I'm majoring in Mathematics with the ultimate goal of doing a PhD in it. Looks like getting into the graduate schools for it are kind of tough if I transfer to a state school. I also need financial aid because my family is poor. If I write a paper and take the SAT should I try to transfer to private uni's? Do I have a good enough chance to get in? Assuming my GPA will be 4.0 but my high school GPA 3.32. Thanks.