I am broadly interested in theoretical computer science and neuroscience. Recently I've been thinking more about existential risks and risks from advanced AI in particular.
Kudos to the speaker, as a (physics) layman I found it really well explained. The connection b/w Renormalization flows and phase transition was really elegant.
Alas, being slightly over the subtly-warped-judgment line is like taking one drink – sure it only impairs your judgment a little, but, the one of the things you might do with slightly impaired judgment is to take another drink. (Or, say, foster more emotional closeness with someone who you wouldn’t endorse eventually having sex with).
This is sort of the situation where you need to erect Shelling fences
One aspect of schooling which is not easily available in home schooling is peer/social learning. Did you find that being a problem?
In case you're fine with an approximation, you could try modelling the #P problem as a CNF (check this paper for more info) and use an approx model counter such as https://github.com/meelgroup/approxmc .
Ahh that's because in India we have a graduate entrance exam called GATE (for admission to IITs and other institutes). And ToC carries a lot of weight-age.
I found Introduction to Automata theory by Ullman on EdX to be extremely useful. It covers most of the basics and there's also a book by the same author. Apart from the lectures you also get access to high quality assignments, problem sets which I think are very essential for a course like ToC.
Yeah even I used to feel the same, Wigner wrote an article about it "The unreasonable Effectiveness of Mathematics in the Natural Sciences" you will definitely find it useful.