I wonder what the merits are of approaching analog electronics from a CE perspective. Digital Signal Processing (DSP) is an important bridge, as are general numerical methods for solving equations -- many tough equations happen to be important to signals and analysis.
So, that includes calculus, linear algebra and numerical methods already. (If you don't know: the most average and boring problem in DSP, is some variation on accumulating values in a variable:
xprev = xnew;
xnew = xprev + ynew;
This is basically the discrete implementation of integration: Riemann summation.)
Maybe throw in some SPICE, or maybe not something quite that advanced, but there are simpler, easier algorithms that can solve nonlinear systems, to modest success.
You might not quite understand why these algorithms are done the way they're done, but DSP has a certain intuitive appeal to it I think, and SPICE you get to see the circuits you're simulating (if you use a schematic entry method, anyway).
It's easy to see that, for example, averaging over the last N samples of a sequence of points, gets you a slower-moving output than the input: a low-pass filter. It is, however, harder to see why this is actually a rather poor filter! (That said, it's so trivial to implement that we do actually use it quite a bit.

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And calculus tells you a big hint about why DSP works, how it can be used to approximate an analog filter.
In typical EE curriculum, circuits are introduced first, then diff eq, then DSP along with other signals courses (transforms, communications..). I'm not quite sure how over-your-head these subjects/terms are, right now. It sounds like you probably don't have most or any of the latter courses, but you probably do have their groundwork!
The biggest thing that you'll be missing from a casual look into DSP, I think, is how to create a filter of some frequency or impulse response. The answer lies in the equivalence between the Fourier transform (continuous) and Z transform (discrete). Kind of like saying: "this Riemann summation, I like it, but do we
really have to take such small step sizes? Can't we do it with step sizes close to the rate change of the input?" Well, as it turns out, you can, but it's kind of weird?
When you solve for some kind of filter, you get a family of polynomial equations, whose values fit the response better and better as the polynomial degree increases, and whose roots or poles are the gain and rate terms in the filter (or L and C in the analog filter). The Z transform, it turns out, is literally a distorted version of the Fourier transform -- a half plane in F space is the unit circle in Z. Weird, right? Quite useful though!
Come to think of it, I never did sit down and fully understand the Fourier transform in computational terms. I should probably just write it out some day. The optimizations (FFT, butterflying?) are weird (especially on most machines not made specifically for it). But, fortunately they aren't necessary to understand the general function of the transform itself!
Relevant comic:
https://www.smbc-comics.com/comic/2013-02-01Tim