I'm a first year graduate student in physics who picked up both an undergraduate degree in math and physics. However, in getting the math degree there were a few courses I either didn't take or simply didn't feel I had learned to the fullest extent. So, to remedy this I'm looking for some book recommendations on the following subjects:
1: Functional Analysis. Never took this course and am looking for two types of books: a mathematical type text that may be done at say the third or fourth year undergraduate level, and a more physics applications oriented one. For example covering Sobolev spaces.
2: Complex Analysis. I only want to look into a more mathematical text for this one, and was thinking Ahlfors but am open to suggestion.
3: Algebraic Topology. Self studied mostly from a collection of different sources and then Hatcher. Was looking for a physics oriented text to go along with this.