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3Blue1Brown Calculus Blog Series

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Re: 3Blue1Brown Calculus Blog Series

#21

Post by behnamoh »

I love learning the intuition behind math concepts, but when it comes to practical things, often you have to deal with unruly and ugly equations in which intuition plays little role. For instance, as much as I enjoyed his Fourier transform videos, when it comes to actually calculating the Fourier transform for arbitrary functions, intuition is outta the window; it goes back to pure calculations again. That’s the part of math that I hated the most-not the beautiful intuitions.

Re: 3Blue1Brown Calculus Blog Series

#22

Post by sunshowers »

3b1b is fantastic.

Another YouTuber I really like is Another Roof [1] -- the videos on Golay codes [2] using an icosahedron, and sporadic groups [3] are fantastic. There are some objects in mathematics that have pretty elementary definitions that a schoolchild can understand, but have secrets-of-the-universe level stuff behind them.

[1] https://www.youtube.com/@AnotherRoof

[2] https://www.youtube.com/watch?v=Tmx-v4FiP6I

[3] https://www.youtube.com/watch?v=dxRf3vHbuoA

Re: 3Blue1Brown Calculus Blog Series

#23

Post by [deleted] »

sureglymop wrote: post #16
WeMoveOn wrote: post #14

Seriously, his explanations on topics go well beyond the lectures some of my professors provide and could probably benefit a lot of students if given as a resource... If only academia wasn't so distrustful of those outside their circles...

But he's not even outside their circles right? Doesn't 3b1b have a PhD? I can tell you at least that we watched some 3b1b videos in my university undergrad math classes last year!

[deleted]

Re: 3Blue1Brown Calculus Blog Series

#25

Post by epgui »

behnamoh wrote: post #21

I love learning the intuition behind math concepts, but when it comes to practical things, often you have to deal with unruly and ugly equations in which intuition plays little role. For instance, as much as I enjoyed his Fourier transform videos, when it comes to actually calculating the Fourier transform for arbitrary functions, intuition is outta the window; it goes back to pure calculations again. That’s the part…

If you don’t have a good intuition for and understanding of the concepts, how can you know when it’s appropriate to cut corners / use various approximation techniques on messy data? Or how can you combine a bunch of techniques for real world applications without doing something nonsensical?

I don’t really understand this critique.

Re: 3Blue1Brown Calculus Blog Series

#26

Post by blovescoffee »

sunshowers wrote: post #22

3b1b is fantastic. Another YouTuber I really like is Another Roof [1] -- the videos on Golay codes [2] using an icosahedron, and sporadic groups [3] are fantastic. There are some objects in mathematics that have pretty elementary definitions that a schoolchild can understand, but have secrets-of-the-universe level stuff behind them. [1] https://www.youtube.com/@AnotherRoof [2] https://www.youtube.com/watch?v=Tmx-v4Fi…

I don't think I've ever heard of Golay codes. Could you elaborate on the secrets of the universe part?

Re: 3Blue1Brown Calculus Blog Series

#27

Post by behnamoh »

epgui wrote: post #25
behnamoh wrote: post #21

I love learning the intuition behind math concepts, but when it comes to practical things, often you have to deal with unruly and ugly equations in which intuition plays little role. For instance, as much as I enjoyed his Fourier transform videos, when it comes to actually calculating the Fourier transform for arbitrary functions, intuition is outta the window; it goes back to pure calculations again. That’s the part…

If you don’t have a good intuition for and understanding of the concepts, how can you know when it’s appropriate to cut corners / use various approximation techniques on messy data? Or how can you combine a bunch of techniques for real world applications without doing something nonsensical? I don’t really understand this critique.

Good point. I see what you mean and I agree that having an intuitive understanding of math concepts helps us choose the right tool for the job, but as soon as that decision is made, intuition doesn't play much role anymore. I really wanted to think that intuition (or even learning about the history of various math concepts) would be useful somehow, but every time I would end up getting lower scores than students who would just memorize the formulae and were able to calculate things quickly.
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