“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 …
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Replying to @Meaningness
I can agree that most computational tasks end up reduced to linear algebra, and comp lin alg is super important and underapreciated - but "you’ll never actually have to solve an integral"? That seems too much, you can't do serious probability without analysis.
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Replying to @Meaningness
Well, not much. My point is just that you can't develop new mathematical methods (that will probably computationaly reduce to linear algebra in the end) without a solid grasp of analysis.
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Replying to @brewingsense
Oh, sure. If you are going to be a mathematician, you need to learn tons of everything, definitely including analysis. But hardly anyone is a mathematician. Math courses are mainly taken by future scientists and engineers.
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Replying to @Meaningness
I guess we don't have a real disagreement, I just reacted to what I felt was too much of a dismissal of analysis.
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Replying to @brewingsense @Meaningness
For example I suppose that if you are an engineer, and you use a Kalman Filter - then what you do computationaly is just lin alg, but to understand why it is the way it is you need some understanding of probability and calculus.
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Replying to @brewingsense
That is a good example, yes! I definitely think everyone ought to go through the basics of calculus and differential equations. If only because you can’t do Newtonian mechanics without it, and that’s essential conceptually even if not in practice.
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Replying to @Meaningness
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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Replying to @Meaningness
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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Replying to @Meaningness
Well, teaching math in a way that is rigorous but doesn't explain why many thigns are defined the way they are, what is the intuition behind them, what they were created for and what are they useful for ... surely can be boring as hell and not create any real understanding.
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Replying to @brewingsense
Yes… maybe the answer is just that there’s Too Much Math and not enough time in life to learn it!
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