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> Such practical examples seem to be almost banned from university math For background, I studied theoretical math. I am also amateur electronics engineer. I

> Such practical examples seem to be almost banned from university math For background, I studied theoretical math. I am also amateur electronics engineer. I agree, theoretical math students and staff are a bit dismissive about everything else. At least where I studied. Where I studied, we would regularly joke about other students claiming that math is hard saying, "what they are learning isn't even math, it is just a bunch of formulae and rote learning". And this included physics or applied math students. Don't even get started about CS students... It is unfortunate, because math concepts were frequently invented to solve a real physical problem. Or they were invented and we found them extremely useful for a physical problem. Historically people would not put much distinction and would usually do both physics and math and there would be a lot of cross-pollination. Just read a bit about how Einstein came up general relativity -- it is fascinating story about how Einstein wasn't good at math but needed a problem solved so he reached out to some friends and those friends basically gave him some private lessons until Einstein clicked and figured it out. For me, I pretty much understood Fourier analysis before I started doing electronics. But the usefulness and practicality of it only clicked after I moved to higher frequency problems and started using frequency domain when working with my circuits. You don't get much significance of it just studying theoretical math.

jampekka 3y ago
> I agree, theoretical math students and staff are a bit dismissive about everything else. I think this does go somewhat both ways. E.g. in the current discussion there are quite a few people complaining about "useless maths". I think a big problem is that different areas of studies don't appreciate that they are, well, different, and it's not trivial to transfer ideas across fields. > Just read a bit about how Einstein came up general relativity Also an interesting story about special relativity: Minkowski (Einstein's math professor) proposed very early on to Einstein that special relativity should be formulated geometrically (with what's now called Minkowski spaces), but Einstein deemed it too mathy and unintuitive, only to accept later that it was the right way to go. Without the geometric formulation it's very possible Einstein wouldn't have developed general relativity later on. > But the usefulness and practicality of it only clicked after I moved to higher frequency problems and started using frequency domain when working with my circuits. One argument for teaching FT more abstractly is that the "useful parts" are quite different in different fields. E.g. in many applications of sound and acoustics (and probably in EE) the main interest is in the spectrum. But in e.g. statistics the main thing is the convolution theorem and the spectrum has practically no use.

jampekka 3y ago

> I agree, theoretical math students and staff are a bit dismissive about everything else. I think this does go somewhat both ways. E.g. in the current discussion there are quite a few people complaining about "useless maths". I think a big problem is that different areas of studies don't appreciate that they are, well, different, and it's not trivial to transfer ideas across fields. > Just read a bit about how Einstein came up general relativity Also an interesting story about special relativity: Minkowski (Einstein's math professor) proposed very early on to Einstein that special relativity should be formulated geometrically (with what's now called Minkowski spaces), but Einstein deemed it too mathy and unintuitive, only to accept later that it was the right way to go. Without the geometric formulation it's very possible Einstein wouldn't have developed general relativity later on. > But the usefulness and practicality of it only clicked after I moved to higher frequency problems and started using frequency domain when working with my circuits. One argument for teaching FT more abstractly is that the "useful parts" are quite different in different fields. E.g. in many applications of sound and acoustics (and probably in EE) the main interest is in the spectrum. But in e.g. statistics the main thing is the convolution theorem and the spectrum has practically no use.