biona001

I think if your top schools are like Princeton, Harvard, Berkeley...etc, and when you say math you mean pure math, then your chances are very low. As you may know, a very large proportion of math majors are pursuing a Ph.D. I did my undergrad studies in Berkeley for math and everyone of my math major friends (not very many of them) applied or will be applying for Ph.D. What about you are better than these people? Quite frankly, six classes, even if they are upper divs, is hopelessly insufficient. Grad math schools care about your research ability above all else, and I don't think six classes can enable you to make meaningful contributions. Research in math certainly helps, but keep in mind that people generally think undergrad math research means basically nothing, so don't expect too much strength from it. In addition, since you are international, it would be considerably harder for you to be accepted compared to residences with equal caliber. You'd essentially have to be "the best" among all international applications (who knows how many there are). Are you one of these people? I'm sure you are bright and desire challenge, and you should certainly do whatever you want with your life. However I personally know people who give up EVERYTHING ELSE to get into a good math grad school. If you still want to be on par with these people and not give up things like they did, then you'd have to make it very clear what makes you so good. Exceptional intelligence and very hard work is expected, not your strength. Perhaps one of the few ways to prove your worth is doing good on the putnam, like honorable mention. Otherwise, maybe you could try applied math in biology or physics, at least that way that field and your background match up better.