Questions about applying to Grad School(Math PhD)

<p>I'm currently a math major finishing up my junior year at a not particularly high ranked state school. Before this, I was previously at community college where I managed to wipe out my Gen. Eds and earn a rather useless AAS in Computer Science. Since transferring, I've maintained a 4.0 and taken several graduate courses(Algebra I-II, Complex Analysis, Representation Theory, Algebraic Topology, ect) and independent studies beyond the standard B.S curriculum. I'll also be participating in an REU (My first REU) this summer in addition to honors thesis project in the fall(On algebraic geometry, hopefully). Beyond that, I'm quite comfortable with much of the material in the math GRE and have done fairly well on recent practice exams(760~ ish).</p>

<p>Assuming the REU and the GRE go well, and I get good recs from the professors I've worked with, I'd like to get a feel for which schools I should I apply to in the fall. My dream school is UCB, but that might be aiming a little too high. Other schools I'm looking at include Columbia, Cornell, Wisconsin, Michigan, Stony Brook, UCLA, NYU, Brown.</p>

<p>Mostly, what I'm wondering is if I should instead plan on applying to a broader spread of schools. Is it too much to hope that I'll get accepted to at least one of the above schools? What non-Top 25 schools should I look at as someone interested in Algebraic Geometry/Topology/Category theory?</p>

<p>Arguably the most important part of your application are your letters of recommendation. Your letters will make or break your application, which is why it’s difficult for us to give you advice from a distance. Your references will be happy to talk to you about the range of schools that you should be looking at. </p>

<p>A few general thoughts:</p>

<p>Your gender and citizenship status matters. Females are at an advantage, international students at a significant disadvantage.</p>

<p>Apply to a wide range of schools. I got into programs that I didn’t think I had a shot at (Princeton, MIT, …) and I also have friends who got rejected from everywhere except their super safety backup.</p>

<p>GRE scores are important. A few of the top programs won’t even read your application with subject scores below 800. Some programs will pre-sort and read applications in descending order of subject GRE score, until all spots are filled. </p>

<p>Your practice GRE score suggest that you might be going though the curriculum too fast. You are taking graduate classes, yet you seem to struggle with undergraduate problems that you should be able to solve in your sleep. Make sure that your foundation is solid before you go any further.</p>