<p>I personally wouldn’t consider any school over a full ride at Northwestern unless the difference between the offer and COA was very small at the other schools. If you have to pay $5-10k a year to go to another university, there’s absolutely no reason to even consider that over Northwestern. Caltech does math and science better, yes, and Yale has better name recognition, but still, at this tier of schools, there will be an incredible amount of academic rigor no matter where you go.</p>