research project and SOP statement of interest don't match?

Graduate School
#1

<p>Hi all,
I will be applying for mathematics grad programs this fall. I was able to take an upper level course in diffeq's this semester, and I was also able to get a research position this summer on PDE's. This fall I'll be taking a graduate course on ODE's. So basically, I'm able to go into depth with diff eq's because my school is strong in that department. However, my interests lie more in topology and algebra. Due to time/course constraints and such, I doubt that I'll be able to do much more with topology before applications - I've only taken one course and can't take any more this fall. How should I address this in my statement of purpose? Some options I'm considering:
1. Write about my general interests and say that I'm undecided about what I want to study. The disadvantage is that it seems like schools want SOP's that are specific regarding research interests.<br>
2. Try to read up on topology as much as I can in the time I have left and write about my interest in topology in my SOP. </p>

<p>I'm sure this has come up for other people too(and not just in math), so your input would be appreciated. Thanks!</p>

#2

<p>Highlight that you have had opportunities to do diffeq because they were available at your department but would very much like to research topology and this is why Program X is a great fit. Emphasize that you are looking to move into that area because you found that diffeq doesn't interest you as much as topology does.</p>

#3