<p>I was an undergrad at CMU and had to take math classes in the math department as part of my engineering degree and there were very few proofs involved. Typically an exam would consist of 3-4 problems and 1 rather light proof (generally something similar to what had been covered in class). I believe math students took the same Calc 1, Calc 2, Calc 3, and Diff Eq classes, but they had a whole bunch of extra discrete courses where they got to redo a bunch of it in a much more rigorous manner.</p>
<p>I think when you’re talking about the preparation Calc BC gives you, you feel it should be teaching different concepts than what it’s doing. Most people out there have little to no use for proving various things in math, they use it as a tool for their work. For the most part they would be ill-served losing out on the applications of the math for the fundamentals behind it (at least, that’s how I feel).</p>