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Studying Self-studying mathematics - Discussion

  1. Jun 11, 2017 #181
    Dear young friend. I did share your interest in physics and I was not bad at school. i think the way the Khan academy proceeds in physics is a good option and I would be you, I would follow their path. The same applies to mathematics. So far to the rational way to proceed.

    Emotionally physics was and is for me a fascinating science and dealing with it opens our sense for what our current science is finding out about it. Forget about quantum physics and relativity theories from your learning of physics. Look for good videos in youtube and find some that speak in a more general public kind about those fields of science. That puts you in touch with those topics and you can start to reflect about what you find interesting.

    With mathematics the way it is taught at school and which you will need to master your tests in mathematics at school the Kahn academy gives you solid information to learn. But as with physics, where there are topics that you need at school in which give you a starting point, mathematics offers at least equally fascinating topics that equal in opening your eyes for a whole new way to see the world around you. i f you allow me, I would to tell you a bit about what I mean!

    I did finish my studies at a technical university in 1979. That was then the last time I had to deal with mathematics in the way I did learn until then! So nearly 4 decades later the science about mathematics has also been developed very heavily. The mathematics as you learn to the end of high school really is not mathematics but is learning to apply formulas to solve equations. The top of this king of "mathematics" goes and includes calculus. Terms like differentiation and integration are ones that you can search via google and find information about it.

    I like very much the current definition about the science of mathematics. Mathematics deals with finding "structures"! There is a course from the Standford University which can be taken for free here: "Introduction To Mathematical Thinking" This course has the purpose to help students to make the transition from the kind of mathematics they have been taught until then and to the kind of mathematics the students are required to learn and apply at the university. Do not let yourself be intimidated. Its even more! As you have not yet been spoiled to think the traditional way mathematics was done until about 200 years ago, you will probably have it easier to grasp this "Mathematical Way of Thinking! If you listen to the lecture of prof. Kevlin that you can see as videos, if you listen to the videos were he very detailed explains interesting topics as help for solving the challenges to think the mathematical way, you could have it easier than older ones to capture what is being taught.
  2. Jun 12, 2017 #182
    Thank you very much for this advice, I will take it into account, and definately check out the course on 'Mathematical Way of Thinking' :smile:. Currently, I am also in another Coursera course of Stanford University in 'Introduction to Logic'
  3. Jun 28, 2017 #183
    Study and practice
  4. Jun 29, 2017 #184
    When I was in your age, I liked Jay Orear's Physics and the Feynman lectures a lot. In general: You cannot learn physics without math. So if you want to learn physics, you must learn math first, namely vectors+matrices, analysis (differentiation and integration) and later vector calculus (the gradient, divergence and curl operations and the theorems of Gauss and Stokes). The Feynman lectures cover all this, Jay Orear expects you to know differentiation.
    Don't waste your time trying to learn physics without math or with as little math as possible. It doesn't work/will give you a pseudo-understanding.
    I'd recommend you start with differentiation (by the way, I don't think the explanation that Feynman gives is very good; I don't think I'd have understood it there if I hadn't known it before). I would simply start here (I learnt it first from the math formula reference book that we used at school, so not really a big difference): https://en.wikipedia.org/wiki/Derivative (sections 1.1, 1.4, 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 3.1, 3.2, 3.3)
  5. Dec 25, 2017 #185
    What are the most reliable (preferably free) online courses for algebra 2, pre calc, and calc A, B, and C that give students a deep understanding of the topics? Would I be better off with textbooks or a paid online program?

    I would like to self-study the math necessary before I dive into physics, however, I would like to not break the bank in the process. I am currently enrolled in ALEKS MAT 130 and MAT 170 for algebra 2 and pre calc by ASU, but I’m not sure if they were intended for students who are getting exposed to the material for the first time. Furthermore, I’m not getting an understanding of the topics when I take algebra 2 from MAT 130. It is simply straight-up memorization. In this case, should I go for a paid online course or textbook? I don’t know about MAT 170, but if it’s anything like MAT 130, I don’t think it would be for me. I am also enrolled in Calculus 1A: Differentiation, Calculus 1B: Integration, and Calculus 1C: Coordinate systems and infinite series by MITx on Edx. I have yet to take anything from it, but it seems promising. If anybody has experience with it or suggestions for a source that provides a deeper understanding of calculus, please let me know.

    Last edited: Dec 25, 2017
  6. Dec 25, 2017 #186


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    ALEKS is useful for review, to check if students have any obvious holes in their knowledge, but it's not actually useful for learning anything well. If you want the best courses for students who love math and are good at it, check out Art of Problem Solving. My kid preferred the books to the online courses because he could go at his own pace.

    In any case, not free. Also not particularly expensive, especially the books. But really, really good.
  7. Dec 25, 2017 #187
    I've heard a lot of great stuff about AoPS! I will definitely check them out, and thanks for the quick response.
  8. Dec 25, 2017 #188
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