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I have recently read the first chapter in the late professor Wilf's book humorously entitled Generatingfunctionology. This has been my first experience with combinatorics, and I am trying to approach the subject through a perspective of complex analysis. I originally wished to study the Lagrange inversion theorem as I saw that it arose from a problem in physics that I wished to study. After reading the introduction and table of contents, I realized that the role of Complex analysis in the book is limited to the fifth chapter, so I feel that my initial foothold with the text was less than what I had initially hoped.

Question: I felt relatively comfortable with his explanations in the first chapter, though I lack an intuition for his motivation about arguments regarding which elements may be excluded from counting a set. The last thing I would wish to do is look through the answer key without thoroughly attempting the material. Does anyone know of an online series of lectures that would nicely accompany his book?

HallaSurvivor
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Talmsmen
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    take a hike thru https://math.stackexchange.com/questions/39127/generating-functions-for-combinatorics – janmarqz Sep 03 '22 at 02:56
  • I downloaded all of the pdfs (even those located on webarchive). Did anyone suggest lectures? If I were to search for lectures released from a university, what would be a good guess for a course name? Would I be looking under discrete mathematics, combinatorics, or some other field? I come primarily from a differential equations and analysis background, and I have recently wished to broaden my mathematical horizons. – Talmsmen Sep 03 '22 at 03:10
  • read all the related sub-subjects on each reference and compare among them – janmarqz Sep 03 '22 at 03:28
  • The answers to this question are likely to be relevant: How can I learn about generating functions? (But the Analytic Combinatorics lectures may be your best bet, as noted by HallaSurvivor.) – awkward Sep 03 '22 at 14:47

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I don't know of a series of lectures that accompanies Generatingfunctionology in particular, but I do know of a series which might actually fit your situation better!

Flajolet and Sedgewick wrote a famous book on Analytic Combinatorics, which is largely about doing complex analysis to generating functions in order to gain information about some combinatorial object. The good news is that this book is extremely comprehensive. The bad news is that it's extremely comprehensive :P. In particular it's 800 (quite dense) pages.

There's more good news, though! There is a professionally produced set of recordings accompanying Analytic Combinatorics. It's meant explicitly to be a resource for people self-teaching from that book, or for combinatorics professors looking to flip their classroom. I haven't watched every video, but those that I've seen I've really enjoyed!

You can find these youtube videos linked on the website for the textbook here, or directly on the associated youtube channel here.

I hope this helps ^_^

HallaSurvivor
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    I enjoyed your post on Galois theory. Thanks again! – Talmsmen Sep 03 '22 at 04:39
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    I took the online course, but I was not aware that the lectures are available on YouTube. Thank you! Just one note: If you read the book or follow the online lectures, be sure to check the errata list at https://ac.cs.princeton.edu/errata/. – awkward Sep 03 '22 at 14:56