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Self-teaching: What topics do I learn first?

  1. Jul 30, 2012 #1
    I've become a bit obsessed with maths in the last month. I'm studying it in all my free time.

    My knowledge is probably at the level of a 1st year student who just finished their 1st semester and did pretty well. I did 3 maths subjects at uni and aced them. However, I've forgotten quite a bit of it over the last 12 months, but have also re-learned a decent amount.

    I've been starting my learning with analysis but I'm not sure it's the optimal way to start things off again.

    Do you guys have any recommendations? I'm not sure what I should focus on first ... linear algebra, calculus, or the proof/limits side of analysis?
  2. jcsd
  3. Jul 30, 2012 #2


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    It might be helpful to self-learn useful auxiliary skills which are not directly taught in courses. This includes programming, writing technical articles, giving talks, applied math/comp.-sci techniques (say, geometric algebra, probability & statistics, local and global optimization) etc.

    Mastery of such things can come in very handy later, and they form a skill axis orthogonal to your main academic skills. Additionally, some of them (e.g., programming) actually cannot be taught decently in courses beyond an elementary level, and are very suitable for self-learning at the same time.
  4. Jul 30, 2012 #3
    Thanks for the post. I'm co-authoring 3 applied econometrics/statistics papers at the moment so I'm fine on the programming/statistics front.

    I'm interested in the more hardcore maths side.
  5. Jul 31, 2012 #4
    A good foundation for mathematical skills would be algebraic number theory. You can begin a study of this with nothing more than high school algebra yet many of its problems will test your ingenuity. My favourite book on this topic is Richard M Burton's Elementary Number Theory.
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