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There is no concrete evidence that Chicago is "extremely rigorous," at least when compared to other elite schools.
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Well, of course not. Such evidence would be either very difficult to find or nonexistent altogether. There is also no evidence that schools like Caltech are extremely rigorous, but it's so self-evident that nobody bothers to question it.
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I'm under the suspicion that you can find challenging courses equivalent to "Chicago level" almost anywhere.
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No, I don't think so. When I compared my language courses to my state school's (which is ~#50 USNWR), I found that we progressed at least 3x as fast here. I also know people there taking advanced math courses, and they don't even compare to the math courses here. At HPCM, et al., you can find extremely difficult courses in no matter what area you look. As for schools below roughly ~#40, I don't think there's even a comparison.
Now, I think there's a considerable difference between certain departments. In some departments, the average grade is perhaps an A or an A-, despite weak students. In other departments with very strong students, the average grade would be a B or a B- (biology comes to mind). It really all depends on your major.