How can a graduate school applicant improve his application for next year's season?

It seems I'm about to have a bad application season, as all schools I'm waiting to hear from have given out offers of admissions to other applicants. I'm trying to come up with a viable plan to turn my application into a successful one for next year's season.

Here are some important things to note:

1. 
   

   I come from an unknown school, but my reference writers earned their Ph.Ds from well-known schools in the U.S. (top 25 via NRC ranking). They all encouraged me to apply to top 30 programs in the US.

   
   



2. 
   

   I am an international applicant.

   
   


3. 
   

   I am interested in pure mathematics.

   
   

Some fall-back plans I have is to actually get involved in research during the summer and fall, and I'm hoping I can get a serious publication out of doing this.

So for the people who have served on admissions committees in the past, what else can I do? Should I not bother to apply to the same programs I applied to this year?

Answer

Publish. I have seen the following pattern more than once. (1) Applicant X applies to my department's PhD program and is rejected, not for any major flaws, but just for not standing out from the crowd. (2) X joins a MS program at a different university. (3) As a master's student, X publishes one paper and has two more in submission (or at least preparation). (4) X reapplies to my department's PhD program, with a detailed technical discussion of his results in his statement of purpose and stellar letters from his new department. (5) X is admitted in the first round, with a fellowship.

If you haven't done so already, show your complete application to the people who wrote your rec letters, and ask for their brutally honest feedback, especially on your statement. Often students who write statements without some faculty feedback write them to the wrong audience. ("I'm smart; hire me." makes a bad statement of purpose. "Here is the mathematics I've worked on and what I'm interested in looking at next." is much better.)

It's a long shot, but if your recommenders know faculty at the schools you applied to, you might be able to get some second-hand feedback through them. Maybe.