Great alternative way to visualize hyperbolic geometry. Good job.

Are you going to do more videos on Einstein-Cartan theory? I would like to know how it is different from GR. I'm also interested in the letters between Cartan and Einstein.

Thank you for these videos!

@慕容忘情

@murongwangqing 见信速联 谢谢

Surely your example is not a valid group. (bb)c is not equal to b(bc), so it is not associative.

thank you very helpful

What a great teacher you are. Thanks a lot for the videos ❤😊

Any dislikes are from physicists

Thanks

Obrigado.

Obrigado!

I appreciate you for your whole courses

My old black labrador passed away a few days ago, and he is Lula's portrait, slept in the same position and he snored the same way...i miss him so much, I've been listening to Lula snoring ever since

You seem to prefer (y-x)^2 over (x-y)^2 in the video, but aren't the two expressions effectively the same? Am I missing something?

Thanks for this explanation . Not sure about the septal manifold though.

Q: In order for a linear map to exist, do the vector spaces V & W have to have the same dimension?

@WHYBmaths how would we represent p (the point on the manifold)? I get how we can give it values and describe it on the two different charts using either (x1,x2) or (y1,y2) but what about while its "on" the manifold. Like how do you talk about the elements on the abstract manifold before you map them into a chart?

When you say that the charts are subsets of r2 in this example, are they unique subsets? The blue point you drew exists in both charts but does it have different coordinate values in those charts? Does this mean that point's coordinate values of a specific chart are only meaningful in relation to other points in the same chart ie in the same open set on the manifold used in the mapping function to the chart?

amazing video. thank you very much

What's the problem with defining Continuity as For any *element* v ∈N, there is a preimg(v) ∈ M without their topologies?

So very helpful.

How would a triangulation of the torus work? how many vertices edges and faces would it have?

Thank you. It’s very helpful at times to dispense with formal definitions.

Thanks very much! Very helpful.

He is either exceptionaly good at teaching or exceptionally good at maths.

Great explanation! Thanks

This video made the subject more obscure.

Good content but please stop dancing while you speak.

I enjoy your videos. Thanks

Small note: At 18:13, I think there should be a -v^2/c^2 not +v^2/c^2

What an amazing introduction to point set topology!

amazing explanation , thank you

Yeah total Meta Physics. What is the math behind the speed of light coming in from two objects, one behind and one in front of a traveller going one third the speed of light towards one of the light sources and away from the other. What is the speed of the light being transmitted to the traveller from behind and what is the speed of the light heading to the traveller from in front of them from the perspective of someone stationary relative to both light sources, sitting in the middle. Only perspective of time changes, time is unchangeable and the speed of light ends up being relative.

For the map of the basis of V to be the bases of W, does it has to be bijectif ?

this is so so helpful, such a good way of teaching, also the cute dog is a site of comfort!

講得不錯！

Great playlist, easy to understand, thank you, I also hope you can make one about general relativity!

I came here for relativity I stayed for the way you explained. Thank you for giving us access to such valuable information

Amazing videos. Thanks for sharing.

Nice tensor playlist, well explained, thank you!

I envy the dog. Learning so much...

This video si a great demonstration of mapping between a sphere and 2D space. kzbin.info/www/bejne/oXqsdWh8ec5lgLM

You are an amazing teacher. Im still in high-school and I feel like I had a pretty good grasp over the concept. Its a very intriguing... topic? Field? Whatever it is, I like it lol.

Thank you for your time and effort.

Nice and easy to understand playlist about Lie Groups, thank you!

Nice playlist to understand manifolds better, than you!

I think I’d rather drink bleach. But thank you.

I hope you can made a series about general relativity .

I find and read many typical textbook about gs but i think your videos are the best