in the US, most engineers take the standard two-year lower division sequence (calculus, linear algebra, a bit of diffeqs). for the most part, you learn techniqu

in the US, most engineers take the standard two-year lower division sequence (calculus, linear algebra, a bit of diffeqs). for the most part, you learn technique rather than proving things. upper division engineering math courses teach more technique (e.g., more diffeqs). but as madhadron says, you can't read/write proofs of upper division or graduate level math without the "foundations" material, which includes naive set theory. do you need any of that to do engineering math? well, there are a couple of standard quotes, relating to the fact that the technique taught is brittle, in weird and subtle ways. the claim is that understanding the proofs tells you what the limits of applicability are. "[F]or more than 40 years I have claimed that if whether an airplane would fly or not depended on whether some function that arose in its design was Lebesgue but not Riemann integrable, then I would not fly in it." - richard hamming, "mathematics on a distant planet" "It is customary to begin courses in mathematical engineering by explaining that the lecturer would never trust his life to an aeroplane whose behaviour depended on properties of the Lebesgue integral. It might, perhaps, be just as foolhardy to fly in an aeroplane designed by an engineer who believed that cookbook application of the Laplace transform revealed all that was to be known about its stability." - tom korner, fourier analysis