<p>The weather at Stanford would be great, and of course the math, but yeah it’s an admissions crap shoot for nearly anybody. Weather and geography do become an issue with some of the others. </p>
<p>One key decision is whether your priority is a world class math department or the outdoorsy small college experience (where there likely will be very few math majors and fewer course offerings.) No good college can ignore math - and what these schools offer is likely to be solid - but if a small school is under financial pressure (endowment meltdown) and has only ~5 math majors, you might want to ask if a course in graph theory or topology would be available every semester. You can check out each school’s Common Data Set to find the number of math/science majors, to help gauge demand for these courses. Carleton as I recall has something like 30% math/science majors (more than many LACs) and a good record of Ph.D. production. It’s in a nice natural setting with a beautiful arboretum, though frigid in the winter and maybe not the most exciting for outdoor sports other than x-country skiing.</p>