High school project in mathematics, original research

[saltkraxen]

I have been thinking about doing my 'high school project' in mathematics and I would like to do some original research.

So my question is: Which areas of mathematics would be most suited for me? Having in mind that I'm still in high school, although I have taken some (fundamental) math courses at my local university. And could you give an example of how a research question could be framed. :)

Areas that fascinates me:
Foundations of mathematics: Proof theory, set theory, mathematical logic.

Sub question: Could a high schooler do original research in say proof theory?

To mod: I put the thread here because I'm mostly interested in hearing about the foundations of mathematics (but all suggestions are of course very welcome), but if you think that it belongs elsewhere; please move it.

 

[Number Nine]

It's unlikely, though certainly not impossible, that a high school student could manage original research in mathematics; there are some branches of mathematics (e.g. abstract algebra) that require very extensive knowledge before you even can even understand the statement of a research question. Combinatorics might be a good branch of mathematics to look into, in that many problems have very simple formulations, can be easily understood, and often don't require extremely advanced techniques to solve.

 

[Stephen Tashi]

saltkraxen,
Are you skilled in writing computer programs or are you seeking a pencil-and-paper type of research project?

 

[saltkraxen]

saltkraxen,
Are you skilled in writing computer programs or are you seeking a pencil-and-paper type of research project?

I have done some programming (I'm neither good or bad), although I would like a "pencil-and-paper type of research project".

Thanks for the answers and keep them coming. :D

 

[Stephen Tashi]

I don't claim to have any qualifications for suggesting research in mathematical logic. However, this problem has always interested me: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem.
You aren't likely to solve the general problem but you might try cases where the boolean expressions have a more restricted form. Part of "research" is just looking up what is currently known about problems. I don't know enough to be helpful with that. Some other forum members probably do.

 

[saltkraxen]

I don't claim to have any qualifications for suggesting research in mathematical logic. However, this problem has always interested me: http://en.wikipedia.org/wiki/Boolean_satisfiability_problem.
You aren't likely to solve the general problem but you might try cases where the boolean expressions have a more restricted form. Part of "research" is just looking up what is currently known about problems. I don't know enough to be helpful with that. Some other forum members probably do.

Thanks, this looks really interesting! Can you recommend any good books on the topic?

 

[Stephen Tashi]

I'm not familiar with any books that cover the boolean satisfiability problem. (But I'm no a logician, so there might be some.)