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I do not know if this is the right place for this question. I am an undergraduate math student entering his junior year this coming fall, but I'd like to teach myself some math that is accessible to me giving my current knowledge. So far I have taken (all undergraduate):

a linear algebra course, a theory of ODE/dynamical system's course, a topology course that went up to basic algebraic topology (Which I did not understand a lot), and Calculus 1-3.

Next semester I am taking real analysis, numerical analysis, and intro probability theory.

So in essence my question is what topics could I self study over this summer?

Sze
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  • 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. – Ѕᴀᴀᴅ May 11 '20 at 02:52
  • I’d say read PMA (Principles of Mathematical Analysis). – Ningxin May 11 '20 at 02:56
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    I'd say some abstract algebra (you can check out Benedict Gross' lectures online), a second course in linear algebra or prepare for real analysis. – J P May 11 '20 at 02:57
  • If you're interested in learning something outside of math: for computer science, I highly recommend working through all the projects in The Elements of Computing Systems by Nisan and Schocken. For physics, I got a whole lot out of reading some of The Feynman Lectures on Physics. For biology, Molecular Biology of the Cell is a great book. For pure Math, you might check out Visual Complex Analysis by Needham, Mathematics and Its History by Stillwell, Calculus by Spivak. For applied math, I like Introduction to Applied Math by Strang. Also Convex Optimization by Boyd and Vandenberghe. – littleO May 11 '20 at 03:31

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