121–130 of 371 posts
https://www.gwern.net/docs/statistics/1957-feller-anintroduc...
this is linear algebra + combinatorics + probability + stats
If you understand the material in this one book it's reasonable to say that you are pretty good at math
As a math PhD I have to say the only way you're going to learn mathematics is if you actually have a pressing need to do so. i.e. You have a project at work that needs some math, you have a hobby that needs some math. In this case you just learn what you need. Just learning math for its own sake outside of a University STEM track is just too hard (I wouldn't be able to do it and I've tried).
I hesitate to contradict someone who has gone through the whole Math PhD process, but I have to say that the best mathematicians that I know treat the problems they're working on as games, or riddles to be solved... and they've taught their kids (and others) this same method of thinking about these problems. There's a huge mental tool set, and often a lot of grinding to get to a solution, but it's just a game (and th…
I learned all kinds of quantitative analysis and statistics in the CFA program ten+ years ago.
I had daily sheets that I would solve equations and answer all kinds of questions. I knew them forwards and backwards. I just looked at one now on fixed income - not sure if could answer any of the questions today to save my life.
And I work in finance daily!!
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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.…
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…
The curriculum guides Susan Rigetti provides are an amazing resource for self-study. And the fact that she worked through all of this is truly inspiring. Not to be greedy, but do any of you know of other thorough curriculum guides like this? I know about https://teachyourselfcs.com already -- another amazing guide. Are there others? I would love to find one for statistics especially, but really any subject would be i…
Susskind’s Theoretical Minimum is fantastic for physics self study: https://theoreticalminimum.com/
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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.…
Not sure I agree with that - you also have to take into account that calculus is a requirement for many other sciences. I suppose you could just of course make it a pre-req for things like that but I found that in highschool rarely did they go that deep. Physics becomes a hell of a lot easier with basic calculus for example. If anything should be dropped from a highschool level its all of the insane memorization you…
What sort of memorizations do you have in mind that you no longer need to memorize once you know calculus?
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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…
Calculus and linear algebra continue to dominate in applied mathematics. "How can I turn this into a problem in linear algebra?" is probably the most fruitful mathematical technique that has ever existed.
And, from that perspective (with which I agree), calculus itself is just another instance of trying to turn a non-linear problem into a problem in linear algebra!
For many, many years I thought I did. I'd have a brief surge of interest for a few weeks, and then get completely bored of it. I'm not someone who finds it inherently easy, so boredom + difficulty = failure.
When I was foolish enough to do this in university, it meant doing great in the first few assignments, and then abysmally in the exam.
So my policy now is to never study maths for its own sake. Only when there's equations in a computer science paper I don't understand.
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 thing that makes it VASTLY better than most self study math programs or books is that there are hundreds of exercises that you can do, and see if you got the right answer. If you didn't, it will in most cases explain how to do the problem so you can try again with a completely different problem, so you're not just memorizing the answers.
Another thing that makes it great is you can do a little bit a day, start and stop, and come back to it and it will remember your progress and where you left off.
Khan is also a gifted teacher. Unlike a lot of math teachers, he has great pronunciation and handwriting and you can watch his lessons as many times as needed.
I really don't. For many, many years I thought I did. I'd have a brief surge of interest for a few weeks, and then get completely bored of it. I'm not someone who finds it inherently easy, so boredom + difficulty = failure. When I was foolish enough to do this in university, it meant doing great in the first few assignments, and then abysmally in the exam. So my policy now is to never study maths for its own sake. On…
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Geometry has really all that is needed for proofs: * Axioms * Substitution * Modus Ponens * Universal Quantification Induction or proof by contradiction are just special cases of this. But yeah, geometry for introducing proofs is difficult, because it is so easy to confuse visual intuition with proof. At the very least, you need a capable teacher who knows the difference. But nobody expects children to understand it…
The thing about geometry is that it does not take long before you've taught those four things, and then you start teaching stuff that is specific to plane geometry.