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Hi, The US system is completely new for me and I've got no idea how tough the competition is. I'm a graduate student in mathematics in Finland, but I've thought about applying to the US next autumn. The problem is that I have no idea how high I could aim with my applications. Here's some stats: + got my M.Sc. in 3 years (5 the norm) + had a GPA of 5.0/5 in mathematics 4.95/5 overall - I will be 26 next autumn (old I suppose) I graduated from the top university in Finland (University of Helsinki) in 2006 with a M.Sc. I'm able to get very good recommendations from my thesis advisor (he already wrote for a scholarship application, that I was his best student ever) who is senior faculty and probably a good one from my current faculty advisor. However, I really don't know who to ask about the third, as I haven't had more than one course with any other professor. Also the teaching system in Finland lets you just pick up the reading list for a course and write the whole course of in one big 4 hour exam, so you never even meet the professor. I did this for almost every undergraduate course that I thought was too trivial. The downside is that I really haven't had any interaction with the professors who tought those courses. As I've understood most US math students are quite young. That's why I'm worrying that my age will be a problem as I would be 27 at the time I would enroll into a Ph.D. program. However, I graduated from high-school in 2001 and spent the following year working for a software company I co-founded while in high-school. I got into a dispute with one of the other owners and left to study CS in the autumn 2002. I quickly realized that I really wanted to study mathematics, so I began studying mathematics in the autumn 2003 after switching to the University of Helsinki. After graduating in 2006 I spent a year in the military (every man has to serve in the military in Finland) and now I've been studying math in a graduate school for about 6 months. This means that I've spent 3 years doing some else than studying mathematics. I'm also going to have already 2 years of graduate study behind me at the time I would begin at a US program. I don't know if this is a positive thing or not. While studying mathematics I've also taken for fun some CS courses at my old university (as there are no tuition costs in Finland, this is possible). I've already done more coursework than required for a B.Sc. in CS, but I don't think I've got time to finish a bachelors thesis there, so I won't get a degree. In these courses my GPA is about 4.6/5, but I haven't put much effort in to them. I'm also wondering wether or not I should mention these studies and send the transcript or could the GPA hurt me if applying to better programs? Thanks in advance.