Do Electrical Engineering Researchers Usually Know Higher Math? e.g. Measure and Distribution Theory, Functional Analysis I am an EE undergraduate student, and I recently took two courses in signals and systems. We were exposed to things like the Dirac delta (without mention of distributions), Fourier series (without mention of convergence or function spaces), the Laplace and Fourier transforms, and the sampling theorem.
I still don't truly understand the sifting property, or why sampling is multiplication with a shifted delta instead of a shifted 1 (which would preserve the value of the signal at that point right?). I'm still not sure how to determine when a signal's Fourier series will converge, when you are allowed to take a Fourier or Laplace transform, or whether the derivations of the transform properties we learned are mathematically justified and rigorous.
This led me to self study books like Tolstov's Fourier Series and Richards's Theory of Distributions, which I could not follow due to my non-rigorous math background. The Osgood Stanford lectures were quite helpful, but I still feel quite sad that I do not have a deeper understanding of my math tools.
According to my school's EE graduate course catalog, there are a couple of classes covering Hilbert, Banach, and L^p spaces, and linear functionals. Is it possible to cover these topics without a formal mathematical background? Should I begin self learning real and complex analysis to prepare for these topics?
Forgive me for this lengthy question. Thanks!
 A: $Q1.$ According to my school's EE graduate course catalog, there are a couple of classes covering Hilbert, Banach and L^p spaces; and linear functionals. Is it possible to cover these topics without a formal mathematical background?
$A1.$ It is the responsibility of the school to provide a curriculum for the students that is both meaningful an doable. Therefore if the graduate courses have classes on some advanced mathematics subjects, then it is reasonable to assume that the undergraduate mathematics curriculum of the school provides the necessary and required background. As far I can see there is no particular reason why you, as an undergraduate student, have to worry about these things. But when you are in doubt you can always ask your study adviser about this.
$Q2.$ Should I begin self learning real and complex analysis to prepare for these topics?
$A2.$ No, I don't think that is necessary.
$Q3.$ Do electrical engineering researchers usually know higher mathematics? For example measure and distribution theory, or functional analysis.
$A3.$ No they don't. They will typically have excellent experimental and theoretical knowledge of analog (electric) and digital (electronic) signal processing. They know physics and mathematics and computer science, but not at the highest level. 
