"The reason you want to go to those schools is not their top-notch academics"
I assume you didn't go to an Ivy League school. Most of the people who are there by academic merit genuinely are at the top of their academic year/class. If you can handle it, you can take math classes with IMO medalists, chemistry classes with IChO medalists, etc. And this holds true for most departments.
The hardest part of getting an Ivy League education is getting into an Ivy League school. The coursework at those schools isn't really much harder than their less prestigious counterparts.
At the lower levels, sure. But once you start getting into more specialized fields, there are generally more courses and more professors compared to less prestigious counterparts.
It's not that there aren't sharp people at less prestigious schools, but that there are generally more at more prestigious schools.
In CS, at least, I haven't seen that. The Yale CS department, for example, has some very smart people, but is not that large, and the specialties concentrate in certain areas. As far as I can tell, the undergraduate education there is roughly on par with the quite small and non-Ivy school I attended (http://www.hmc.edu). Possibly even somewhat lower standards due to undergraduate education there being a lower-priority focus for their faculty (their tenure cases are evaluated based primarily on graduate supervision and research, not teaching), and more grade inflation meaning that it's virtually impossible to fail.
edit: Though to be clear I'm not really claiming "Yale is worse than [X]", just that past a certain level it depends more on what you care about. Do you care about small class sizes? About the opportunity to engage in undergraduate research? About big projects happening in your department? Do you care about AI, compilers, graphics, or theory? About practice-oriented programming or software engineering? Depending on your preferences there are more like 50 schools that will provide a top-notch education, not 8.
Harvey Mudd will give you a first-rate CS education, so I'm not surprised by your experience. It shouldn't be surprising that its on par with Ivy schools. I bet you'd get something similar from CMU or MIT too.
(Disclaimer: Not an alumni of any of these schools, but know and have worked with many people who attended them)
I suspect Caltech beats Yale hands down in I direct comparison of the student body's intelegence. But, if you want to go into politics Yale is a far better choice. Rich may be well educated, but it's got little to do with raw intelegence.
My point wasn't really the amount of smart people that exist at either schools. It is more so that existence of smart people does not equal a more challenging or more educational experience.
Although I agree with you that the further you get in a field, the more likely a prestigious school will be better. But I would credit that to having a more direct relationship with professors. When you are actually helping a professor with their research, the quality of the research matters more than when you are simply being lecture by that same professor.
>It is more so that existence of smart people does not equal a more challenging or more educational experience.
Huh. I don't have any hard data, but I always thought the opposite. I mean, I didn't go to school, but I put a lot of effort into being around people who are better (at things I want to be good at) than I am, and I attribute much of my success to surrounding myself with people who are better than I am.
I mean, I agree about the second bit... my understanding is that undergrad at a prestigious school offers little contact with the (usually very good) professors (thus, my assertion that it's all about the quality of the other students.) - thus, grad school there, where you get more contact with the (very good) professors would be even better.
Perhaps I am unqualified to say, because I didn't go to school. On the other hand, I managed to learn enough without school to get a job that often requires a degree, so maybe I am qualified?
In my experience (Brown undergrad), literally every undergrad I know who wanted to do research with a professor has gotten to. And usually they had plans on working with specific people by their freshman or sophomore year. And this is in fields as varied as Sociology, CS, Chemistry and Comparative Literature. Though, this may not be a function of going to a prestigious school, so much as a school that has 2000 grad students and 6000 undergrads, so professors are forced to interact and teach undergrads.
I don't think that is the case in many engineering fields at least. A greater presence of smart people sets the bar that much higher for grades/tests/projects.
Most engineering courses are based on a curve. If the rest of the class is brilliant, it's significantly harder to compete and get a good grade.
Which means that exams need to be much more difficult. When I was a grad student Teaching Assistant at Harvard we had a newly hired professor who'd spent the last decade at Cal Berkley. He decided to give the same midterm exam he'd given many times before at Berkeley. When we TA's saw the exam we politely told him he needed to change it or the whole class would ace it. "Nonsense!" he said, "Harvard students aren't that much smarter than Berkeley students." We had to write and administer a second midterm because everyone scored 98, 99, or 100 on his Berkeley test.
This is the problem with anecdotes: your experience seriously does not mirror my experiences with top colleges and UC Berkeley. I took several math classes at Stanford and had to repeat them at UC Berkeley, and they were significantly easier (coursework and testing) than the equivalents at UC Berkeley, even considering the fact that when I took the classes at Berkeley I had already covered the basic foundation of the material at Stanford.
If this was an exam for a freshman/sophomore course, I might believe it since lower-div classes at Berkeley have an exceptionally wide audience with non-uniform levels of prior mathematical experience. However, if this was an upper-div course, I highly doubt your anecdotal experience holds true in general. Source: majored in math at Berkeley, went to MIT for grad school.
Depends where you draw the line. Compared to a public state school, the Ivy League course cover far more material faster in more depth, because the students are better prepared harder workers and can handle it.
Harvard has 4 levels of Multivariable Calculus, for example, whereas most schools have just 1. The 2nd-highest level is basically Real Analysis, except (a) it is more deep/accelerated than the actual Real Analysis class, and (b) it is only taught to first-years.
The highest-level class was designed for students who were expected to learn an undergraduate math degree curriculum "on their own time" and pursue more advanced topics in clads.
I did go to an Ivy League school, and I didn't go for the top-notch academics, even though I was at the top of my class in my department.
And even if your reason was actually the top-notch academics, you still benefit very much from a strong old boys' network of professors and researchers.
certainly, but those top notch academics are more relevant for graduate research than undergrad courses. with the swarm of ivy graduates going to work on wall st, I doubt the advanced botany course with a medalist in the field is as relevant as the name of the school.
I assume you didn't go to an Ivy League school. Most of the people who are there by academic merit genuinely are at the top of their academic year/class. If you can handle it, you can take math classes with IMO medalists, chemistry classes with IChO medalists, etc. And this holds true for most departments.