I need some help. I'm a kid who loves math and physics. I taught myself calculus(single and multi), linear algebra, ordinary differential equations and some basic point-set topology. I know basic number theory and I'm good with proofs. In physics, I taught myself a lot of graduate classical mechanics, E&M, thermodynamics and some statistical mechanics, quantum mechanics at the level of Griffiths.I don't like physics as much as I love mathematics, so I've decided to focus on it. Now, the problem is that I'm confused about what courses to take, in what order and whether I'm good at the prerequisites of each course.I'm taking now an Abstract Algebra course by ICTP. I like number theory and geometry (differential and algebraic) . What courses should I take after Abstract Algebra or at the same time (because I already know about groups ,fields, rings, vector spaces, I don't have any problem with proofs or set theory, for example ,I'm familiar with the construction of R,Q,Z from equivalence classes...) ? in what order? could you please suggest me a good and fun book on real analysis? Would it be better if I learn each topics in the syllabus separately? I plan to publish something so as to get a scholarship to a good university because we have none in our country.I'm 15. I would really appreciate your help. Thank You!


closed as off-topic by KReiser, Derek Elkins, Lee David Chung Lin, Alex Provost, rschwieb Mar 20 at 13:18

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "Seeking personal advice. Questions about choosing a course, academic program, career path, etc. are off-topic. Such questions should be directed to those employed by the institution in question, or other qualified individuals who know your specific circumstances." – Derek Elkins, Lee David Chung Lin, rschwieb
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Welcome to Math SE. Don't get disheartened by the downvotes, this is the internet and there is some cranky people out there. I'm fairly sure you'll get good answers to your question. $\endgroup$ – Martin Argerami Mar 19 at 23:11
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    $\begingroup$ Might I suggest some numerical analysis as well? If you like Algebra... $\endgroup$ – System Mar 19 at 23:23
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    $\begingroup$ You could do a degree in Mathematics, Engineering Mathematics, Mechanical/Electrical/Electronic Engineering or Computer Science. Look into what interests you the most $\endgroup$ – Henry Lee Mar 20 at 0:20
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    $\begingroup$ Also consider taking a break, from time to time, to learn about writing. It will aid you in mathematics, and also every other subject, if you write well. I say this because your post is very much in need of things called paragraphs. $\endgroup$ – rschwieb Mar 20 at 13:21
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    $\begingroup$ As for advice about how to proceed: the best I can say is that this question is not useful. Someone may lay out their "royal road" but I can almost guarantee it is not much better than 1000 others like it, and probably not better than one you would create for yourself. Make a list of the topics you'd like to study, and make a pass at all of them. If you get stuck somewhere, you might have to switch gears and study that temporarily. Beware of going "depth first" on the first pass because you might miss out on things you would have seen in a broader look. Good luck. $\endgroup$ – rschwieb Mar 20 at 13:28