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So you want to study mathematics

susanrigetti.com

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Re: So you want to study mathematics

#311

Post by q-big »

novok wrote: post #274
kjasdfj3 wrote: post #239

Earlier quoted context omitted.

> 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…

Unless you are dealing with subjects that would actually use calculus, people in their day to day lives would do much better to understand probabilities, statistics and experiment design. Most of our lives are dealing with the results of empirical studies, in business, science and policy and humanity could use a big reminder that life is not a binary black or white, but a huge pot of maybes. Otherwise it just gets ab…

> Unless you are dealing with subjects that would actually use calculus, people in their day to day lives would do much better to understand probabilities, statistics and experiment design.

Probability theory is applied analysis. For example a measure density is a derivation of a measure with respect to another measure (Radon–Nikodym derivative). Or how do you often assign probabilities to measurable set: Lebesgue-Stieltjes integral.

So you better have a very good understanding of calculus before starting with probability and statistics.

Re: So you want to study mathematics

#312

Post by igravious »

Not to be too negative but I wouldn't have super high hopes for this if it's anything like, “So you want to study philosophy”[1][2]

[1] website :- https://www.susanrigetti.com/philosophy

[2] discussion :- https://news.ycombinator.com/item?id=28367416

A shame I missed out on that discussion.

Re: So you want to study mathematics

#313

Post by crispyambulance »

brimble wrote: post #31

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.…

> Are there any "math for people who just want to use it" tracks in math pedagogy?

If you're talking about college level, "math for people who just want to use it", is basically all it is (outside of math departments and perhaps outlier curriculums in some elite places) and that's a problem.

Learning just the applications without picking up the theorems and without a true understanding of the concepts makes more advanced work in whatever discipline one chooses more difficult. Why? Because you'll have to follow mathematical arguments and it's so much easier to do that when you got the background to fall back on.

I think students before college need more focus on mastering the basics. They're rushed so much, and tragically, math is very cumulative. Any one who has tutored before will notice that it's disturbing how many people don't really understand how to manipulate fractions as they enter a calculus course.

Re: So you want to study mathematics

#314

Post by radlad »

eternityforest wrote: post #279
joatmon-snoo wrote: post #197

Earlier quoted context omitted.

Education is a Hard Problem TM because the knowledge of those links isn't useful without sufficient existing knowledge, and you need to introduce things in a way such that the things you hand-wave away are tolerable knowledge gaps. Knowing that a CDF is an integrated PDF isn't useful for someone who doesn't even have a notion of what a PDF is. Describing a state machine that satisfies conditions X Y Z as an Abelian g…

What would someone other than a scientist use regressions for? I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through. But that's not actually doing a regression, just knowing it exists and computers can do them…

> Most everyday people just trust the p values and move on to wondering about confounders they forgot.

Perhaps because they never took statistics.

Re: So you want to study mathematics

#315

Post by dunefox »

rg111 wrote: post #272
dunefox wrote: post #179

Earlier quoted context omitted.

Thing is that I just can't read PDFs.

Use an iPad, or any tablet, rather than smartphones. I also read PDFs full-screen on my high-res, high-dpi laptop. Try these two. I have read tens of thousands of pages in PDF. (Yes, I checked)

Almost the same thing imo. It's a screen and I already sit so much in front of screens... all the more now that Elden Ring is out.

Re: So you want to study mathematics

#316

Post by xtiansimon »

brimble wrote: post #31

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.…

History of mathematics is a cool and relatable subject in so far as you can imagine the problems of ancient Egyptian worker paid in bread, and land survey/architecture. problems to Nazi code breaking, yeah?

Re: So you want to study mathematics

#317

Post by Jensson »

radlad wrote: post #314
eternityforest wrote: post #279

Earlier quoted context omitted.

What would someone other than a scientist use regressions for? I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through. But that's not actually doing a regression, just knowing it exists and computers can do them…

> Most everyday people just trust the p values and move on to wondering about confounders they forgot. Perhaps because they never took statistics.

Basically every person who writes papers using statistics has taken a course in statistics. Medical doctors do it, psychologists do it etc. And the statistics course you'd replace calculus with would be even lower level than that, basically worthless to everyone. At least calculus trains you to think about rate of change and slopes, statistics gives you nothing practical. It isn't like people remember those formulas so they can apply them in their daily lives.

Re: So you want to study mathematics

#318

Post by BlackFly »

brimble wrote: post #205
Jach wrote: post #144

Earlier quoted context omitted.

Yes, all tracks of math involve people using math. Proof writing is a part of use for a lot of it. There are also very many tools within the use of proof writing where a lot of education is around learning a bunch of tools so that you can better "recognize which tool to apply, then apply tool", in a future real-world use where you want or need to prove something. I'm a little snarky, but you have a broken idea of wha…

> I'm a little snarky, but you have a broken idea of what math is. I do not, which is why I explicitly acknowledged that what I want is not "real math". I don't care about math for math's sake, even a little. Not my thing, never will be. Basically I want to learn to apply useful results from hundreds-of-years-old "advanced" math the same way I learned math in grade school: memorization, pattern recognition, heuristic…

Haha, you were so careful and still got the classic "That's not serious mathematics!" response.

You might want something less applied, but I highly recommend Burden & Faires "Numerical Analysis" and Trefethen "Numerical Linear Algebra". The various interpretations provided by Trefethen for understanding a matrix, eigenvectors, singular value decompositions, etc. are amongst the most insightful descriptions I've come across.

Re: So you want to study mathematics

#319

Post by caddemon »

jll29 wrote: post #62
joatmon-snoo wrote: post #49

Earlier quoted context omitted.

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.…

Calculus and linear algebra seem to _totally_ dominate the curriculum in most (all?) countrie. What about meta-mathematics? Topology? Logics? History of mathematics? Philosophy of mathematics? Combinatorics? Number theory? Discrete mathematics? Graph theory? In the post, the fieds under "electives" are by far the most interesting ones, IMHO. And I fully agree, in-depth knowledge of probability theory as well as descr…

I fully agree with your general point, but in the US I've found calculus to be much more dominant than linear algebra. I went to an "elite" high school that still does not offer any course in linear algebra, despite having enough juniors in AP calc to fill a room. Senior year options for those students are AP stats or multivariable calc. At my college, everyone was (and still is) required to take through multivariable calculus, but there's no such requirement for linear algebra.

I have some appreciation for calculus now but I really did not enjoy it much in high school or even in college. It turned me away from learning more math for some time which is unfortunate - linear algebra isn't my favorite either but I liked that much more off the bat, so I wish I had some exposure to it in high school. Then again, maybe the high school teaching style is what made me dislike calc to begin with.

Re: So you want to study mathematics

#320

Post by lordgrenville »

throwamon wrote: post #273
Buttons840 wrote: post #109

Earlier quoted context omitted.

Khan Academy. Finish a course, retake the course exam once a year afterwards, fill in knowledge gaps as needed. Doing this should keep all undergraduate math fresh in your mind.

I wanted to like Khan Academy, but the pacing of the exercises is so frustrating. They become too easy too fast and then it's an extremely repetitive slog of useless computations. I wish for a service just like them but with many more difficulty levels and less (non-spaced) repetition.

I recently came across brilliant.org, which I think aspires to be this. I didn't stick with it but it might be what you're looking for.
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