Hi everyone, I'm currently in the midst of applying to graduate schools and I am looking for advice any where I can seem to find it. Could anyone suggest schools that I should be applying to on the basis of my interests and the strength of my application? Undergraduate School: Top 10 National Public University Undergraduate GPA: 3.63 Undergraduate Major: Mathematics Undergraduate Major GPA: 3.76 GRE Scores: 780Q 620V 4.0A (Math Subject GRE Still To be Taken) Prior Research Experience: I have two extensive REU's under my belt. One was more applied mathematics that led to an unpublished paper, a brief internship at NASA, and the opportunity to run experiments in a microgravity environment. This opportunity also gave me grant-writing and technical document writing experience. My second project was based on an open, but possibly obscure problem whose result was conjectured by a well-known control theorist. I came up with the problem myself and brought it to the attention of my advisor, who that it was a great idea. However, my paper merely gathered more data on the problem and the theorem is still left unproven. That being said, the paper resulted in a minor forth-coming publication. The project also resulted in two conference appearances (one poster and one talk) at University of Washington and UC Berkeley. Professional Development/Awards/Related Work Experience: I was selected to be a NASA Aerospace Scholar in junior college. I was one of forty students accepted with over a hundred applying. I also was selected to be apart of a NASA Reduced Gravity Flight Team (this coincides with my first research project above). Over 70 teams applied and only 13 got in. I was selected to become a McNair Scholar at my University. The McNair Scholars program is a competitive undergraduate program whose main goal is to diversify the doctoral degree by providing research opportunities to underrepresented or low-income groups. As a part of this program, I conducted my second research project in close proximity with my mentor and attended two conferences. Letter Writers: I have 3 LORs (thank god). The first of which comes from my research advisor and should be extremely personal. I expect this letter to be very positive and insightful. I have had many personal conversations based on my future goals and my interests with my mentor. My second letter writer mentioned that my mentor is an up-and-coming name in the field of probability and that any probability department will be familiar with his name. I hope this turns out to be beneficial for me. My second letter writer will not be as personal but should be very warm as well. It also comes from a respected probabilist but I am not sure of his exact standing in the field. My third letter writer will be the least personal of all of them but comes from a revolutionary topologist. He seems to be enthusiastic about my future pursuits but I am not sure how that will turn out in the letter. My Dilemma: I believe that even though my research experienceh as not resulted in a publication, it still holds as the strong point of my application along with my professional development/awards section. My grades aren't the best (3.76 Major GPA) but I've covered all of the hard classes (Analysis I, Analysis II, Topology, etc). Some of my advisors who are non-math people have urged me to apply to top 20 programs. However, I don't think they realize that math is one of the most competitive fields as far as getting into a PHD Program goes. I plan on applying to mostly schools in the Top 40, based on the strength of their probability department. NYU is my first choice as there are a few probability researchers who work on probability in non-linear dynamics. However, I am also interested in more discrete probability (I think that's the word for it) and the work of Persi Diaconis (Stanford) and David Aldous (Berkeley). Realistically, where should I be applying to? I plan on retaking the general GRE to get a perfect Quant score. I had a few mishaps that day and some external factors hindered my ability to completely focus.