🎓Become a Math Master With My Intro To Proofs Course!

I honestly believed this guy was writing backwards until I realized you can just flip the video :p

Funny story: When I was in college, I took a course designed for people who wanted to be math professors. One of the presenters showed us (old tech alert) a calculator that you could put on the glass surface of an overhead projector. It would even integrate functions, something I hadn't seen done on any calculator at the time. For fun, I asked the presenter to have it integrate e^(-x^2). She didn't even understand why I was asking for that particular function until the professor explained that it didn't have a closed-form antiderivative. She dutifully typed it in and it responded (whatever the constant is) times erf(x). I protested, "That's cheating!"

I'm literally taking an upper-level mathematical statistics course right now and immediately saw that equation and thought "Wait..... isn't that the pdf of a standard normal distribution???"

You're the Bob Ross of math

I think there are some confusing elements here. The y domain does not "become" the theta domain, it's more of a double substitution (x,y)->(r,theta) and maybe explain more why it is that dxdy=r*dr*d(theta) from the jacobian etc.

Great presentation! We see, again, why Pi is one of "holiest" numbers in mathematics. Cheers

Damn that was clean. What a smooth transition to pi

I don't think he's actually left-handed.

Figuring this out on our own was a homework problem in the calculus course I took last semester

I thought in stats we just let that area equal 1. The chance something will appear under that circle is 1.

"Did you expect a pie to fall out of here?" THAT'S WHAT SHE SAID.

I often deal with Gaussian curves in many dimensions as an electrical engineer with signal processing. The really cool part is that (given that the covariance matrix is diagonal), the pdf is constant over an N-D sphere! I think that is a beautiful way to connect the two concepts.

Another Amazing Integral!

I haven't even learned about integrals in school. Why am I watching this?

As soon as you started talking about using y in the second integral I saw it.... that is so cool

A few comments from a statistician:

I am really really trying to understand this, but I have not taken any form of a Calculus class yet (not even precal) and it is very difficult.

Im taking integral calculus in college rn and our teacher told us this integral would be the last one we'd integrate at the course, but yesterday she made us demonstrate it comverges. It always impresses me how creative you gotta get to solve some math problems.

Slowly learning claculus and understanding these types of videos better and better is the most satisfying thing ever