math_applicant

Hi all, I have been checking mathematicsgre blog post for admission results in 2012 and I was startled at how seemingly very strong profiles got turned down by most top 15-20 schools. I was in the process of preparing a list of possible schools to apply to for a PhD in pure math but now I am not really sure anymore how my list should be organized. Here is my profile: University: 2 top Egyptian universities but not recognized internationally. Majors: Math, Computer Science + Medicine. GPA: overall GPA in the CS+math uni is 3.9, Math major GPA 3.95, CS major GPA 3.93. overall grade in university where I studied medicine is equivalent to B+. Upper Math grades: Analysis I, II, Topology, Number Theory, Complex Function theory, Theory of Computing, Linear Algebra, Formal Logic, ODEs, Discrete Math, Galois Theory, Algebraic Geometry and Intro to Elliptic curves arithmetic, 2 statistics courses -- All A's. Numerical Analysis, Abstract Algebra A- . I have some research projects in Computational Biology and in Computer Vision (in Microsoft research lab cairo) but no publications. As for LORs, I think I can get 2 really good letters from 2 american math professors and 1 from my research supervisor at MS. I think the letters will be strong but the professors giving them aren't well known. I had in my mind for a list of schools 3 top 20-50 , and the rest ranging 50-100. Is that reasonable? Should I be aiming higher/lower? Do you guys think I got the wrong picture from mathematicsgre?