>A fully qualified EE understands circuits at a deep mathematical level.

this is so funny. i have a buddy who's finishing up his phd in ee that works on SDR and who lead a team that won the darpa spectrum challenge a few years ago. he has no idea (absolutely no idea) how odes model LRC systems. i'm closer to CS than EE so he was explaining SDR to me and at some point i said "oh like the ode representation <something something>" and he had no clue what i was talking about. sure he took the class where that was covered but he completely ignored it (probably barely passed).

just one data point.