[aoriste]

As for me, I eschewed the applied topics (no ODE's no PDE's) in favor of the "pure" (algebra, analysis, topology, etc) only to discover that, because I had little interest in becoming a professor, most of it would only serve to keep my happily diverted on what are now ridiculously rare lazy Sunday afternoons. In these topics, so long as one is interested in the propositions in need of proof, real study is relatively useless. I first learned what it meant to study in the "real world" - in the lowly field of IT - when the fiat came down the line to transform format X into formats Y and Z, and ensure that changes to one translate to the others, keeping in mind that simultaneous changes may occur, in which case on the 'right' change should be kept. The old dictum is true: there is no substitute for experience.