Counting with Calculus: The Magic of Generating Functions

This is an introduction to generating functions and a combinatorial technique known as the symbolic method. This technique allows us to count a wide range of objects by simply carefully writing down their structure and then using elementary calculus.

If you want more information on this topic, I recommend the book Analytic Combinatorics by Flajolet and Sedgewick and Generatingfunctionology by Herbert S. Wilf, the latter of which can be gotten for free as a PDF on the author's website.

For a lighter resource, I also recommend the following Wikipedia links:
https://en.wikipedia.org/wiki/Generat...
https://en.wikipedia.org/wiki/Symboli...)

Corrections:

At 3:16, there should be a minus sign between the sums and between the two phis. I also made an algebra error in the partial fraction decomposition, the denominator should read +1/phi not -1/phi. This mistake carries forward and in the final formula for f_n, we should get (-phi)^-n.

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Music:
Gymnopedie No. 1 Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
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Gymnopedie No. 2 Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/b...

Gymnopedie No. 3 Kevin MacLeod (incompetech.com)
Licensed under Creative Commons: By Attribution 3.0 License
http://creativecommons.org/licenses/b...