I have the opportunity to pursue an independent study in functional analysis (using Kreyszig's book) or calculus on manifolds (using Tu's book) next semester. I think that both of the subjects are interesting and I would like to study them both at some point in my life, but I can only choose one of them next semester. I have studied a bit of QFT and I looking to study the interface of quantum field theory and condensed matter physics in grad school. I originally thought functional analysis would be more useful, but some of the feedback that I have gotten suggests that it may not be as useful as I thought. Which of these subjects would you choose to study/ do you think would be more helpful, and why?