Research for school admission

Can anyone give me a nudge on how to research given that I only know basic mathematics (Through calculus and below) but the mathematics that I do know, I know very well.

I'm not expecting to publish or anything like that, I just want to research something that a school would find intriguing and also to try my hand at the heart of mathematics.

To me it just seems like every problem that I can try my hands on is too basic and boring or that every problem in my reach has been solved (but of course it isn't much like every song has not been written) and I just want a nudge in the right direction or an idea on what to 'research' :)

Thanks!

Re: Research for school admission

Completely depends on your interests. I doubt you would be able to come up with something that is completely new, but you can try your hand at some solved problems (without looking at the solution). A popular area for high school students is in number theory. If you are just looking to improve your problem solving skills, try looking at maths Olympiad problems. You can learn quite a bit from them.

Re: Research for school admission

Quote:

Originally Posted by

**Gusbob** Completely depends on your interests. I doubt you would be able to come up with something that is completely new, but you can try your hand at some solved problems (without looking at the solution). A popular area for high school students is in number theory. If you are just looking to improve your problem solving skills, try looking at maths Olympiad problems. You can learn quite a bit from them.

Thank you for your answer.

I could have guessed that there weren't too many options for me in my current position but it didn't hurt to check :)

Perhaps I could try venturing into some sort of mathematical art like Vi Hart. It just feels like I have all these tools but no way to use them. I'm sure many mathematicians have had that feeling when they started :)

Re: Research for school admission

are international math Olympiad problems good to practice?

Re: Research for school admission

Quote:

Originally Posted by

**mathlover10** are international math Olympiad problems good to practice?

Well from this thread, I decided to try my hand at the Olympiad problems. They are high caliber math problems that don't necessarily pose a threat to your mathematical knowledge, but they do pose a challenge for your problem-solving, logic and general intellect, I suppose..

I did end up solving one with, what I believe to be, a unique proof (http://mathhelpforum.com/geometry/21...-solution.html) and I'm going to try another one in a few days when I'm done with my final exams.