What is Continuity? According to a Mathematician.
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- Опубликовано: 5 июл 2024
- What is continuity and what is the popcorn function? From primitive notions to the modern day, there have been a variety of attempts at understanding continuity and functions. We talk about them here, in this video.
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0:00 Start
0:55 Intuitive Continuity
2:39 Something is wrong with Power Series
3:41 Making Popcorn in MATLAB
5:33 Frechet and his Metric Spaces
7:10 Making popcorn... no really
10:15 Continuity in Metric Spaces
11:10 Discontinuity of the Popcorn Function
12:23 Topology was STOLEN!
14:26 Continuity of the Popcorn Function
15:27 The last words on Continuity
To try everything Brilliant has to offer-free-for a full 30 days, visit brilliant.org/ThatMathThing/ . The first 200 of you will get 20% off Brilliant’s annual premium subscription. (This video was sponsored by Brilliant)
"Popcorn is corn!?" Greatest moment!
this channel is underrated. keep up the good work
Cheers!
Always a good day when prof uploads
Happy to have you here! I hope you like it!
Most looked forward to videos on RUclips! Especially with the blue book!
This is so fascinating! Thank you!
I’m glad you like it! This video took a lot of research and editing.
@@JoelRosenfeld I like it a lot; outstanding! I somehow have the impression that it happens relatively often in mathematics that mathematicians do not get the recognition they actually deserve. I hope to be wrong. However, the history of mathematics seems to put the facts in perspective, which is awesome. Btw: also thanks for the MATLAB code! I’ll try it out! 😄
I loved your presentation and the historical tidbits you shared. While it may be somewhat unrelated to this video, I would like to mention that it would be amazing to see you explore topics from Operator Theory, like Beurling's Theorem regarding shift-invariant subspaces. I find it personally intriguing as it connects Complex Analysis with Operator Theory.
I’m glad you liked the video! Yeah, I can add the Beurling theorem to the list. I can link it with the invariant subspace problem when I finally put that video together. Might be a little while from now though. Lots in the list :)
LOVE this stuff! Thank you good sir!
You’re welcome!
Please upload a survival guide on abstract algebra
I’ll give it some thought. I can certainly talk about undergrad and intro grad abstract, but I’m not an expert on the topic like I am analysis. Anything you’d like to know now?
7:36 you made a child have the greatest realisation of their life and just doesn't comment on it as if it wasn't important
lol blew her mind!
Amazing. Can u make video on calculus of variation
I’ll give it some thought. Anything in particular you’d like to know?
@JoelRosenfeld i am first year PhD student in control systems with electrical engg background. My potential area of work is optimal control and reinforcement learning. Through some literature survey i found optimal control involves calculus of variation.
Your vidoes are very informative and source of motivation to learn mathematics. I would appreciate if u guide me in this regard.
@@mohsinirshad2862 yeah optimal control is pretty intimately connected with the calculus of variations. The keywords you’d want to look up would be the Hamilton Jacobi Bellman equation as well as the Pontryagin maximum principle. A really good book on this topic is Calculus of Variations and Optimal Control by Liberzon.
Gelfand also wrote the standard reference on the Calculus of Variations, which is still a good read. This was before optimal control theory took off during the Cold War.
Wow. Very interesting story telling❤️❤️❤️
Thanks! I spent a lot of time working it all out
your kids are so cute hahaha indeed 3 + 4 is 7
LHL=RHL=Function value
Indeed. That works for the real line. Funny how many tools from ordinary calculus survive to more advanced math.
Reddit moment