Possible Research Topics for High School

Question

I am a highschool student some experience with Math Olympiads and I will be taking a Scientific Research class next year. I would like to ask for interesting Mathematics topics that I could consider - I have tried going online for possible research topics but I couldn't determine which was for my level.

I would like to also ask for resources that I could use for carrying out my research. I do not have access to programs such as PRIMES as I live outside the US.

Thank you.

The earlier MO question, "Interesting and Accessible Topics in Graph Theory", may help. — Joseph O'Rourke, Aug 25 '13 at 22:47
@MatheMazier: You might want to consider learning a some programming using a Computer Algebra System — Amzoti, Aug 25 '13 at 23:50
You might browse the Open Problems Garden and The Open Problems Project, both of which contain accessible research problems. — Joseph O'Rourke, Aug 26 '13 at 00:32
In addition to learning a CAS as suggested by Amzoti, another possibility is look at books in the reference section of Experimental Mathematics wiki page. They will have a lot of examples how to use numerical experiments and visualization to explore new ideas and ways to prove them. — achille hui, Aug 26 '13 at 11:05
Ask a friendly math professor from a university near you! Who knows -- someone might be willing to take you on for a summer project! — Nilay Kumar, Aug 27 '13 at 02:25

score 1 · Answer 1 · answered Aug 27 '13 at 01:05

I'm a fan of mathematical games for projects like these. They are fun, don't (necessarily) require advanced math -- I 've taught basic theory to groups 10 year olds -- and there are lots of open problems. Check out Winning Ways, by Berlekamp, Conway, and Guy, and M. Albert, R. J. Nowakowski, D. Wolfe, Lessons in Play. Here's a good website with a link to a list of open problems http://www.mscs.dal.ca/~rjn/Site/Game_Theory.html

For motivation check out an award winning work by a (then) high school senior. http://www.emis.ams.org/journals/INTEGERS/papers/dg3/dg3.Abstract.html

score 1 · Answer 2 · answered Sep 18 '13 at 19:59

There are quite a few undergraduates who have done significant research in mathematics at your level. Even if you don't end up with a published paper, you will gain significant experience into what doing original research in mathematics means. Anyway, I think expecting to find a problem to work on yourself, rather than have a mentor suggest one (or several) to you, is unrealistic. Find a mentor (one of your professors maybe) who is willing to suggest a problem that you can deal with at your level, and (hopefully) give you ideas if you get stuck. On these websites (http://www2.edc.org/makingmath/mathproj.asp#rsproj ; http://wumath.wustl.edu/undergraduate/undergraduate-research/ideas) you will find some interesting topics. As I said, you will be better off talking to a mentor, but on the first website I've listed, you will find some non-so-banal problems and also some useful hints and resources for tackling them, which are very useful if this is your first experience in research.

Possible Research Topics for High School

2 Answers2