What is Continuity? According to a Mathematician.

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  • เผยแพร่เมื่อ 20 ก.ย. 2024

ความคิดเห็น • 25

  • @JoelRosenfeld
    @JoelRosenfeld  11 หลายเดือนก่อน +4

    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)

  • @joeeeee8738
    @joeeeee8738 11 หลายเดือนก่อน +6

    "Popcorn is corn!?" Greatest moment!

  • @Cxlver
    @Cxlver 11 หลายเดือนก่อน +7

    this channel is underrated. keep up the good work

  • @lemonflavouredtnt6969
    @lemonflavouredtnt6969 11 หลายเดือนก่อน +7

    Always a good day when prof uploads

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +3

      Happy to have you here! I hope you like it!

    • @mmariokart231
      @mmariokart231 11 หลายเดือนก่อน +1

      Most looked forward to videos on TH-cam! Especially with the blue book!

  • @gabitheancient7664
    @gabitheancient7664 11 หลายเดือนก่อน +2

    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

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +1

      lol blew her mind!

  • @ashishKjr
    @ashishKjr 11 หลายเดือนก่อน +1

    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.

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +2

      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 :)

  • @mmariokart231
    @mmariokart231 11 หลายเดือนก่อน +2

    LOVE this stuff! Thank you good sir!

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน

      You’re welcome!

  • @solaris413
    @solaris413 11 หลายเดือนก่อน +3

    Please upload a survival guide on abstract algebra

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +3

      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?

  • @mohsinirshad2862
    @mohsinirshad2862 11 หลายเดือนก่อน +1

    Amazing. Can u make video on calculus of variation

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +1

      I’ll give it some thought. Anything in particular you’d like to know?

    • @mohsinirshad2862
      @mohsinirshad2862 11 หลายเดือนก่อน

      ​@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.

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +1

      @@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.

  • @surajpowar4915
    @surajpowar4915 11 หลายเดือนก่อน +2

    Wow. Very interesting story telling❤️❤️❤️

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน +1

      Thanks! I spent a lot of time working it all out

  • @s.k6962
    @s.k6962 11 หลายเดือนก่อน +1

    LHL=RHL=Function value

    • @JoelRosenfeld
      @JoelRosenfeld  11 หลายเดือนก่อน

      Indeed. That works for the real line. Funny how many tools from ordinary calculus survive to more advanced math.

  • @oscarballesteros225
    @oscarballesteros225 9 หลายเดือนก่อน +1

    your kids are so cute hahaha indeed 3 + 4 is 7

  • @TheOWLCITYADDICT
    @TheOWLCITYADDICT 11 หลายเดือนก่อน

    Reddit moment