the semester starts on Monday and i still haven't been able to decide which of these 2 subjects to take (i won't be able to take both due to time concerns). both are offered by the same professor who's a great expositor, so it's more of a question of which topic would i be better suited to
i am interested in algebraic stuff primarily (will be taking topology and representation theory in this semester as well) and am not particularly good at analysis, although that does not stop me from being interested in these subjects. i was interested in complex analysis because of how "exotic" it is (compared to real analysis) and because of its connections with number theory (i'd like to learn analytic number theory at some point), while functional analysis interests me as a continuation of linear algebra (a subject i like ) and for its broad applications to pretty much every area of math. also as i imagine it, functional analysis is the cornerstone of a modern pure mathematician's arsenal and i kind of want to study it simply for the challenge of it (the subject looks to be pretty difficult). finally, i feel like i could possibly self-study complex analysis at some point, while functional analysis would be too difficult
what would you guys recommend? i'd love to hear from the algebraists in particular, if there are any here, as that is the field i want to (at least at the moment) specialise in in the future