interested in topology and geometry

[broken_symlink]

My situation is a little unique. I went to a small liberal arts college and majored in pure math and minored in physics. I took courses in linear algebra, multivariate calculus, discrete math, real analysis, complex analysis, differential equations, topology, and abstract algebra. I also completed two independent studies with a professor in differential topology and differential geometry. I worked with him one on one for a year, and I also took real analysis and topology with him, so I was a student of his for about two years.

My school had a special program where if you finished your degree in 3 years you could apply to another school to study engineering and get a second bachelors in engineering in 2 years. I applied, and I am now currently studying computer engineering. I've found that I just don't enjoy engineering as much as I did pure math. I am now pretty sure I want to go to grad school for math.

I am not sure what to do next though. I'm only in the first semester of my engineering degree, I have 3 more left. I've been trying to find a professor at my school that I can do some work with informally, like not even an independent study that I would get credit for, but just read a book, meet, and discuss. I'm just hoping to find another professor that I can build a relationship with and get a second good letter of recommendation.

The other thing I'm a bit unsure about is when to apply. I was thinking about applying next year, but then I would only have 1 semester's worth of work with whoever I find at my new school. The reason I'm trying to get really good letters is because my gpa is kinda bad. I finished my math degree with a 3.42. There is a very strong upward trend, because my freshmen year I took the honors calc sequence and did really bad (c's in both courses). However, my sophomore and junior years are pretty good, 3.5+ every semester.

The problem with waiting until after I finish my computer engineering degree is that I would need to find something to do in the year between when I finish my degree at start grad school. I thought about teaching high school math for a year, but I don't know how easy it is to do that without going through the whole process of becoming a teacher.

Realistically, I don't think I have a good chance at a top 10 school, but I'm fine with that. I'm just not really sure where to apply. I think my dream school might be Northwestern.

Edited November 7, 2011 by broken_symlink