Research Experience for Undergraduates: Summer Programs (that accept non-American applicants) There are many summer research programs in the United States, targeted at good motivated undergraduate students majoring in mathematics. 
The main aspects that characterize such programs are: (a) a great deal of lectures on specific topics; (b) the chance to gain some hands-on experience with research projects. 
Most of these programs, however, (if not all of them) are hosted by American Universities and require that the applicants are American or permenant residents in the United States. Also, even if students outside the U.S. are allowed to apply, they generally do not receive funds. 

Question: Are there any such programs outside the U.S.? Or are there any programs in the U.S. that accept also non-American applicants?


Remark: A similar question was asked on MathOverflow, but it seems appropriate to share this question with the larger (and maybe younger) community of Mathematics Stack Exchange.
 A: Here are some summer research opportunities in the US that fund non-US citizens. (I realize that you were asking for programs outside the US, but you framed your question in terms of being disappointed about having to fund it yourself so I thought this list might be helpful) 
(I'm new, so the system won't let me post more than one hyperlink)
Research in Industrial Projects for Students (RIPS) 2011 at UCLA (Also has a program in HongKong)
http://math.williams.edu/small/application-information/  (their website says they have funded non-US students in the past)
NIMBios 2011 Summer Program
National Institute for Mathematical and Biological Synthesis (NIMBioS)
at the University of Tennessee, Knoxville
DIMACS REU
DIMACS/DIMATIA REU
CCICADA REU
Rutgers Math Department REU (foreign students enrolled at a U.S. university are eligible under the CCICADA program)
Mathematical and Theoretical Biology Institute MTBI Summer Research Program
A: As an undergraduate in the UK, I did a summer research project in analytic number theory that was funded by the EPSRC Vacation Bursaries Scheme.  It involved working under the supervision of an advisor on an individual project for approximately 8 weeks, and was a really good opportunity to gain research experience.  I'm not sure what the constraints for eligibility are regarding nationality/citizenship, but the website I've linked to provides information about participating universities, who might have further information.
There is a similar scheme specifically for mathematics funded by the LMS
A: Individual universities may have funding available, so it would be worth asking your own university. Three programmes I know of are:
University of Toronto (Canada): http://www.fields.utoronto.ca/programs/scientific/15-16/summer-research15/
Weizmann Institute (Israel): http://wws.weizmann.ac.il/feinberg/index.php?q=content/about-program-0
Not strictly research, but PROMYS in Europe are looking for counsellors. It's based in Oxford, UK: http://www.promys-europe.org
But be aware that deadlines for this year may have passed. 
