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Looking for a insightful roadmap to learn math

  1. Feb 28, 2015 #1
    I have drop out school at high school. All the subjects taught in school were senseless to me, so I've decided to leave it. After that, I've decided to learn things by myself. Nowadays I'm working as software programmer developing computer vision programs, without any college degree.

    I think I need build a solid foundation on my math knowledge. I've plans to study subjects like algorithms (e.g. Knuth's TAOCP) and I still can't read the maths expressions used to describe algorithms that I find in computer vision papers. So I think this solid foundation should be oriented to fit a computer science curriculum, but I don't want to be stuck with it. I also want to develop a mathematical vision of world, to be able to solve real problems using math, to be able to get in at any subject where math is used, like physics.

    How can I achieve this?

    My first step was to get a copy of The Elements, Euclid. I'm in the very early propositions and I'm loving it. I found this book after realize that I don't needed to master arithmetic or algebra in order to read it properly, and we use geometry a lot at work. This book is very comprehensive and straightforward.

    But, I really don't know what to do next. I would prefer a classical approach instead a khan-video-site one. I feel like video lectures are too passive. I would prefer textbooks instead.

    I'm already considering two possible next steps: get a copy of Gelfand's Algebra or to read Euler's Elements of Algebra.

    What should I do? How can I build this roadmap to self learning math?

  2. jcsd
  3. Feb 28, 2015 #2


    Staff: Mentor

    My suggestion is to checkout the website Mathispower4u. It has videos covering a wide range of math from algebra to linear algebra, differential equations and Multivariable calculus.

  4. Feb 28, 2015 #3

    Simon Bridge

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    Welcome to PF;
    You can get a solid road map from the introduction pages in the more comprehensive text books or by looking up your local national education curriculum online.
    There is no one path through math. You seem to have chosen to start with geometry ... that is an old fashioned approach but it seems to have worked for you.
    Your next foray should be number theory and statistics ... so your instinct to go to algebra next is a good one.

    You liked Euler's geometry, so you may like the algebra one. These texts you are using are very old though - education has progressed since then. You are better advised to go for something much more modern. There are self teaching guides which tap into the fact you probably did some in secondary school at least - but ages ago.

    Apart from that, I'm afraid the question is wide open.
  5. Feb 28, 2015 #4
    @Simon Bridge, thank you for your reply. Unfortunately, my local national education curriculum to the high school is a joke. Here we have a thing called Vestibular, which means "a competitive examination and is the primary and widespread entrance system used by Brazilian universities to select their students.". This crap only exists here because there are no enough vacancies for students in the public universities (which are the best universities in the country). And as a consequence of this model, all textbooks are oriented to turn the student the best one in this competitive examination, without caring about comprehension of subjects. Also, Brazil isn't a good reference on education, just look at our ranking in PISA. That's why I'm looking for U.S. curriculum and/or Russian books :)

    @jedishrfu, thank you for the recommendation, but like I've said I would prefer books instead video lectures. I don't know why. Khan sounds like comprehensive and complete, but I can watch 10 hours of videos and do 5 hours of online exercises and after that I feel like I haven't studied yet.
  6. Feb 28, 2015 #5


    Staff: Mentor

    If checkout the video table of contents on Mathis power4u you'll have your roadmap. After that you can choose to watch them or not.
  7. Feb 28, 2015 #6
    @jedishrfu, Oh I see. This table of contents seems to be complete. Thank you.
  8. Feb 28, 2015 #7
    I think I need start with Algebra I. So, would Gelfand's Algebra book be a good and enough kickstart?
  9. Feb 28, 2015 #8
    After thinking about these questions, I've realized that I don't need a full roadmap for now. I just need a simple and concrete plan to guide my weekly study, thus I will touch the most important subjects that I want to learn for now: algebra, geometry and computer algorithms.

    To algebra, I'm going to use the Serge Lang's book Basic Mathematics for theory and Gelfand and Shen's Algebra for exercises.

    To geometry, I'll keep studying Euclid's The Elements, which is a beautiful book :)

    To computer algorithms, I'll start with Knuth's TAOCP. I know there are lots of math over there, but the author have said that "the single requirement that the reader should have already written and tested at least, say, four programs for at least one computer" and "a knowledge of elementary calculus will suffice for most of the mathematics in these books". So, while I know nothing about calculus I'll just skip the math parts in the book (or do my best to understand the math expressions).

    After that, I think I can advance by default curriculum: Trigonometry, Precalculus, Calculus and so on.
    Thank you
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