Such as topics in topology, complex analysis, etc.?
I've never used topology for anything. Complex analysis is rather important in many subjects. It used to be the most widely used method for analyzing airfoils.
Topology finds a bit of use in any field concerning nonlinear dynamical systems. Working in phase space in these situations lends itself nicely to topological analysis in some cases.
Complex analysis is used at the very least a little bit in aerodynamics and electrodynamics or any field that uses potential theory.
There are also a whole heck of a lot of signals analysis techniques in use such as various Fourier analyses, wavelet decompositions, Hilbert transforms and the like.
It might be a coincidence that one of the guys we have working on superplastic forging technology has a PhD in topology. Or it might not be...
Very interesting. What area do you specialize in?
I have yet to see applications of other topics in math to engineering such as set and number theory. Are they just not practical for applications in engineering? I have seen quite a few applications of these topics in computer science, though.
They aren't that practical. There are niche areas where you will run across a little bit of that sort of stuff, but on the whole it isn't all that common, at least as far as I have experienced.
It's all field dependent. Advanced math is critical to engineering research.
I have made a good bit of use of vector and tensor analysis, curvature tensors, calculus of variations, and Fourier analysis, both finite and infinite.
Thanks for all your input, very interesting to hear of applications of advanced math in engineering.
What I'm mostly interested in at the moment is signal processing and control systems. It seems applied math departments also do research in these topics of engineering, which I find to be odd. For someone interested in eventually doing research in these fields, which topic in mathematics would be best to get well acquainted with?
Fourier analysis would be your number one target to start with. Then maybe things like statistics, proper orthogonal decomposition, Hilbert transforms, etc.
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