PG:
I could not agree more. I'm having a hard time, especially tonight (medical issue) wrapping by head around the mathematics. Intuitively, though I think I can make some intuitive sense out of some of it.
Taking a really simple example of an amplifier with a gain of 10. No matter where in time you apply the input signal (say a sin wave) it will have the same output, so it;s time invariant.
Remember that funky function called u(t) or the unit forcing function that was probably around in the Lalpace Transform stuff? Same deal, in most of the cases, the system has the same response no matter when the stimulus is applied. Your delaying the application of the signal, NOT applying the signal after a delay. I think that's important.
Now if you has s(t) representing the path of some bug on an airplane propeller and at t=0 you pushed the propeller, the bug can be anywhere, so it's time variant.
PS:
The instructor doesn't necessarily have to be the weed killer, it could very well be the topic. "Introduction to Discrete Mathematics" and "Dynamics" were two of those courses and no where near subjects like Physics I (basically materials) or Physics II ( Electricity and Magnetism) and Physics II (Relativity). The point is the engineer will teach the math courses from a practical standpoint. The Electrical Engineer might never see this stuff, so the engineer won't think it's that important.