I'm looking at applying for PhD in CS and trying to narrow down which schools to apply to. My profile:
Undergrad at a fairly good state university, double major in math and CS.
GPA: 4.0
GRE: 170Q, 168V, 4.5AW
Two semesters of research experience (in graphics), and one internship at a large engineering company in software research and development.
Recommendation letters will be from my research advisor and other professors, none of whom are particularly famous as far as I know.
Do I have a reasonable chance of getting into a top 5 (MIT, Carnegie Mellon), top 10-5 (U Washington, Princeton), or 20-10 (Columbia, UCLA) school? Or should I stick to mainly lower than that? I know it probably varies by school, but I'd like to narrow my aim down a bit.
Thanks!