<p>A couple of additional thoughts:</p>
<p>Some have questioned why top students need to go to “top schools” for undergraduate work, when they can get into a top-flight school for graduate work. </p>
<p>On the one hand, it does often happen that a strong student at a large, public research university can gain admission to a top-notch graduate program. </p>
<p>On the other hand, in my opinion, there are several reasons for the “truly superb” students I have mentioned to go to “top schools” in their intended fields, if possible (and I also think that the schools should admit them). </p>
<p>First, a student in at least some of the sciences needs to go to grad school with a specific mentor in mind, often agreed-upon even prior to enrollment. Schools that enforce a waiting period after graduate registration, before a student can sign up with a research adviser, still often have some sort of under-the-table pre-agreements set up between some students and some advisers. If you take a school like UC Berkeley, the experiences of a grad student can vary substantially from adviser to adviser. A student who wants to work with a Nobel laureate is advantaged by having recommendations from faculty members whom the Nobelist knows. This may be easier for a student coming from Harvard than for one coming from some of the public universities. On the MIT forum, molliebatmit has mentioned that she believes that she was helped in getting into Harvard and working with the research mentor of her choice, by the recommendation based on her undergrad research experience at MIT.</p>
<p>Second, the research experience that one can gain as an undergrad differs from university to university. Scientists identify “problem selection” as a key issue differentiating the most significant work from other, equally difficult work that does not advance the field as much. Students who have the advantage of working as undergrads with truly top people will gain insight into good problem selection–I see this playing out all the time. </p>
<p>Third, in my experience, there are a few people in mathematics and the physical sciences who have an elegance of thought and depth of insight that is just extremely rare–here, I am talking about a small subset of people–perhaps 20% of the faculty at the “top” schools would fit into this category. On very rare occasions, one encounters a student of this type, and this student is not well-served by most non-top-schools.</p>
<p>When it comes to the UC system, UC Berkeley is definitely a top school in my field, regardless of the CC classification. So I don’t regard the experiences of someone who was an undergrad at UCB as a counter-example to my analysis.</p>
<p>Also, I don’t regard the experiences of pre-med students as a counter-example. Medical school admissions committees place a heavy emphasis on grades, given that the required courses have been taken. They do not conspicuously reward the choice of the most challenging courses, including graduate-level courses, as far as I can tell. However, in the physical sciences and mathematics, the people making the grad-school admissions decisions–within my range of experience–do look quite carefully at course difficulty as well as GPA.</p>
<p>(Edit: Wanted to acknowledge the possibility that MiamiDAP’s D took the most challenging courses available in the pre-med curriculum. The comments about pre-med programs were not meant to contradict MiamiDAP, just to say that pre-med programs are a different ball game.)</p>