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Self-Teaching Math Sequence: How to Build Strong Foundation?

  1. Dec 22, 2016 #1
    I'm currently an Aerospace major/Physics minor who's interested in delving further into mathematics. What is the optimal sequence of topics that I should follow for self-studying. I know this forums has links to a lot of interesting books, but I don't really know which one to start with.

    Thanks for helping and sorry if this isn't the correct place to post about this.
  2. jcsd
  3. Dec 22, 2016 #2


    Staff: Mentor

    The usual answer to this question would be without any risk of a wrong choice some linear algebra and calculus. However, I guess we may assume that you already have these foundations which raises the question of where to start with and even more important, where to go to. So what do you want to learn? Abstract concepts like logic or topology out of interest or more sophisticated tools in the field of your studies, e.g. in aerodynamics, in which case differential geometry might be an appropriate answer.
  4. Dec 22, 2016 #3
    Pretty much echo @fresh_42 . There's a lot of math out there. Some may have no bearing on your main area of study. Are you looking to deepen your knowledge in relevant math or branch out into other types of math just for fun? (i.e. number theory or something. Won't help you but it's fun).

    -Dave K
  5. Dec 22, 2016 #4


    Staff: Mentor

    Don't be a pistolero! I've heard (without knowing it for sure), that numerical analysis is used in arms industry.
    I guess because of its algorithmic approaches to problems that cannot be solved otherwise. So even number theory might be a step towards applications - oops, wrong thread.
  6. Dec 22, 2016 #5
    haha. Well like I said, (also in another thread) studying any kind of math will help you think better. I would just warn the O.P. not to lose focus.

    -Dave K
  7. Dec 22, 2016 #6


    User Avatar

    Staff: Mentor

    Starting from what? Have you done the calculus, differential equations and linear algebra that engineering and physics majors usually have to take? Are you thinking along the lines of "pure math" (theorems and logical structures) or "applied math"?
  8. Dec 22, 2016 #7
    I was a bit more interested in branching out into other types. I'm pretty sure that I'll learn differential geometry in one of my classes, but the area of mathematics with topics such as number theory definitely won't pop up in my curriculum. Besides, a lot of my classes are kind of programming-heavy, and I'd assume doing some practice in that area would help me understand Computer Science aspects easily.
  9. Dec 22, 2016 #8
    I'm not sure how to answer really for self study, since you could justify studying just about anything on the grounds that a) you never know what you can use later and b) ANY math is good for training rigorous thinking. I'd say if you're going to branch out, you should do it within the confines of your school, i.e. see what interesting classes pop up in the math department and see if you can take those. For self studying you probably would want to stick closer to the kind of math you need in your major.

    I didn't see an answer to the earlier inquiries posed to you here. What have you taken so far?

    -Dave K
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