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://www.youtube.com/watch?v=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 https://www.youtube.com/watch?v=sD0NjbwqlYw Fourier series https://www.youtube.com/watch?v=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 ------------------ 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 ------------------ 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 Various social media stuffs: Website: https://www.3blue1brown.com/ Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown