“Too Much Calculus” by Gilbert Strang, who taught me linear algebra in the late Victorian era and is still at it. Linear algebra is what we use for everything in the real world. Calculus is elegant, but you’ll never actually have to solve an integral. http://www-math.mit.edu/~gs/papers/essay.pdf …
I do think there should be a track of applied mathematics that omits a lot of the details and special cases that aren’t relevant for most purposes. Maybe the hard part is figuring out exactly what to leave out, though! Everything is useful for someone/something.
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The best approach might be highly modular, with small chunks you could combine depending on what field you are going into. But that would be hard to fit into the semester-based structure of the current university model.
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Yeah, deciding what to leave out is hard. For engineers you want to drop a lot of rigour in math to cover more ground fast, but I often feel very uncomfortable about it - it can lead to subtle but serious errors and a general feeling of confusion.
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Personally I do much better with a foundational-principles-first approach, but that doesn’t work for most people, apparently.
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