I remember an undergraduate homework question that was just asking you to calculate the fourier transform of a gaussian of mean 0 and variance a. You get out a gaussian of mean 0 and variance 1/a.

I missed the significance of this, until we went over the homework with the TA and pointed out the implications of this result, heisenberg, etc.

It was very enjoyable that something I had previously taken as a sort of spooky truth of the quantum universe (Heisenberg's uncertainty principle) was actually just a pretty mechanically apparent consequence of some basic algebra on an EE homework.