Manifolds #2 - Topological Manifolds

In this video I formalise the concept of a (topological) manifold. We will see that a manifold is a topological space which we have 'covered' in charts. A chart is an open subset of the manifold along with a chart map which maps the chart into R^d.
These charts can be interpreted as giving a way to talk about the points of an abstract topological space using concrete coordinates. I briefly allude to the notion of changing coordinates using a transition function (discussed in more detail in the next video).
If you like my videos and want to consider supporting the channel I am now accepting donations in DOGE and BTC (other cryptos on request) See my channel description for the addresses!

[@bent3809]

It's a shame the algorithm hasn't noticed your channel yet. This videos are serving as a crash course for my differential geometry class and have improved my understanding quite a bit. Good job!

[@WHYBmaths]

Thank you so glad it helped!:)

[@datsmydab-minecraft-and-mo5666]

I cannot even express how wonderful an explanation of manifolds you have given me. Please never stop making these videos.

[@softwarephil1709]

Your videos are my introduction to manifolds. Even with no background, I’m able to understand them. Thank you.

[@harrycraig2077]

Explained like a genius

[@thomasvogel4340]

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.

[@sumitsahu896]

Bro, you are a genius. You explained it extremely well!

[@pinklady7184]

"Genius is making complex ideas simple, not making simple ideas complex." Quotation by Albert Einstein.

[@WHYBmaths]

♥️ such a good quote, and I agree it's definitely what I try to do!

[@andrewsheehy2441]

I just want to say that this is simply EXCELLENT - by far the best explanation of manifolds I've encountered.Please keep going. My goal is to understand General Relativity and for that I need to master vector calculus and this is a wonderful step along the way. Thank you very much. Subscribed.

[@michaelcheung6290]

So exciting to hear someone with the same life goal as me! Could you please share what books/resources you are reading as well? Big thanks! This series is seriously good!

[@manaoharsam4211]

Well outstanding job again. Making subject interesting. Congrats.

[@valor36az]

Awesome even I can understand this, keep on making videos in higher mathematics please.

[@guilhermescorza4412]

really good, watching from Brazil!

[@pranaviyer8178]

Here from your post on reddit! Great job! Keep on going!

[@user-fl1bk6yx3d]

This is the best series of vedio I have watched for the explaination of manifold. You are a genius.

[@WHYBmaths]

Thankyou I'm glad it's helpful!

[@A_Box]

Holy cow, I just found your channel and this is quite the gold mine. I was trying to understand manifolds for their applications in machine learning. It is crazy how little math people take in engineering. Keep it up!

[@kevon217]

This has been so helpful as a novice trying to learn about topology. Thanks!

[@ivanvoid4910]

Golden content, thanks man

[@mohamedalisouyad7405]

amazing explanation , thank you

[@aryanpatel7050]

this man is genius!

[@nancyyang]

Compliments to the video, your handwriting and the dog

[@harrisonbennett7122]

Amazing Video WHYB, so much better than my diff geometry lectures at uni!

[@satyajitsaha29ss]

Wonderful explanation.... really you made the idea of manifolds simple. 👌

[@peterhunt1968]

Really good clear video - thanks 🙏

[@zVincoo]

Great explanation! It clicked for me. Thanks :)

[@carissak4425]

Thank you for the explanation! It means a lot

[@igorlemke6569]

Thanks from Brazil!

[@ch272h]

great content!

[@ROS-group]

very informative

[@waficel-ariss2646]

Hi :) Your video series was incredibly helpful in my research, and I thank you for the quality content. Can you please refer us to either a book or scholarly work which we could use as reference for the concepts and equations you have shown us throughout? Thank you!

[@seanriopel3132]

I thought Atlas was holding up the world now you're telling me he's part of it?!? 😉

[@jackgaul5144]

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?

[@randalllionelkharkrang4047]

Man. I'm doing a master's in Machine learning, and I'm getting real interested in topology. Your channel is gem 💎. Thank you for your work. Is there a way to sponsor you?

[@WHYBmaths]

I'm so glad it's helpful! I'm also getting very interested in machine learning (CNN) now that I'm pursuing a programming career! And that's very kind, I'm accepting donations in BTC and DOGE! The addresses are on my profile / in the descriptions of all videos:)

[@pinklady7184]

Do you ever consider doing book reviews? There are some of us self--studying while not in college. I have vague ideas what books students in college are reading.

[@WHYBmaths]

Yes I would like to! People always ask me for suggestions so I should just get them on video once and for all 👀

[@h.h.c466]

The existence of a map(-ping) for the open space U at p, how can it be given? Also Is it possible to do this with one map and the open set covering all of the manifold? What is the role of those abstract points in the manifold in this (trying to create one map covering it all), why abstract in the first place?

[@ador4047]

How do I show that the intersection of U and V with the restricted function is also an atlas

[@tantohk.r.audacious802]

U=V=M

[@morrisonshirmer1742]

DON`T TRY JUST DO IT, THE BEST CHOICE.................

[@lloydhughes2389]

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