# Please suggest some good topics for Maths research paper

1. Dec 27, 2012

There is a student in US. He has completed 4 hours of high school and is applying for college. As part of the application procedure, he has to submit a research paper in Mathematics. He is a very good student.
He accelerated math and enrolled for Differential Equation, while still being in high school, although differential equations is a college level course.
The colleges to which he is applying want to see a Math Research Paper.

I am not from US. So I do not know what kind of paper will be good. Could you suggest some good topics?
And also, any idea how long should the paper be (i.e. how many pages?)
Please give any other details you think appropriate.

2. Dec 27, 2012

### Staff: Mentor

3. Dec 27, 2012

Than you.
I am looking for some topics in differential equations. The research paper has to be submitted by only those students who accelerated their Maths course. This student accelerated and took differential equations. So I think the colleges expect the paper to be related to that.

4. Dec 27, 2012

He has studied the following:-
* vectors in Euclidean space
* vector analysis
* analytic geometry of three dimensions
* curves in space
* partial derivatives
* optimization techniques
* multiple integrals
* vector fields
* Green's theorem
* Divergence theorem
* Stokes' theorem

So, I am wondering what interesting topic to choose which involves one or more of the above.

5. Dec 27, 2012

### Staff: Mentor

okay navier-stokes equation for fluid flow its a millenial problem quite difficult and quite interesting as well.

6. Jan 13, 2014

### Staff: Mentor

A simpler problem than solving Navier Stokes numerically is solving advection-diffusion problems numerically and economically, for situations in which the diffusion coefficient is low. The objective is to avoid using a very fine finite difference grid (which increases computation time and storage), while obtaining accurate solutions that do not feature physically unrealistic oscillations. Methods that have been tried often employ upwind differences, but this leads to numerical dispersion and associated inaccuracy.

7. Jan 25, 2014

### Stephen Tashi

Is he applying to attend college as an undergraduate? - or applying to attend some special summer program at the college? I don't know any US colleges that require a research paper as part of the admission process. In what country is the college?