251–260 of 371 posts
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My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. The analytical type of thinking that proof-writing is certainly useful, but you can make much the same argument of many other curricula, and besides, it's not like most intro calc courses even do any proofs.…
> My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. I'm questioning your math pedagogy. Calculus is the single most important math anyone, of any field, can learn as it's the first "practical math" you actually learn. Life behaves like calculus and in order…
I was a math major and this is not exclusive to calculus or analysis. If anything, algebra classes in things like group theory were much more instructive on this point. Everything from my third and fourth years (when I specialized into combinatorial optimization) was built on a cornerstone of proofs and theorems.
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You can certainly make significant headway with some basic combinatorics and basic tables for things like the normal distribution, no calculus needed. This is in fact how most people currently learn statistics.
What happens when you dont have tables? In the land of the blind the guy with one eye walks everyone off a cliff.
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> My strong opinion as someone who majored in math is that, at least within the US, the standard calculus requirement should be replaced with statistics. So much more useful and so much more important as an adult. I'm questioning your math pedagogy. Calculus is the single most important math anyone, of any field, can learn as it's the first "practical math" you actually learn. Life behaves like calculus and in order…
I think calculus and trigonometry shouldn't be taught to non-math majors. You have the perspective of someone who is passionate about calculus, which is great, but considering many people aren't as passionate, what you're suggesting (status quo) doesn't work. Or maybe you have ideas on teaching calculus better than how it's currently done? Calculus is obviously extremely important, but I don't think it's useful to dr…
For science-oriented high school curriculums, calculus is necessary, and should only be optional in a few cases where the student already really knows what they want to do.
By the time a student wants to specialize at say 20, they should have already had some foundational ability for that specialty, otherwise they wouldn't be able to compete internationally. For people who don't end up using calculus, it's a waste, but there is a trade-off. As a result, much of the high school curriculum is to build a broad foundation to prepare for multiple possible specializations.
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YES! This is exactly my complaint about math. I find the abstract proof-oriented math kinda interesting (although How to Prove It is an exception that I discuss below) but I _really_ want practical real-word applications of these maths. Even though I've learned linear algebra decades ago, Andrew Ng's example of using a matrix to encode 5,000 images then doing linear algebra on it blew my mind. I've since used that pe…
> Not once have I applied a proof to solve a programming problem. There are people in this very thread insisting that proofs are extremely useful in programming. I dunno if I just picked up the same skills elsewhere (Logic? Philosophy? Just... IDK, thinking and developing an absolute shitload of heuristics through years of experience?) or am entirely missing out and in fact don't have a clue how to program, but I don…
For example, I might not remember how to code bisection search but I can figure out the loop invariant and from there it's easy enough to code a working binary search. And even if you have right bisection search down to muscle memory, you can modify the loop invariant to create left bisection search if you need it, while if I tried to keep two binary search algorithms in my head I feel like it would be more error-prone.
For the other 99.99% of us, it would take many lifetimes worth of free time to make a substantial dent in these materials. To me, guides like these are too intimidating to even begin. Maybe what's needed is a meta-guide on structuring one's time and developing the necessary focus to be able to do this within one human lifetime.
Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…
The working title is "Practical Math for Programmers," and the idea is to build a collection of 60-75, 3-page long, _compelling_ demonstrations of mathematics used in production settings, biased toward stuff a generalist programmer might find useful. Not going into proofs or foundations, but providing lots of references to further reading.
I'm aspiring for it to be like a Hacker's Delight, or Programming Gems, but just for math that is genuinely useful.
Read more here: https://buttondown.email/j2kun/archive/a-week-of-book-writin...
Sign up to hear when it's released here: https://jeremykun.us11.list-manage.com/subscribe?u=99aa071e9...
If doing math is essential to conceptual understanding and application, could the interface of math and physics be made more human-centered? For instance, the shift from Roman numerals to Arabic numerals made doing math easier. Based on your experience, might it be possible to increase accessibility by revising some of the arcane conventions of math and physics? See Brett Victor’s 2011 proposal: http://worrydream.com…
Are there any "math for people who just want to use it" tracks in math pedagogy? I don't care a bit about proving any of it's true, or even reading others proofs of same. "Recognize which tool to apply, then apply tool", all focused on real-world use (so, yes, it wouldn't be "real" mathematics). That's the math education I'd like—try as I might, I just can't make myself care even a little about math for math's sake.…