I am a high school student (junior) and am looking to do some research over the summer and maybe enter a project into Intel or Siemens-Westinghouse. However, I will not have the opportunity to work with someone at a university. My background in mathematics isn't very strong, as I have only completed single-variable calculus (AP Calculus BC). I was just wondering if anyone could give me an idea of what topics I could study with this type of background. Also, where can I find a problem to tackle if I want to do research? I have gone to sites like PlanetMath, and looked through the "Unproven" section, but it is all much too advanced for me at this point. Any suggestions? Thank you.