A lesson on generating functions, and clever uses of complex numbers for counting
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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
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
Thanks to these viewers for their contributions to translations
Hebrew: Omer Tuchfeld
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https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/
You can find code for specific videos and projects here:
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Music by Vincent Rubinetti.
https://www.vincentrubinetti.com/
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