<p>I would look into UChicago’s Vigre summer math program. My math major friend adored it, and it was a factor in his decision to come here: [VIGRE</a> at the University of Chicago](<a href=“http://www.math.uchicago.edu/~may/VIGRE/]VIGRE”>VIGRE at the University of Chicago)</p>
<p>And the Paris math program might be worth a look as well. It is taught by UChicago faculty, but it takes place in Paris the spring: [Department</a> of Mathematics: Undergraduate Program Contact](<a href=“http://www.math.uchicago.edu/undergraduate/paris_program.shtml]Department”>http://www.math.uchicago.edu/undergraduate/paris_program.shtml)</p>
<p>The pure math track is fairly popular at UC. All of the people I have talked to are extremely happy with the courses and overall experience–it seems to be a pretty close-knit department, at least from my observations.</p>