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Systems and electrical engineering graduate students often take a course on stochastic systems (a.k.a. "Probabilistic Systems Analysis"). A typical course will present such topics as multivariable probability distributions, auto- and cross-correlations (and Fourier transformations of them), Ergodicity, stationarity, etc.

Students wanting a more advanced treatment after completing the above often gravitate towards a more rigorous Stochastic Processes course in the math department, which normally smacks them over the head with the concept of Measure Theory, which throws them for a loop, even if some have taken a course in advanced engineering mathematics.

What is the best way to bridge the gap between what is a more applied treatment of these probabilistic concepts into the more abstract notions, particularly for students that may not have had a graduate-level Real Analysis course?

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    $\begingroup$ That mismatch would mean they require an intermediate analysis course... I haven't seen any engineering calculus courses including measure theory, and most probability courses don't cover it either. $\endgroup$ – vonbrand Jul 15 '14 at 17:39
  • $\begingroup$ @vonbrand That was my impression as well. Any paths between these two courses seem to require quite a bit of a mathematical detour that I think puts off most engineers, even though they would benefit greatly from the Stochastic Processes course. Having more theory would never hurt anyone, but it's slightly impractical. $\endgroup$ – jonsca Jul 15 '14 at 18:37

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