Let's say I had a friend who fucked off in school and now understands fundamental concepts in mathematics less intricately than he would like to. Would you lovely folks have any recommendations for resources that may help this friend of mine? Asking for a friend. Friend of a friend, even.
Thank you to everyone who has replied so far, to add a little context now that I have had time to think about it. Suppose I wanted to produce a small knowledge base of mathematics information for the layman, someone who has not had the opportunity of a formal education but would like to understand the fundamental concepts of math, building the groundwork to take their understanding into their own hands. What resources would you recommend in that case?
@deianeira any specific field your friend wants to get into?
@jere Primarily interested in applications in art and programming, geometry, statistics, rendering, etc. Just genuinely interested in a good platform from which to spring from. Definitely not starting from 0, just missed out on core concepts that an average educated individual might know in a time of apathy.
@deianeira I'd recommend starting with some linear algebra then (I've read good things about the foundation to frontiers course , but I had to learn using books written by my professors, so no idea). Regarding statistics, my only approach to it so far has been through "for engineers" book, which are pretty dry. I think the best option would be to pick a project and find a book that covers the material needed to implement it. Otherwise, it'll feel too abstract
@jere Thank you, this seems like a reasonable addition to a self-imposed curriculum. I appreciate your willingness to share.
@deianeira no problem! let me know if you need help with this. I'm not great at maths, but I can try to help you ^^
@deianeira I would highly recommend 3Blue1Brown's Essence of Linear Algebra series on yt.
I struggled with many concepts before i found his videos; everything is explained visually and algebraically which really helps.
@deianeira Does Khan Academy cover the levels needed?
@maloki I don't know, but I will certainly take a look!
@deianeira Khan Academy began as a maths thing, I think they still have a lot of good, down-to-earth, often hand-drawn and authentically narrated maths classes.
@deianeira What level do you need? Anywhere from 'just starting out' through 'can I get a PhD from this couch' is a possibility... =] There's folks here who are helpful, there's mathstodon.xyz which is a mastodon instance just full of math folks, there's scholar.social for larger community .. and that's just on mastodon. If you can pin down the level to begin from or area of focus, I'll start digging out resource links...
@feonixrift I completed a fairly traditional primary and high-school education in Canada. By the time I was finishing high school I was failing math classes because I refused to pay attention or solve the practice problems on a daily basis. It would be useful to review concepts from the bottom up, with no interest of acquiring a PHD but interest in understanding the fundamental concepts of math and how they may be applied to design both digitally and physically. This is probably too vague.
@deianeira Not too vague at all, and a wonderful position to be in. A lot of us hated the endless repetition; I don't know if I would have gotten through it without knowing 'the good stuff' (in my view at least) came later.
A lot of people like https://www.khanacademy.org/math/ up through ~ the beginning of calculus. It's good for reviewing algebra without falling asleep on the page. I did all my trigonometry that way; it got me straight into calculus when I went back to college.
For calculus, I used to use WolframAlpha a lot but they locked the Step-by-Step mode. :( Lately I'm really fond of https://www.purplemath.com/modules/index.htm (the free lessons pages) for clear explanations -- they're the site I go back to every time I've forgotten a formula.
If you're into older books, there's a great archive here: http://historical.library.cornell.edu/math/ that I've occasionally pulled gems from. Very hit-or-miss, but also relaxing.
I will doggedly say don't ignore geometry -- there is so much beauty there, and so much of the gritty algebraic stuff can be transformed into it. This is my favorite edition of euclid: https://www.c82.net/euclid/ It's nearly unreadable by itself but hard to put down because the diagrams are so wacky. The linked volume at https://archive.org/details/firstsixbooksofe00byrn/page/n19/mode/2up is more readable.
Pencil constructions are the best part of geometry, but I rarely work with them; so I will tag @_cr0_tab in for those...
But in beautiful books, here is one in my wheelhouse: https://archive.org/details/ElementaryNumberTheory_841/ It should be within reach to understand each question well enough to ponder it -- solution, as is often the case in number theory, can be far harder.
Communities! I mentioned mathstodon.xyz (yes, I have an alt over there). Elsenet, there are https://math.stackexchange.com/ and https://mathoverflow.net/ which should not be confused with each other because the cultures differ greatly -- and vary greatly by sub-discipline. Some other sites like https://artofproblemsolving.com/community despite having marketing stuff upfront also have community forums that are very active.
@deianeira So uh, I tend toward long replies on occasion. =] Welcome back to math, I hope you find something you enjoy.
@feonixrift Thank you for all this. I am compelled by the possibility and by the great minds that have utilized it. It seems like a missing piece of this life's puzzle that I will certainly find joy in. Thank you for putting this together, very much appreciate it.
@deianeira What level of math/school are we talking about? Regardless the best way to really understand it would probably be to acquire a textbook and work through the problems in it, starting at the beginning. Any sort of book or course that explains concepts but doesn't have you work problems for yourself isn't going to lead to real understanding. As a prof of mine once said, it's not a spectator sport.
@corey This is solid advice that I will take.
Enough understanding to utilize and reason about mathematics as a tool in design (digitally and physically) and as a procurer of those designs (digitally and physically) would be my ultimate goal. I know that is very vague.
I feel like when solving problems, I am unable to think about math fundamentally or abstractly enough to be an asset to me. I am forced to find implementations by others to use as a started point because of this.
start with a specific small application. work backwards to fill in gaps superficially (use wikipedia and other low effort sources)
once you identify an area that seems core, find a celebrated textbook and invest time to build a broader base (going through a whole textbook would take an entire term - focus on the good bits)
iterate this process. the brain is a muscle
you have a huge advantage over a typical maths student: you actually want to do something with the knowledge :-)
@deianeira At a more introductory level than those, I can recommend Larry Gonick's Cartoon Guides to Algebra and to Calculus.
@deianeira I don't know how "fundamental" you mean, but
I enjoy videos from Vi Hart https://m.youtube.com/user/Vihart and Numberphile https://m.youtube.com/channel/UCoxcjq-8xIDTYp3uz647V5A
They often go way beyond "fundamentals" but that's kinda the point, it's the way they both bring humor and relatability to the topic that makes math feel approachable and playful even when I don't fully understand it
This probably won't help if your question is more like "how do I learn basic algebra at 40" tho
@deianeira Khan Academy.
Math is ridiculously fun, and I say that as someone who hated math
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