Manifolds #1 - Introducing Manifolds

Here I begin to introduce the concept of a manifold, building on our intuition gained from studying topological spaces. I will formalise all of the terminology used in this video in future sections but for now I'll be speaking in fairly loose terms about manifolds.

We will see that the essential idea behind constructing a manifold is to take a topological space and cover it in charts. These charts are open sets which are homeomorphic to R^d and are viewed as giving coordinates to a local patch of the manifold. This can equally be viewed as saying that a manifold is a topological space which is locally homeomorphic to R^d.

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[niceperson]

I think someone without a masters can also understand this easily. The transition from topological spaces to manifolds was beautifully shown

[FlareGunDebate]

I've just starting this series but so far this is the best video I've found on topology and manifolds. Thank you.

[arnobchatterjee]

What an amazing introduction to point set topology!

[petermarshall]

Thank you for sharing your gifted understanding … really quite wonderful …

[mireazma]

Compared to many other videos, you explain clearly, thanks.

[sofiyavyshnya]

Excellent videos! I love your entire series on Manifolds. You explain things so that even I can understand :) Keep up the good work!

[ghadaalradi]

I have an exam in a short while and I don't know where to start, but your way of explaining is great, so great I hope it lasts.❤

[fizikchy]

10:04 Türkiye, long live :))
Great video series. I also visited your github page, found some pdf files so on. You're doing a great job. <15 min videos, shooting just to the hearts of concepts. Thanks.

[MathUniversity.]

This is such a wonderful series. Thanks for making it pretty basic and accessible yet interesting so as to cover the essence of manifolds. I subbed in the first 2 minutes -- literally. Looking forward to more math content!

[stevemenegaz]

Very nicely done. Easy to understand.

[febojarlock]

I was about to give up on manifolds until I saw your series! Thank you dude!

[cannoli]

Great explanation and such a BRILLIANT outro!

[andrewsheehy]

This is so good. I loved the jab at the flat earthers! It would be cool to print out series of patterns on paper and then stick them together accurately with the result that you'd end up with a 3D object.

[bobtanto]

I have physics background and found this to be greatly helpful. Thanks!

[sathitm]

Nice explanation. Really helpful for beginners. thanks

[michaelhaag]

lucid explanation, thank you very much

[lolitoomaaan]

What a great explanation! Many thanks!

[gpas]

Clearest explanation I’ve found, thanks.

[nbphd]

What a great fucking series! I have been building to understand optimizations on manifolds (send resources) and this has been very useful! Thank you!

[slash]

So am I right to think of manifolds as spaces that can be represented by a collection of lower dimensional sets?

We can talk about the points on a sphere using a coordinate system. But there is an advantage in "dimensionally reducing it" to a set of simpler portions/patches?