What are my chances for math grad school?

<p>I am a senior who is applying to PhD programs in math. I am almost done with the applications, but should I apply to more schools?</p>

<p>Undergraduate Institution: One of the top state schools (ranked top 10 in math)</p>

<p>Overall GPA: 3.88
Math GPA: 3.95</p>

<p>Courses: I have taken graduate level algebra, topology, commutative algebra, real/complex analysis, functional analysis, algebraic geometry, algebraic topology, algebraic number theory, analytic number theory</p>

<p>Math Subject GRE: 820/86%</p>

<p>General GRE scores: 168/156/4.0</p>

<p>Research/Publications:</p>

<p>-REU at William and Mary, which resulted in a paper that was recently published in Finite Fields and Their Applications</p>

<ul>
<li>REU at Williams College (SMALL), we just recently submitted a paper for publication</li>
</ul>

<p>-Research with one of the professors in my school; we have gotten some good results but have not written a paper yet</p>

<p>Other awards:</p>

<ul>
<li>Putnam score of 50 (top 200)</li>
<li>I received the annual undergrad algebra award from our math department</li>
<li>IMC Third Prize</li>
<li>2nd place in the annual math competition at my school</li>
</ul>

<p>I have applied to:
-Harvard
-Princeton
-Stanford
-MIT
-UC Berkeley
-UCLA
-Columbia
-UChicago
-Northwestern
-Brown
-Wisconsin
-Yale
-Cornell</p>

<p>I am a little worried now because all of the schools that I have applied to are really competitive. Should I apply to a couple of safety schools? Will I be able to transfer to one of the schools listed above if I attend some other school?</p>

<p>Transferring in graduate school is practical after finishing the M.S. Just looking at your test scores, academics and research experience and having looked at a lot of graduate applications at my university, I think you are OK with that group. UCLA is a very high probability and you have a decent chance at many of the others too.</p>

<p>I’m only a grad student myself, but to me your profile looks strong enough to be competitive yet not outstanding enough to be a shoe-in. </p>

<p>I have a number of friends with similar “stats.” Some of them got into every tippy-top program they applied to, others are now attending their safety outside of the top 20. As far as I can tell, admission decisions will boil down to your letters of recommendation. If your professors want you to be successful and vouch for your potential, your application will be received vary favorably. </p>

<p>Do have a contingency plan in case you don’t get into the schools on your list, but only apply to graduate programs that you would actually be happy to attend. I have several friends who tried to “transfer up” and none of them succeeded.</p>