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