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Your philosophy towards mathematics education is interesting. If you don't mind me asking a direct question: what's the point? Here's my take on the purpose of

Your philosophy towards mathematics education is interesting. If you don't mind me asking a direct question: what's the point? Here's my take on the purpose of math courses in college: any college graduate should be able to teach themselves something "like" calculus or linear algebra upon graduation. So you should teach calculus and especially linear algebra in such a way that a student who has never seen e.g. graph theory can pick that up a bit of graph theory their own using the thinking skills they acquired by studying linear algebra or calculus. Ditto for dynamic programming or combinatorics or basic probability or... So if you're not teaching proofs, wth are you teaching all semester? A few conceptual underpinnings that take about a week to explain, and then a whole bunch of crap Mathematica can do for you anyways. > computational mathematics like calculus and (linear) algebra.. move proof-based mathematics into a targeted graduate degree Memorizing symbolic calculations and/or understanding (how to use) numerical algorithms do not endow students with the skills required to learn new mathematics. Proof-based calculus and algebra courses do teach those skills. The recent post on HN about PID control comes to mind. I'd expect someone with a bit of practice at writing proofs to be able to teach themselves why PID controllers work and avoid pitfalls. But I would not expect your average human-meat-based-derivative-and-integral-calculator to be able to understand the same. To put it in terms of a folk saying about fishing: if you teach a man to calculate, he can perform a specific calculation. If you teach a man how to write proofs, he can learn any calculation he might need throughout his lifetime.

dsacco 9y ago
I think you and I mean different things by computational mathematics. Calculus isn't analysis, but it still has substantial rigor to it. You might not be able to develop calculus from scratch after studying it, like you could by working through real analysis, but that doesn't mean studying calculus has to be hollow and rote. For example, I find Spivak's Calculus to be a good compromise between full on analysis and the kind of formula memorization you're talking about. Ideally computational mathematics teaches more than just the simple "what" - it should address at least one of the "how" or "why", but it doesn't necessarily need to address all three. I also disagree that the point of the education should be for students to be capable of teaching themselves novel mathematics (and to be honest, I'm pessimistic most graduating math undergrads could do that simply because they made it through something like Rudin).

dsacco 9y ago

I think you and I mean different things by computational mathematics. Calculus isn't analysis, but it still has substantial rigor to it. You might not be able to develop calculus from scratch after studying it, like you could by working through real analysis, but that doesn't mean studying calculus has to be hollow and rote. For example, I find Spivak's Calculus to be a good compromise between full on analysis and the kind of formula memorization you're talking about. Ideally computational mathematics teaches more than just the simple "what" - it should address at least one of the "how" or "why", but it doesn't necessarily need to address all three. I also disagree that the point of the education should be for students to be capable of teaching themselves novel mathematics (and to be honest, I'm pessimistic most graduating math undergrads could do that simply because they made it through something like Rudin).