2 + 2 is 4 minus 1 that's 3 quick maths.
Ask HN: How to self-learn math?
61–70 of 215 posts
Re: Ask HN: How to self-learn math?
#62Re: Ask HN: How to self-learn math?
#63haskell(common knowledge) -> category theory(compare it with set theory here you will read about math foundation crisis) -> type theory(curry howard correspondence or logic == program) personal perspective
I highly recommend Bartosz Milewski series in category theory https://www.youtube.com/watch?v=I8LbkfSSR58
Independently of whether this is a helpful answer for the original question, thanks for that link, was looking for some good lecture introduction on category theory and this looks really nice.
Re: Ask HN: How to self-learn math?
#64Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can save you weeks of table head-butting. (But obviously you can't rely only on the teacher.)
As for books, it's not a spectator sport: you gotta do it yourself. Read a sentence, then work it out yourself with pen & paper. You can't get it just from reading alone.
Finally: in mathematics there's many many roads to Rome! If something isn't working for you, try another way.
Re: Ask HN: How to self-learn math?
#65Bill Shillito's lecture series for Project Polymath is by a mile, the best introduction to higher level mathematics. It requires absolutely no prerequisite knowledge.
Introduction to Higher Mathematics: https://www.youtube.com/playlist?list=PLZzHxk_TPOStgPtqRZ6Kz....
If you find he talks a bit slow, change your playback speed to 1.5x. Enjoy! :-)
Re: Ask HN: How to self-learn math?
#66I’m going to go with a few assumptions here: a) You don’t do this full time. b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach. c) You are skilled with programming/software in general. In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Eve…
What's your opinion of Mathematics for computer science?
Have no opinion - haven't read it and Amazon has no preview for it.
Re: Ask HN: How to self-learn math?
#67Nothing beats having a (good) teacher. Self-learning, no matter how smart you are, is pitifully slow without a teacher. Half an hour with a good teacher can save you weeks of table head-butting. (But obviously you can't rely only on the teacher.) As for books, it's not a spectator sport: you gotta do it yourself. Read a sentence, then work it out yourself with pen & paper. You can't get it just from reading alone. Fi…
If OP lives in a city, it shouldn't be hard to find a sharp college kid who will tutor.
Re: Ask HN: How to self-learn math?
#68I’m going to go with a few assumptions here: a) You don’t do this full time. b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach. c) You are skilled with programming/software in general. In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Eve…
The Princeton Companion to Mathematics is a good resource consisting of a huge collection of detailed articles on many mathematical subjects by knowledgeable contributors. It requires no specialized background and is curated by Fields Medalist Tim Gowers. Whoever reads it from cover to cover is my hero, but failing that there's always an interesting article to jump to.
Don't just be a consumer but write something as soon as you're inspired. I wish there were more emphasis on writing mathematics in school prior to the graduate level. Leslie Lamport says if you're thinking but not writing you're not really thinking; you only think you're thinking. For Feynman the act of discovery wasn't complete until he had explained it to someone. There's also the rule of thumb that if you can't explain a mathematical concept to a ten year old, you don't understand it yourself.
Edit: typo
Re: Ask HN: How to self-learn math?
#69I’m going to go with a few assumptions here: a) You don’t do this full time. b) By “bottoms up” you just mean “with firm grasp on fundamentals”, not logic/set/category/type theory approach. c) You are skilled with programming/software in general. In a way, you’re ahead of math peers in that you don’t need to do a lot of problems by hand, and can develop intuition much faster through many software tools available. Eve…
The Princeton Companion to Mathematics is a good resource consisting of a huge collection of detailed articles on many mathematical subjects by knowledgeable contributors. It requires no specialized background and is curated by Fields Medalist Tim Gowers. Whoever reads it from cover to cover is my hero, but failing that there's always an interesting article to jump to. Don't just be a consumer but write something as…
> The Princeton Companion to Mathematics is a good resource...
I think Princeton Companion to Physics curated by Frank Wilczek, a Nobelist, is due to be published this year.
> Whoever reads it from cover to cover is my hero...
Yeah, I'd die an accomplished man if I would grok just a few books I treasure, amongst which are TPCTM and MICMAM.
> Don't just be a consumer but write something as soon as you're inspired.
Absolutely. That's why I recommend just a small amount of comprehensive resources. It's hard to get motivated by a pile of books complemented with synthetic problems related to a particular chapter. The idea is to just go about your daily life and start to slowly see more and more math problems everywhere around you; it does wonders to motivation.
Re: Ask HN: How to self-learn math?
#70> My current proficiency level is pre-high school mathematics as I didn't pay much attention in high school, learning effectively nothing.
I took a look at your other comments and submissions, to try to get an idea of whether or not you are a programmer. The fact that you are on HN makes the odds pretty good that you are or were, but there are enough people here who are not that I didn't want to assume. It's relevant because programming requires thinking in ways that overlap a fair bit with the kind of thinking required in mathematics, so whether or not you are/were a programmer would affect my recommendations.
What I found puzzles me, particularly concerning your current "pre-high school" proficiency level. In a post a few days ago, you said that you are "graduating a university with a civil engineering degree in a few months" [1].
Most sources say that civil engineering requires calculus, differential equations, linear algebra, complex analysis, and probability and statistics.
I'm having trouble understanding how you could have gotten into a university civil engineering program in the first place if you math proficiency level is really just pre-high school, let alone got to within a few months of graduation.
Also in that post, you are asking a quite similar question to this one, except it is about CS fundamentals instead of about math from the ground up:
> Hi, I am a front-end developer since 2 years freelancing for local clients. A week back I fell in love with computer internals and now want to learn CS fundamentals and become a full time software engineer.
...
> Could you give me a roadmap for how I should go about learning CS fundamentals? What books and papers should I read? How did you learn, what step and approaches did you take?
I'm not normally suspicious of these types of questions...but something seems off here.
If the question is on the up and up, and you really do only have pre-high school math, take a look at ck12.org [2]. Go to one of their subjects on that page, such as algebra, and click it. On that page, click where it says "FlexBook Textbooks". That will take you to some freely available textbooks meant for K-12. Click where appropriate to get the high school ones. These should give you the high school math you are missing. I think you can also find on that site material for teachers, which could help for self-study.
Get this material down cold...it's not all that college level stuff is going to assume you know it well, so push through even if it sometimes is not a lot of fun. If you need something fun while going through the high school stuff, take a look at the books that collect Martin Gardner's old "Mathematical Games" columns from Scientific American.