3. Divide & Conquer: FFT

Erik is Demaine man!

Its always a pleasure to listen Eric's lecture. Great professor.

holy crap, the tau thing

How can i find the full playlist?

From Algeria 🇩🇿🇩🇿🇩🇿🇩🇿🇩🇿🇩🇿

frizby baby

Is divide and conquer a genetic algorithm?

How does one perform FFT on a larger domain consisting of multiple cosets of a multiplicative subgroup of the field? I've heard it can be done but couldn't find any sources that explained how.

Is it too complex or just a first impression?

I miss blackboards.

I like this guy

Nice lecture! I thought MIT classes would be very hard.

I first encountered the FFT derivation of the DFT thirty years ago when I took a digital filters class while a graduate student at Georgia Tech, and I am as bolled-over now as I was then by this most elegant and incredibly useful algorithm. Thank you, Professor Demaine.

--

at last, absolute detail!

come from veritasium

It's unfortunate that there's no discrete examples.

This makes me want to blow my head up.

As he puts it, this all was "very cool, very cool".
Thanks, Erik.

Dude, why are you erasing the chalkboard before I finish taking notes?

that MIT chalk...

Implemented FFT algo for both polynomial multiplication and integer multiplication

Deadly algo :)

% java FFTPolynomialMultiplication
i/p polynomial A :
2 + 3x + xˆ2
i/p polynomial B :
1 + 2xˆ2
n (=2ˆk) = 8
o/p polynomial C :
2 + 3x + 5xˆ2 + 6xˆ3 + 2xˆ4

% java FFTPolynomialMultiplication
i/p polynomial A :
8 + 7xˆ2 + 3xˆ3 + 9xˆ5
i/p polynomial B :
4 + 5x + 6xˆ2 + 7xˆ3 + 8xˆ4
n (=2ˆk) = 16
o/p polynomial C :
32 + 40x + 76xˆ2 + 103xˆ3 + 121xˆ4 + 103xˆ5 + 122xˆ6 + 78xˆ7 + 63xˆ8 + 72xˆ9

% java FFTIntegerMultiplication
i/p integers :
A = 123,456,789
B = 956,227,496
n = 32
product = 118,052,776,209,670,344

% java FFTIntegerMultiplication
i/p integers :
A = 2,147,483,647
B = 2,147,483,647
n = 32
product = 4,611,686,014,132,420,609

So what is the math doing in practical terms? If I understand correctly, it's using the behavior of a signal over time to determine specific properties of that signal at specific moments. Is that correct?

The tatoo gag is amazing!

Pro Erik is fabulous

Erik: " I didn't go to high school, but I assume in high school algebra you learn this...."

Me: Drop from CS and cry...

Did I come here planning to learn about the nth roots of unity and how polynomial representations can be exploited to improve the scaling of computational complexity... No

Did I just spend an hour watching this guy because it is freaking interesting and incredibly well presented? You bet I did 😅

I love how he advocates for tau with so much passion he got a tattoo!

Professor makes his lecture seems the learning material is so easy! Thank you!

Marvellous

"I didn't go to high school but I assume in high school you learned this"
you dont have to flex like eric :(

This is what reaching GOD Level feels like in teaching?

This guy oozes brilliance! Amazing lecture!

Erik: "I didn't go to high school but I assume in high school you learned this..." reminds me seldon cooper

This is THE BEST FFT lecture ever. Erik is simply awesome!

this lecture is freaking amazing

FFT sounds like fast Fourier transformation I don’t know what it is though

Sir what is the best programming language for analysis and design of data structures and algorithms??...

"Screw Pi" - omg i nearly died. That was hilarious. I deeply regret my decision to avoid STEM classes in high school and college. That was a terrible mistake.

Throughout the whole video i could not stop wondering about him(he is a child prodigy, became a professor at MIT at 20 )

This was hard. Hope i will understand it soon.

TAU IS A WHOLE CIRCLE

Amazing to see that such a brilliant guy can also be a brilliant educator. From my experience this is pretty rare!

Me: Has a school assignment where I have to implements an algorithm dividing two polynomials and I have no idea what to do
This man: I'm about to save this man whole career

Real men cried at the end when he brought up those applications. Truly beautiful mathematics