I am currently a junior attending a small high school that requires a project called senior thesis. Each one of us will have to come up with a topic/question on our own, work on the project and do research for an entire school year, and present it in May.
For some background.
- I have mastered all standard high school mathematics.
- I got a 5 on AP Calc BC last year, hence I am decently proficient in single variable calculus.
- I am working on AP Stats this year.
- I have been working on some real analysis and have been making good progress.
- I have learned some linear and abstract algebra, but perhaps just the most basic things.
- Set theory and mathematical logic have been some of my favorites. I have spent quite some time on those topics.
- I do not really have any background in geometry or topology beyond high school geometry or the topology required in analysis courses.
- I have learned a bit of number theory and probability theory beyond the high school requirement.
- I am taking AP Physics 1 this year.
All that to say, I'm looking for a topic/question that is not too easy nor too hard for me. Here are my thoughts on what the topic/question might be.
- I'm willing to learn more stuff and challenge myself in the research process (after all, that is what research actually is).
- The topic can be in any area of math (or even physics), but preferably the ones that I'm more comfortable with.
- The topic/question should have some real life application if possible. The application does not have to be in everyday life (aka. it could be complicated).
- The topic/question should take me about 6 months or so to fully solve. That is, if I start learning new concepts or techniques in September, then I should be able to fully understand and solve it in around February.
Thank you in advance.