Knowing the axioms for a vector space, the definitions for manifolds and chart maps. Having done some abstract algebra helps! But, while the math is general, for this video it suffices to picture the manifold as a 2D curved surface that is continuous (no tears or holes - so that you can put coordinate systems on it) and smooth (no sudden folds or bumps - so you can differentiate at all points). The rest is calculus done in a different notation. See Frederic Schuller's lecture series in the description for more detail!
@@MoreinDepth I'm glad I watched your most recent video lol. I used to do quantum gravity research when I was in college and I never understood a lot of the complicated tensor stuff that was passed around a lot. I know I wasn't supposed to since I wasn't quite there yet with my math understanding but it was infuriating not knowing how to do things. Thank you for your videos, they've been a massive help!
If you make it clear that you are evaluating the derivatives at certain points (which we do by putting the (0) evaluation parentheses) there's no need to bother with a dot. I think the principle that most people follow is: "Put the dots properly until you get sick of doing so" :=)!
