I don't deny the need for a thorough and disciplined understanding of math and physics. But... I didn't understand the need for calculus until I needed a way to go from pos/time to velocity/time. I didn't understand linear algebra until I needed to transform vertices in 3d graphics. Personally I don't understand a hammer unless I see the nail. Engineering school is all about showing you everything there is to know about a tool except what to use it for.
I think E-schools should be like obstacle courses where you have projects that REQUIRE understanding of a concept in order to complete them. Classes about said concepts are given as the NEED arises.
Most E-schools suck. Just take as many project based classes as possible (CS is decent for this) and get a degree. Universities also have lots of grants that nobody knows about where you can get money to build cool things.
Maybe this is just me, but I don't think I'm alone. And it probably explains why I failed to hang my pictures with a chainsaw.