I am a math PhD student in a top US math program. Most international students in the top math programs in the US seem to fall into one of the following three categories:
- They have accomplishments that are externally recognized (i.e. by someone outside of their own department). For example, the majority of international students in my department did extremely well in math competitions (IMO, Putnam or IMC). As another example, my office mate got an award from his foreign university for the best Bachelor thesis that year across all departments, and a national award for the best physics thesis from all universities in his country. Recognition solely from within your department will suffice if your university is known for the high caliber of the math students it produces. (For example, if your department sends several students to the top US graduate programs each year and your letters of recommendation say that you are the strongest student in your year, your odds are pretty good.)
- They come highly recommended by someone that the admissions committee trusts.
- A professor in the department wants to work with that particular student.
The rest of my post refers solely to graduate programs in the US as well, since I have no experience with graduate programs in the UK.
Research experience is always good, but not a deal-breaker unless you published in a reputable journal or a trustworthy reference vouches for your work. It's well known that any crap can be published somewhere, so a publication in a "crap journal" won't do you any good.
Re grades: you want grades that place you among the top students in your department. I don't know what GPA that corresponds to at your university. However, your GPA is one of the less important parts of your application. Your letters of recommendation and math subject GRE score are much much much more important.
Random advice to increase your odds of admission: if your department doesn't have any connections to the US, you might benefit from visiting a different department. The goal would be to get a strong letter of recommendation from someone that the US admissions committee trusts. I have met several foreign students who pursued this strategy, and they all fared quite well in admissions.
Last edited by b@r!um; 11-12-2012 at 04:16 PM.