Possible Research Topics for High School 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. 
 A: 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
A: 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. 
