What would be the fastest way to get from half of a class worth’s of (graduate) measure theory, same of functional analysis and generalized functions (or distributions), and only differential geometry from general relativity and quantum field theory classes to a barely decent understanding of noncommutative geometry. I also have a bachelors in math. (And, I took an easy graduate class in complex analysis – part 1 of two part course). But, maybe my bits and pieces of graduate math knowledge should be ignored to better serve people also looking for what I have in the title (meaning sticking strictly to just undergrad background)?
It seems the normal trajectory is something like: real and complex analysis, functional analysis, topology, differential geometry, algebraic geometry, and then noncommutative geometry? What are the smallest pieces that I can take from these (or whatever the trajectory is) to get there with the background would I need but minimizing unnecessary stuff along the way?
Also, if this isn't the right place to ask this, or if my tags are not good (or anything else), can you please let me know what to do instead?
Edit: The main question here is "What are the smallest pieces that I can take from these (or whatever the trajectory is) to get [to my first book on NCG]? If you can answer this (or if it's in your links), I will accept your answer (and many thanks to you). If you can also say which books (and which parts to skip), and which NCG book to go with after all of said books, that would be great, and I imagine you'll get a lot of upvotes from undergrads (and probably a lot of the curious people searching around too). (Or, textbooks that happen to avoid parts from the books on real, complex, and functional analysis and differential geometry (and w/e else) that weren't intended for a direct path to NCG.)