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Ask HN: How should I structure my mathematics self-teaching?

by trwhite on 8/12/24, 8:19 PM with 12 comments

Recently (~2 months ago) I decided to start self-teaching myself mathematics again, having last formally studied it when I was only 16 (I am 30 now).

My goal is to spend a little time doing it every day, not to attain any specific qualification, only to "learn maths".

There are lots of online resources, though it's hard to know where to begin or to go. "What interests me" is difficult because I don't really know the answer yet.

I have been following some of the GCSE syllabus, effectively re-learning what I studied at school (today it was completing the square), but I'm not sure if I'll find this motivating enough.

  • by calebjosue on 8/12/24, 8:58 PM

    When Judea Pearl was asked how Mathematics should be taught, he answered: Chronollogicaly. [1]

    Now, What do You mean to "learn Math". You have to be more specific with your goal. This is funny coming from me because I haven't able to specialize in any single topic.

    Let's suppose You somehow saw The Beauty of Math somewhere and You are ready to continue your journey in such a beautiful topic.

    I really believe You Will enjoy reading "Mathematics for The million" by Lancelot, I saw this recommended by Sir Anthony Hoare[2], You Will be amazed by its content (I have only ready chapter one).

    What's Mathematics?

    Are elementary school children doing Math when they solve addition and subtraction problems?

    Is The High school student crunching mechanical procedures, plugging numbers into formulas doing Math?

    Is theorem proving Math?

    Daphne Koller said in an interview that we are all doing probabilistics when Thinking and making certain decisiones[3]. Are we all Mathematicians?

    Do You want to study Math as a tool to help You in some other areas or study it itself as a subject?

    It doesn't matter, You Will enjoy it and love it.

    Trying yo answer your question. Learn some Arithmetic, just enough. Crunch some elementary algebra (in The fashion of Visualizing Algebra provided by Udacity). Read The book Geometry by Tatiana Alekseyevskaya, learn some Discrete Math (I recommend You the book on the topic by Thomas VanDrunnen), read the other four books in the gelfand series. Learn some logic. Read Introduction to Mathematical Thinking by Keith Devlin. I think at this point You Will able to read some resources o calculus or abstract Algebra.

    If this seems like a Lot, don't dismay. There was this guy George Green having to take care of mill to make bread and do also found time for Mathematics, apparently DeMoivre was struggling financially. There people are just like You. Enjoy your Math journey

    [1] The interview is available on Lex Fridman YouTube channel.

    [2] The conversation between him and Leslie Lamport is available on YouTube

  • by AudiomaticApp on 8/14/24, 7:36 PM

    I enjoyed Art of Problem Solving books as a kid. Some of them are online, and you can probably get them second-hand for relatively cheap. They're better at provoking critical thinking than most math textbooks, and favor puzzle-solving and proofs. They're targeted towards K12, but are much more rigorous than most school curriculum, so they should be a good fit if you're currently reviewing GCSE-level math.

    https://artofproblemsolving.com/store/online

    Each of their courses have an "Are You Ready" quiz. You can take the quiz associated with the textbook you're interested in to see if it's at an appropriate level.

    https://artofproblemsolving.com/school/recommendations

  • by mettamage on 8/13/24, 9:15 AM

    I decided to fork over the money and follow the Dutch mathematics B certification. It's a high school certification that seems to be at the level of AP AB in the US. I think they offer it in English as well [1]. They focus on exercises and you can ask questions in the forums.

    Now I know that I know enough to start learning linear algebra and whatever calculus course they offer at uni.

    I'm a bit odd though as I have some stats knowledge and did a college level course in graph theory. Also, I understood most of the math in information retrieval. So for me, I know that I need to simply fill up some basics.

    [1] https://kdvi.uva.nl/education/mathematics-deficiency-courses...

  • by calebjosue on 8/14/24, 12:18 AM

    I came back to see the different answers op was getting, and I am seeing lots of resources available, to the point in which I have decided to teach Math too! (The basic knowledge I have on the topic).

  • by bpmedley on 8/12/24, 10:32 PM

    I’m working through https://calcworkshop.com/

  • by vismit2000 on 8/13/24, 4:32 AM

  • by vismit2000 on 8/13/24, 4:30 AM

  • by sn9 on 8/13/24, 5:26 PM

  • by codeful on 8/12/24, 9:41 PM

    check out Hania Uscka-Wehlou (Phd) on Udemy. She teaches mathematics and problem solving the proper way. From the beginning.

    Her precalc is ~200h and she goes the rigorous path, by proving things.

    She is multiple times awarded by universities for her skills in teaching and you will understand why.

    Course is exeptionelly well organized, quality of presentation is... 11/10? Coupon codes are in lecture materials.

    Just start with precalc 1. I believe that after a while the path will emerge for you by itself

    Edit: combine with professorLeonard on Youtube if you need some practice by computing.

    Welcome to the joy of mathematics!