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I'm curious about two things:

1) how essential is taking real analysis prior to functional analysis?

2) how essential is functional analysis to someone interested in computational science, simulation and general mathematical modeling (including statistic/stochastic modelling)?

Until now, I've assumed both courses to be no-brainers for people interested in a career in applied math, but if both real and functional analysis are abstract and proof driven, bordering on "pure math", maybe ones focus should be elsewhere.

Given infinite time, I'd be happy to take both courses. But if they're competing with programming courses, advanced linear algebra/numerical analysis, fluid dynamics, quantum mechanics etc, are they really worth it?