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You'll have to go to somebody else for an even longer post. But the bottom line is that while Yale ranks above Pton in GRADUATE chemistry and Pton ranks above Yale in GRADUATE mathematics, because they are both top 15 in all three and close to each other in actual rankings, any differences will almost certainly be imperceptible at the UNDERGRADUATE level. It is worth noting that only 1/4 or less of your undergraduate courses will be in your major while 3/4 will not. Moreover, I CANNOT UNDEREMPHASIZE HOW MUCH OF YOUR COLLEGE "EDUCATION" COMES FROM OUTSIDE TEXTBOOK ACADEMICS AS WELL. Consequently, imo, this discussion about specific departments is unnecessary at the undergrad level when both are more than good enough.
Rather, if you get into Pton and Yale, I'd say choose based on the other parts of the college. What gives Yale the edge over P imo? 1) Happiness -- Yalies LOVE it, 2) Grade deflation -- this kills Pton students and makes them more unhappy, 3) Res. Colleges -- Pton tried to create some kind of "res. college" but it doesn't come remotely close to Yale's system! Yale's RCs create a small community within a larger university, allow friendships to blossom that otherwise wouldn't occur, great for intramural sports/competitions, etc. 4) Pton's Eating Clubs -- lame imo. Yale may have secret societies but they are senior-only and they are a SECRET (therefore they don't affect campus life as much) 5) Research opportunities -- Yale has poured so much money into sciences that they hand out jobs like candy 6) Facilities -- all of Yale has been renovated in past few years or is being renovated. That makes a big difference. 7) Graduate placement -- Yale continues to outperform Princeton in graduate school placement.
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