2022-05-23

[public] 121K views, 66.3K likes, dislikes audio only

3Blue1Brown

A lesson on generating functions, and clever uses of complex numbers for counting

Help fund future projects: https://www.patreon.com/3blue1brown

An equally valuable form of support is to simply share the videos.

Special thanks: https://3b1b.co/lessons/subsets-puzzle#thanks

Artwork by Kurt Burns

Music by Vince Rubinetti

Nice writeup and video giving solutions to the exercises at the end, by Benjamin Hackl

https://benjamin-hackl.at/blog/2022/06/generating-functions-3b1b.html

https://youtu.be/9SzwfM-S9sk

102 Combinatorial problems, by Titu Andreescu and Zuming Feng

https://amzn.to/3wAPoNq

Generatingfunctionology by Herbert Wilf

https://amzn.to/3sPJ8Al

Visualizing the Riemann zeta function

/youtube/video/sD0NjbwqlYw

Fourier series

/youtube/video/r6sGWTCMz2k

Timestamps

0:00 - Puzzle statement and motivation

4:31 - Simpler example

6:51 - The generating function

11:52 - Evaluation tricks

17:24 - Roots of unity

26:31 - Recap and final trick

30:13 - Takeaways

Thanks to these viewers for their contributions to translations

Hebrew: Omer Tuchfeld

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These animations are largely made using a custom python library, manim. See the FAQ comments here:

https://www.3blue1brown.com/faq#manim

https://github.com/3b1b/manim

https://github.com/ManimCommunity/manim/

You can find code for specific videos and projects here:

https://github.com/3b1b/videos/

Music by Vincent Rubinetti.

https://www.vincentrubinetti.com/

Download the music on Bandcamp:

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

Stream the music on Spotify:

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe

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