this post was submitted on 16 Dec 2024
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Hell yeah, I'm currently trying to teach myself proof based calculus and linear algebra because I forgot everything since school and would like a place like this for when I get stuck on practice problems!
That's rly cool :3 Am unfamiliar with proof-based calculus but if that means likeee..... formal methods in calculus, that sounds quite fun (I came into this whole thing out of an interest in formalism lol). Should def have a place to help you if you get stuck
Is there any particular reason you're interested btw?
Right now I'm just trying to get through Apostol's Calculus Volume 1 and 2. Almost half way through volume 1 right now. My previous understanding of the topic was whatever I needed in my AP Calculus AB and BC classes from high school which never included any proofs at all.
No particular reason other than I'm also interested in physics and want to improve my math ability to get a better understanding of that.
That does sound like a good way to figure out physics more
I am also working with a high school math education here , except not rly cuz it mostly didn't stick in my brain lol (and it didn't include any calculus courses sadly). Idk... the only way I actually understand things is understanding them as systems and my classes never included anything about proofs and, more broadly, that fact that "math" is more than just a massive set of disconnected rules that you have to remember for manipulating static, already-existing formulas or something lol. The only way I have been able to make any of this make sense to me is by understanding math as.... basically a very complicated constructed language with high social status and multiple overlapping formal-systematic definitions lol. Not saying we should be teaching primary school children set theory necessarily (unless??) but it would have been nice to get some of that in school
One thing that has been rly helpful to me are computer proof systems. Like not only can I look at math concepts and structures proved in these things and see how they relate to the most basic fundamentals/axioms (and how they are proved from them) but I can also attempt my own proofs and have a computer tell me if I'm right or wrong :3
I have mentioned this system before on here but in particular Metamath and its associated database has been essential for me to even barely figure out what is going on lol. If you're unfamiliar, highly rec checking out, for example (related to your study) they actually have a computer-verified formal definition of real and complex analysis proved all the way from the axioms of classical prepositional/predicate calculus and ZFC set theory here: https://us.metamath.org/mpeuni/mmtheorems.html#dtl:13. One of the founding goals of the Metamath project was actually to make abstract math accessible to everyone, not just people who had tens of thousands of dollars (at least) to get a university education. Really cool project, honestly liberatory in a way. It's uhhh not so good as a complete, easy-to-use proof assistant (right now) compared to others but I am attracted by its relative simplicity hehe (the core Metamath program is legit just a few thousand lines of ANSI C code)
Thanks for the link! I'm not yet very fluent with working in logical notation, but this looks like a handy reference for when I get better at it. I feel I learn best when reading more conversationally toned textbooks like Apostol's, but having the same information fully compressed and indexed is extremely useful for getting multiple perspectives when I'm stuck.
And I feel the same way you do about the way math is taught in high school with zero regard for rigor. It hardly gets into what math even really is, it's an extremely misleading introduction to the topic that blindsides people who then go to college intending to pursue it further.