confusion in mathematics [closed]

manpreet Best Answer 3 years ago

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!