My experience was that undergraduate engineers spend their time learning how to use mathematics to solve engineering problems. That is, you learn the mechanics and some background of the mathematical operations and then practice using them. In the one course I took in the mathematics department (Fundamentals of Complex Variables) we spent our time proving propositions in complex variable theory.
That’s pretty much what we do. How’d it go for you, if you don’t mind my asking? Most engineers I know who tried to take proof-oriented math classes didn’t do so well.
i didn’t do all that well. I didn’t realize that it was a mathematics dept. course when I enrolled and I was expecting the usual applications approach so I got off to a rocky start. This was in graduate school at UCLA and if you’re slow on the pickup in grad school it’s hard to catch up. By the end of the semester I was beginning to improve but I didn’t help my GPA much in that course.
Math is the (irritating to mathematics people) American colloquial term for Mathematics. Maths is the UK equivalent.
What an undergraduate engineer in the traditional engineering areas (Civil, Mechanical, Aeronautic) gets much more of is in differential equations(partial and ordinary, linear and nonlinear), and more transformation theory(LaPlace, Fourier, etc.).
A proper “hard” mathematics degree will touch substantially on DiffEqs, but will view it as an extension of calculus, and the PDEs aren’t usually dealt with unless the student elects it. Additionally, this degree will touch more upon logic, proofs, and the underpinnings of Calculus and DiffEqs, the Real Analysis. There’s also Probability Theory, Mathematical Statistics, Combinatorics and Game Theory,…
In short, a proper undergraduate mathematics degree will spend lots and lots of time not focusing on differential equations.
And part of the reason for the engineering degrees being “hard”: there are more people who are capable of being engineers than there are 1)jobs and 2)resources for training. Hence, as in medicine, there is the weeding out process, which makes such degrees artificially hard to get.
My brother did pure Physics and said the same thing.
He went on to get a Doctorate at the Clarendon.