I'm a junior in HS and I have an interest in math. I wanted to pursue some research in math but I have trouble deciding which subject since there's so many. I know calculus (I took Calc AB, learned derivatives, limits, integration, theorems; here is a good page summarizing the material) and so I was wondering if there are any good research topics in the calc field. But I'm open to suggestions of other areas of math. Can someone please suggest a research topics? Thanks.

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    $\begingroup$ None. So far, you learned math of 18th century and some of 19th century. You still have ways to go until you are ready for research math. $\endgroup$ May 22 at 21:06
  • $\begingroup$ I think the best place for you to start is to read over published papers in topics that you're interested in. A large part of math research is just finding out what others have done and seeing what you can do to expand on it. Plus it'll expose you to math that you probably haven't encountered in your career so far. $\endgroup$
    – Jake Brown
    May 22 at 21:16
  • $\begingroup$ Instead of research (which at this point for you is like making first string on your high school varsity basketball team and wanting to know how to try out for a professional basketball team), I recommend looking at articles in Pi Mu Epsilon Journal and Mathematical Spectrum and Quantum, and pursue further reading into one or more of the topics that captures your interest. $\endgroup$ May 22 at 22:00
  • $\begingroup$ You're probably not ready for research, my recommendation is to start reading books on real analysis, non-Euclidean geometry, abstract algebra, and other aspects of math you're not going to see in high school. It'll help you get a sense for what different branches of math look like and what direction you might want to go. $\endgroup$
    – Amaan M
    May 22 at 23:36

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