Since there's a long summer ahead of me with no traveling contained within it at all, I have been thinking about doing some sort of research, though considering that I am a recently graduated high school student, I won't have as much access as someone in college or more would have (though I think I might be able to have access to CU Boulder's library(ies)). I'll probably be e-mailing my Physics teacher fairly soon, but I wanted to post here to see if I could get my mind working and find some resources and whatnot that would help me accomplish this.
As far as a topic, I'm pretty much solely focusing on the topics of Physics and Math. Of course, being the person I am, I don't want something simple to do with results that would be fairly obvious. I'd like it to be fairly advanced that require a good deal of thought. I hate trivial things <,<. Hardest thing is finding something like this, though >.> So any suggestions on where to look and any suggestions on how to go about doing this would be helpful.
Here are my "qualifications", both objective and subjective:
Math: I have a good amount of knowledge in Calculus up to Calculus 3, as well as a decent amount of knowledge in Complex Analysis up to residue theory and in Linear Algebra up to eigenvalues and eigenvectors. I'll also have Mathematica very soon, if that matters.
Physics: I'm very proficient in the topics required for AP Physics C (especially E&M) and can follow the introductory courses of Physics in colleges fairly easily.
This doesn't seem to be organized very well and it's pretty fail, but oh well. Thanks for any help.
