<p>To go back to the original topic, of the rigor of the Ivies: As with most universities, including the Ivies, the rigor depends considerably on the specific set of courses that the student selects, and not just the major. </p>
<p>In a typical large, public research university (LPRU), first-year students who are taking math will often be distributed over 7 to 10 courses of different levels. At the Ivies, I would estimate the the students are distributed over 5 or 6 different levels in math, to start. Even Caltech has multiple math levels for first-year students (including an honors course that covers Galois theory). </p>
<p>My university offers about 6,000 courses, giving an extremely large number of possible routes to a degree, of varying levels of difficulty. I doubt that even the “slacker” path through an Ivy is as easy as the path taken by the bottom 30% or so of students at a typical LPRU. At the high end of difficulty, particularly with the choice of large numbers of honors and graduate-level courses at the LPRU (and at the Ivy, too), the experiences are probably more closely comparable, although I would have to say that I suspect that the highest-level Ivy course selections would be more challenging. </p>
<p>When posters remark on this forum that students would not be admitted unless they could do “the work,” I don’t think this is an accurate representation of the college experience. The level of difficulty varies a lot with course selection at the Ivies, as at the LPRU’s. One could talk about AP Calc in terms of “the work,” but even there the variation in classes in different high schools is fairly wide. To talk about all of the possible choices at universities as “the work” tends to obscure the fact that there are many different levels that could be selected by the student. </p>
<p>The service academies come closest to having “the work” of all of the colleges/universities with which I am familiar. Caltech and some of the other universities that require a common core curriculum might also come close to having “the work.” The service academies have associated preparatory schools, with one-year programs to prepare applicants they would like to admit, but who are not yet prepared by academic background to handle the first-year academic courses. I think this is a good approach, although it may be hard on the students who wind up at MAPS, NAPS, . . . Caltech just doesn’t admit the students. This has the advantage of reflecting the actual demands of Caltech in an honest, upfront way. However, if I ran Caltech, I’d offer CAPS, too, as an alternative–maybe even a two-year or three-year program. (Also, Stanford could have SAPS! and Yale could have YAPS!)</p>