And we can model differential equations in a first order theory of real numbers, which requires no set theory
Your conception of "differential equations" is probably too narrow for this to be true.
Nope. It is literally possible to reduce the theory of Turing machines to real analytic ODEs. These can be modeled without set theory.
It is literally possible to reduce the theory of Turing machines to real analytic ODEs.
Okay, that sounds interesting (reference?), but what about the rest of my comment?
Did computer programming make you a clearer, more precise thinker? How about mathematics? If so, what kind? Set theory? Probability theory?
Microeconomics? Poker? English? Civil Engineering? Underwater Basket Weaving? (For adding... depth.)
Anything I missed?
Context: I have a palette of courses to dab onto my university schedule, and I don't know which ones to chose. This much is for certain: I want to come out of university as a problem solving beast. If there are fields of inquiry whose methods easily transfer to other fields, it is those fields that I want to learn in, at least initially.
Rip apart, Less Wrong!