell differenciate, I suspect the cells knows their location in collective through some kind of cordinate chart which is establish by set of chemical gradient within collective this help them do different thing based on where they are located.

[jai_nasu]

Math textbooks be like:
“Ok here is 1 + 1 =2”
(Next page)
“Every module is a direct limit of finitely generated submodules”