<p>Critter:</p>
<p>Hampshire is considered an excellent program. I was recently sent some information about a very prestigious undergraduate research summer program. The head of the program specifically says he favors kids who attended PROMYS or HSSIM and/or have participated in Olympiads. Since Hampshire College is pretty much in the middle of cornfields, it's a very different experience from the urban environment of BU.<br>
Re your D not being sure about a math career: Larry Summers has claimed that he started as a math major but switched to economics when he saw how bright other math majors were. Math classes in fact include many economics majors. There are a number of careers that are math heavy and do not involve sitting in a cubicle. My H works in a firm that is filled with economists. The set-up is open platform, which may be worse than cubicles as far as privacy is concerned, but they all seem to get along fine and socialize quite a bit.
Harvey Mudd is an EXCELLENT math school. One of the profs there wrote a book, Mathemagics, which launched my S on his math quest. One of my S's PROMYS friends will be going there this fall and is very excited about his choice.<br>
If your D does not need to access advanced classes, there are some terrific LACs with very strong math departments: Williams, Swarthmore would be at the top of my list; Carleton, Colby not far behind. </p>
<p>After Calculus in 8th grade, my S took Multivariable Calculus and Linear Algebra. That is a fairly standard sequence. Because of scheduling issues, he then took courses that fitted his high school schedule rather than what ordinary undergraduates would have taken, which is real and complex analysis and abstract algebra. Instead, he took a course in classical geometry and another in mathematical probability. These are normally considered undergraduate courses. When he goes to college he will take the courses he did not have a chance to take before, but I'm not sure about the abstract algebra course. He's been complaining that the seminar on algebra at PROMYS is going a bit slow and covering stuff he already knows. So manybe he's picked up knowledge from different sources, more specifically his Math Circle classes.
S is indeed very happy to be back at PROMYS. I've calculated that his circle of friends makes up about 1/8 of the participants. It makes for a lot of socializing.</p>