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> It prepares you for one of the most fundamental of skills for white collar jobs: critical thinking

Right, because they certainly don't teach that in engineering school.

Depends. While I haven't studied mechanical engineering myself, a lot of my friends who have, seem to have spent a lot of their time learning to use steam tables and working with lathes (something I personally would love to do, btw) instead of racking their brains to solve problems in physics/math.

Personally, I think everyone should learn at least the basics of modern Algebra (not high school stuff, but: groups, semigroups etc.), Topology etc. (Note that I did not get an education in either Physics or Math, but am jealous of those who did)

This probably differs from school-to-school. At my school most engineering majors had senior projects or capstone classes in which you had to apply the things you learned to produce working products.

Applied projects and practicals are more along the 'working with lathes' line, forcing you to practice what you've learned.

"Critical Thinking" (and its development) is perhaps more nebulous, but I imagine that it comes with extensive work on proofs and problem-solving in more abstract situations.

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