Given that khan academy is free, I think 50/month is a steep ask for trying something out. Especially when it is labeled as beta.
Relearning math as an adult
141–150 of 268 posts
Re: Relearning math as an adult
#142Nice Ad post, there are A LOT of free resources to learn math on the web, why go through $49/month ? People are citing Khan Academy which I warmly recommend, there are a lot of good Math teachers teaching math on YouTube, and there is also OpenStax.org [1] which releases free public books on different subjects including... you guessed it... math ! Go check it out ! But maybe for some people, spending money is a neces…
There are plenty of resources that will go through proofs and tell you about math. Much fewer resources that will give you exercises and some sort of framework to help you move through them.
Khan does this really well for up to high school. Not really sure about beyond that.
I think a good service could be worth $50/month, but I agree it’s a tough ask.
Re: Relearning math as an adult
#143The "math" used in ML/AI papers is usually just a sort of 'whiteboard math' which is a domain-specific mishmash of linear algebra, calculus, set theory and statistics. If you could find a book just going through the relevant bits you wouldnt really have to "learn math again", it can be translated into english straightforwardly -- very very few ML papers relevant to industry have extended proofs, etc. that require eg.…
Normalizing flows and neural ODEs are becoming a bigger thing, and they do involve some more heavy maths.
Yes, and if you look at neural operators, then you're in for something that even math majors need to put a bit of effort into.
Re: Relearning math as an adult
#144I feel like the author, and did like the author for like year now. And I know lots of people feel this way, and we're telling each other to like "learn math, man, coding is something LLMs be doin in 10 years".
Indeed, these ML/AI papers are indeed full of cryptic writing, but in essence they are not so difficult compared to like... understanding what a FSM is and how to produce a minimal automata it from regex (hey ML guys, would like to see you do this on paper!). The greek-letters-infused-notation is what scares most people, and you know what - this notation has its origins in pre-computing age. Perhaps ppl need a new notation, or like magazines should require math geeks to also provide pseudo-code for dummies.
I also note that lot of things in ML seem to be about algorithms really, and very much about how things are engineered when implemented. Then I love graphs, discreet math, et. and were surprised to relearn that stuff like Markov chains is something very natural to me. Then the linear algebra needed for ML is not so much also - matmul, diagonal matrix, eigenvalues, inverse matrix, Hessian... wait! that's a lot already. But not so difficult, it is basically a lot of definitions. And some of these were not in the curriculums back in the day. Like... my mother does not have any recollection of learning about median and mode in statistics, even though they (with my father) attended a technical (by nature) university in the 70s.
You know, I'm starting to realize that even our professors in the university back in the day did not fully grasp what all these things were about, because I remember them reading from educational sources, and also being very punctual about the material, which is not something that s.o. who groks certain domain is going to do. And only few of them gave some actual examples why all the math nonsense could come handy. Well perhaps they are to blame that we have to le-learn, or perhaps it is the natural thing to happen in this new brave world.
Re: Relearning math as an adult
#145Parsing math notation has been a big weakness for me, especially with AI stuff. If I can see it in code, or at least pseudocode, stuff clicks much more intuitively. Wish there was a more efficient way to bridge that skill gap. Maybe condensing variables to single letters that have to be kept in mind just annoys me too much.
Re: Relearning math as an adult
#146About a year ago my wife and I made the joint decision to get her into college for a bachelor's degree in either English or computer science. Here in Finland, university admissions are based around how well you did on various end of school exams, and she fortunately did quite well on all of them a decade ago - except for math. She bombed math due to health and family problems as a teenager decimating her ability to p…
> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.
please tell me that how can I get question for practice in math of university level? most of textbook even don't contain answers of practice in the book...
Re: Relearning math as an adult
#147Earlier quoted context omitted.
I think you don’t realise how much math you know. I’ve heard of set theory, but never studied it.
sure, but you dont need to understand actual set theory -- it's just notation for mostly obvious programming stuff, R means float, Z means int R^2 is actually notation from linear algebra, but here it means a point is 2 floats with a measure of distance between points etc. A lot of this could just be given in a "crib sheet" for tech people, and you'd get 80% of it straightaway. It's years of work to understand this n…
> sure, but you dont need to understand actual set theory
How would you know? You sound like you understand set theory. Ironically, a body needs a rather extensive grounding in the theory and practice of set theory to look at something and think "I don't need to use the tools of set theory here" with deserved confidence.
A lot of maths is about having a huge repertoire of tricks that you know won't help solve the problem at hand. Saves weeks of fruitless attempts. But I'll bet you didn't notice the things you know not to do. That does matter for interpreting these papers.
Re: Relearning math as an adult
#148Earlier quoted context omitted.
sure, but you dont need to understand actual set theory -- it's just notation for mostly obvious programming stuff, R means float, Z means int R^2 is actually notation from linear algebra, but here it means a point is 2 floats with a measure of distance between points etc. A lot of this could just be given in a "crib sheet" for tech people, and you'd get 80% of it straightaway. It's years of work to understand this n…
> sure, but you dont need to understand actual set theory How would you know? You sound like you understand set theory. Ironically, a body needs a rather extensive grounding in the theory and practice of set theory to look at something and think "I don't need to use the tools of set theory here" with deserved confidence. A lot of maths is about having a huge repertoire of tricks that you know won't help solve the pro…
> > sure, but you dont need to understand actual set theory
> How would you know? You sound like you understand set theory.
Easy: most mathematicians don't really care about set theory (beyond the fact that it exists and is the standard foundation).
Understanding set theory goes deep. For example: why does the Banach-Tarski paradox exist in ZFC (C: Axiom of Choice (https://en.wikipedia.org/wiki/Axiom_of_choice)), but not in ZFD (D: Axiom of Determinacy (https://en.wikipedia.org/wiki/Axiom_of_determinacy))? Or another one: why does the statement "every field has an algebraic closure" not hold in ZF (but in ZFC)?
Never heard of this stuff despite having studied mathematics? Just like I said: most mathematicians don't really care about set theory.
Re: Relearning math as an adult
#149Earlier quoted context omitted.
> I guess education in the US has local standards? Very much so! The US didn’t have a Department of Education until the 90s.
90s? You're off by a bit. The current Department of Education started in 1980, but it came out of the Department of Health, Education , and Welfare, founded in 1953. That, in turn, came out of the FSA which included an Office of Education (1939). Prior to that, the Office of Education had been part of the Department of the Interior. Before that it was its own Department, starting in 1867. Though "90s" is delightfully…
Thanks. I have no idea where I read that, but have been carrying around that “fact” for over twenty years!
Re: Relearning math as an adult
#150Earlier quoted context omitted.
> set her nose to the grindstone Worth calling out the key observation: it takes practice, and lots of it (for most people, anyway) to get good at math. Just reading about it does zilch.
please tell me that how can I get question for practice in math of university level? most of textbook even don't contain answers of practice in the book...
That's mostly because proofs are too long to write out easily in the back of a textbook, imo. Your best bet here is to learn the proofs of the theorems proved in the book first - they're usually much harder to come up with at first glance than the problems one bases on them. Or, if you're using a commonly used textbook, you can usually find people's own proofs online. Sourcing an easy to grok and easy to check proof is a very good skill to build in any case, it minimizes wheel reinvention at the neural level.