I will be applying to grad school for my Math PhD this upcoming fall and I had some questions: How important is who is writing your letter of reccomendation??? I am from a top 30 Math university according to the NRC rankings and US News World and Report rankings, but I doubt I can get a reccomendation from a full Professor. I can get a reccomendation from 1 associate professor (2nd rank) at my school and I've done research with him, i'm sure he will write me a great letter. I'm currently doing an REU, but it's not at a big school and the professors aren't well known, but i'm sure I can get 2 publications and a great reccomendation. Basically, here is my question, by the time I apply, I'll have all the numbers part of my application down pat, 3.8+ GPA, i've taken a ton of math courses in both pure and applied, probably will have a good GRE score and a good GRE math score. The only thing I'm worried about is reccomendations. So far i have: 1) a letter of reccomendation from a professor at my school who is very highly regarded in his field, and i've done a year's worth of research under him already, and I have a very good relationship with him. but he's only an associate professor. and he got his PhD overseas. 2) a letter of reccomendation from my REU where I will probably have 2 math papers published but he is not from a big time school at all. for my 3rd letter i am scrambling to find a professor at my school who will do an independent study with me. I don't think doing well in a course will give me a great letter. I want to do an independent study and hopefully garner a 3rd letter from a big wig at my school. I can probably get one from a post-doc fellow at my school, but how does that look? I would rather get one from a full blown professor. any help from professors or people who have been through the grad school application process? if you are wondering, I am hoping to get into Columbia, CalTech are my top two choices. I know I can get into the good-really good schools in the NRC rankings. But I would love to get into one ofthe top 10-15 schools.