Undergraduate summer activities in the US or Europe? I a currently a college freshman and I would like to do something math-related in the summer. I will have taken all of the basic courses except for analysis and set theory by the end of the summer (calculus,linear algebra, modern algebra, topology). I would like to know if there is anything out there for me, preferably something to which applications have not yet closed. 
I think there are both summer schools and research summers or something like that. I have never done any research before though (not even close). And I doubt I could be able to without a lot of help.
So mainly I would like to know about the current panorama for math summer opportunities. I would also like to know if a dedicated student would be able to profit from a research summer. And finally if it would be plausible for a freshman to be accepted (I'm from Mexico if it helps).
Thank you very much in advance.
Regards.
 A: The PROMYS and Ross program are always looking for counselors! You get to mentor advanced high school students who spend $\approx$ 6 weeks learning proofs via elementary number theory. There's also lots of opportunities to learn and study math with the other undergraduate counselors. 
A: Budapest Semesters is a well-known study abroad program for math, and it looks like it has a summer program (whose deadline is March 1).
There are also all kinds of REU's (research experience for undergrads) at various places across the US (I'm not sure if there are any citizenship restrictions, there may be). As far as having no research experience, that is not a problem. You have to start somewhere and REU's are kinda designed for that. Nor are they really competitive to get into (notable exceptions being the UM Duluth one or the one that Ken Ono runs.)
A: A popular mathematical profession is actuarial science. The math needed for this major includes fundamental calculus and linear algebra, but it focuses on probability, statistics and finance. Anyway, it's a highly regarded profession and it also pays well. There's plenty of insurance companies looking to hire actuarial summer interns so you could try looking into that if it interests you.
