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As for U of I, of course it is relevant. It is not one of but THE top school in several of the most difficult disciplines offered at a university. Applying to these schools within the university is equivalent to applying to your elite group (admissions and selectivity). It's faculty is renowned especially in its graduate schools (faculty and graduate schools). A degree from it is an assurance of an immediate and high paying job from a company of choice (job placement). However, if you apply to the school of agricultural sciences you will find some lesser lights.
I never denied that U of I has several good programs with good students. At the top schools, though, EVERY program is one of the best. Find a program at Harvard that isn't top 5 or top 10. It's difficult to do. That's the difference between a place like Harvard, Yale, etc. and U of I. U of I supporters can't stop talking about their engineering school because it's one of the best. At Harvard, they don't talk about specific programs as much because EVERY program there is regarded as the best. Further, U of I is a safety school for people who don't get into the Ivies, etc., not the other way around. Again, it is not an elite institution. But it does have a few elite programs.
As for Notre Dame and the rankings, I don't care what U.S. News says, though I am surprised that it has jumped up as high as it apparently is now compared to where it was a few years ago (in the 30s). Every college admissions officer knows that the USN criteria is a joke because it changes from year to year and the survey data can be manipulated by clever university administrators. Unless ND has radically altered its admissions criteria and degree requirements over the past couple of years, there's no way it is on the same plane as the U of C in terms of academics--Chicago has greater selectivity and a much more difficult curriculum. But U of C typically gets penalized in the rankings because it is more of a graduate institution than an undergraduate institution and it kills its students academically so they are not as "happy" as at other schools. For the purposes of graduate admissions, though, U of C is regarded as a top-tier school while Notre Dame is in the next one or two groups.