Why choosing Carnegie Mellon over Harvard?
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In my younger, naive days I used to. believe that the most important aspect of a university is the quality of professors, research, etc. I now believe that after a certain threshold is passed all of them are pretty much equivalent, give or take epsilon. So how to choose among this equivalence class? Choose the one with the best possible network! That's why Harvard and Yale unbeatable, and depending on where you want to go Stanford. The alumni network's distribution within the American workspace is key, not only because those will be your future classmates but also because that's how will perceive you. Why so many important people from Harvard Law School, just because it's hard to get into?
This may be a simplistic approach but at least it gives you actionable items for your decision, I think. BTW, I'm no expert either, I got my degrees from Purdue. My decision process was simple: choose the only American university that gave me admission and TAship.
Which one will give the better scholarship depends strongly on your family income. If you're from a well-off family then U of Michigan will probably end up a better deal (lower tuition + merit scholarships). But if you're from a less-well-off family, then the prestigious private universities typically have more generous aid, due to their huge endowments and insulation from state budget crunches. For example Harvard waives all tuition and provides a living stipend for students whose family income is < $65,000, which is more generous than U of Michigan's scholarship policy. Between $65k-$150k there's a sliding scale so you'd have to make a more detailed comparison; above $150k you pay the full Harvard tuition.
So for example, if I were a manager hiring for a security position, I would probably place more weight in a CMU graduate than a random Ivy graduate.
I would also say it's probably not coincidental that they churn out very competent individuals and also are very academically rigorous. Sometimes theory and practice do align.
To be fair, quora is impossible to use behind the GFW: choose a google login (that goes through YouTube) or a Facebook login. So copying quora content makes sense.
Last time I checked, which was decades ago, Harvard required proof that you can do algebra.
MIT is not, however, a flunk out school. It believes that every admit can do the work, and the pattern is that people who've chosen an appropriate major make As and Bs, unless they have personal problems, which of course are statistically inevitable. No legacy admits if they can't do the work (which means few in practice), every minority in the student body deserves to be there (at least in my personal experience).
Also, if the average person is making As and Bs, you have pretty bad grade inflation (but then again I'm coming from one of the least inflated systems in the country).
What MIT does is grade on mastery of the subject, not on some curve that might be appropriate for a "flunk out" school but not for one like MIT that can admit the very best in the world. A bit of time with Google indicates Harvard also doesn't grade on the curve.
Going further in what I said above, last time I got figures a few years ago, MIT thought about 3,000 of its applicants can do the work (back when there were 12-13,000 applicants/year). So once that bar has been passed, they can be fairly selective about who they admit for the class target of around 1,100, and in my experience in the '80s by and large those admits can "do an elementary analysis of, for example, a piece of legislation or historical account" (although very few seemed to know history ... then again that's a life long interest and study of mine).
Harvard being Harvard I would expect the student body to be better at "do[ing] an elementary analysis of, for example, a piece of legislation or historical account" than MIT's student body, but Harvard, along with MIT (and CalTech, which has significantly stiffer general graduation requirements than MIT) are special cases.
CMU was the top school in the North American region at the 2013 ACM ICPC World Finals
I'd venture to guess that 10-15 years into the real world, very few Harvard grads say "I wish I'd gone to CMU," while probably quite a few grads of CMU (and other engineering programs) wish they were better networked.
In his New Yorker interview, Michael Saylor made a similar contrast between MIT (his alma mater) and Harvard. In his view, Harvard grads did better in life because they had learned to develop relationships, and had more of them.
I went to college in Switzerland. The group that was doing CS was maybe 75 students on day one. There's a very simple criteria to be kicked out of the faculty: fail any exam 3 times. 7 have graduated with me 4 years later.
And I say this as a non-American.