Anyone got suggestions for what a web dev should read or what classes he should take to understand what this guy is saying?
Here's a short-ish overview: http://www.math.uchicago.edu/~may/VIGRE/VIGRE2011/REUPapers/...
For a more extensive overview, try this textbook by Michael Sipser (Amazon Affiliate Link if feeling generous: http://amzn.to/2fy9tKZ, Google Books link otherwise: https://books.google.com/books?id=1aMKAAAAQBAJ&dq=introducti...).
Edit: to be honest it's the maths notation that is a big barrier for me. Until one can read it relatively fluently it's very hard to translate the ideas into a meaningful mental model .
Seems like a few lectures are missing but if you google around you might be able to find them somewhere.
I later on picked up the first two editions of Hopcroft & Ullman for $1 each at a used book store. I don't think either edition can really hold a candle to the Sipser book, which is shorter, more thorough, and (imo) easier to understand.
One caveat: it's super-expensive. I'd recommend finding a used copy or even an "international edition" (which will be soft-cover rather than hard-cover, but the content is the same).
Essentially, "does being able to quickly recognize correct answers mean there's also a quick way to find them?"
The rest of computational theory will follow.
Not all that in-depth, but it's a great starting point.