Discussion Anyone interested in math?

SteveGrabowski

Diamond Member
Oct 20, 2014
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Just ran across this really cool video on a Lie algebra called the Witt Algebra


This guy is doing a whole course on Lie algebras, having just released the first video of the series today


He does interesting one off videos if you like math on his main channel, Michael Penn:


And then he has another channel called Math Major which are like full courses in subjects such as algebra, number theory, complex analysis, differential forms, linear algebra, and differential equations


Anyways, probably my favorite youtube channels I'm subscribed to
 
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SteveGrabowski

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Or this one cracks me up when he busts out an isomorphism theorem to derive a result involving the product of the greatest common divisor and least common multiple of two integers

 

SteveGrabowski

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Oct 20, 2014
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Or this one is funny when he takes a convergent series that isn't absolutely convergent and shows you how to rearrange the terms to sum in a different order and make it converge to any of an infinite set of other numbers. The fact a convergent series that isn't absolutely convergent can be rearranged to converge to any possible number is something you might prove in a first analysis class but it's pretty cool seeing him show a simple way to make this specific series converge to an infinite set of different values by rearranging it.

 

SteveGrabowski

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Oct 20, 2014
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Another channel I really like is Math 505. He does a lotta of really cool integrals on his channel. I loved this one


and how it lets you do a really famous integral called the Dirichlet integral almost trivially

 

SteveGrabowski

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Oct 20, 2014
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This one solving the Basel problem, eg how to sum 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + 1/49 + 1/64 + 1/81 + 1/100 + ... is also really cool

 

SteveGrabowski

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Penn also had a pretty fun series where he taught a physicist a quick intro to Lie algebras and in return the physicist taught him back a quick intro to Heisenberg's uncertainty principle


 
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BoomerD

No Lifer
Feb 26, 2006
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I wish I understood math...arithmetic I'm fine...as soon as you add letters or squiggly lines...it become some obscure Chinese dialect and I'm lost.
 

lxskllr

No Lifer
Nov 30, 2004
57,037
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Not a fan. I use it every day at work, but aside from knowing what I need to know, it doesn't come easily to me.
 

skyking

Lifer
Nov 21, 2001
21,647
4,170
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I try, really I do.
I used trig to fab up all sorts of things back in the day.
If I try to build my own foiling catamaran I suppose I will get back into it. There will be a boatload of integration to do, pun intended.
 

herm0016

Diamond Member
Feb 26, 2005
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after linear algebra in engineering school, they kinda lost me. Not sure how I passed DiffyQ.
 

nakedfrog

No Lifer
Apr 3, 2001
57,389
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I am not. I like Veritasium's channel, but whenever he does a video that starts going heavy on formulas, my eyes glaze over and I'm out.
 

Ajay

Lifer
Jan 8, 2001
14,802
7,421
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Well, I didn't like using Ring theory to solve certain problems in E&M (even though I was very good at math). Since Lie Algebra is a subset of Ring theory - I decided to skip the vid. Enjoy.
 

SteveGrabowski

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Oct 20, 2014
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after linear algebra in engineering school, they kinda lost me. Not sure how I passed DiffyQ.
Differential equations is a weird class. It can be taught in so many ways. A lot of them start off with cutesy examples that can be solved in closed form. Sometimes you'll get a class that studies linear differential equations and you spend a lot of time with linear algebra and matrix exponentials. Or you might study phase portraits for qualitative understanding of equations that can't be solved in closed form. Or you might do power series solutions. Or Fourier series. Or numerical solutions. And so on. I had a PDE class where we spent 95% of the course on the heat equation and building up Fourier series / Fourier transform to be able to solve it. And I think we mentioned the wave equation and Laplace's equation one time in the whole course. Strangest thing in it though was we learned how to price European put and call options using the Black-Scholes equation because there was a hedging strategy that could take the probability out of it (most of the time, eg when the volatility could be modeled well by a quadratic if I remember right) and allow a transform to a simple heat equation. Of course not long after taking that course Russia defaulted on their debt, sending market volatility crazy and violating that volatility assumption in the "most of the time" above, and a bunch of Wall Street lost their asses on using that Black-Scholes equation that was supposed to take chance out of options trading. :tearsofjoy:
 
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skyking

Lifer
Nov 21, 2001
21,647
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^ Never heard of using trig to fap. Interesting
Oh come on man.
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Surely you've heard of the angle of the dangle?

It's part of the Heat of the Meat equation.

https://www.urbandictionary.com/define.php?term=heat of the meat
 
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SteveGrabowski

Diamond Member
Oct 20, 2014
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Well, I didn't like using Ring theory to solve certain problems in E&M (even though I was very good at math). Since Lie Algebra is a subset of Ring theory - I decided to skip the vid. Enjoy.
Lie algebras are vector spaces with a Lie bracket defined on them that behaves kind of like the cross product. Commutators like you use in quantum physics are an example of Lie brackets.