Generating functions, as applied to a hard puzzle used for IMO training.
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Books mentioned
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://youtu.be/sD0NjbwqlYw
Fourier series
https://youtu.be/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
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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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