<p>The one curve ball would be if your are intending to study mathematics while abroad. As a mathematics major who did similarly in taking an exchange for research purpose at UC-Berkeley, I would say the intensity and cut-throat nature of the CAL-Math experience seriously detracted from the experience (California was amazing while it lasted, but then it does strike you immediately that CAL-Math meant business to an academic level</p>
<p>Out of all of those, I would suggest Boston College; as an undergraduate exchange student.
It seems that you want to experience a major city and thriving culture; on the other-hand, you want a worthwhile intellectually-stimulating academic experience.</p>
<p>While a number of colleges on the list can offer you the former, my concern is which will offer you the latter.</p>
<p>As a mathematics and law student, I have studied/researched at Amherst College, UC-Berkeley, American, and Georgetown (which I would not say Boston College-equivalent, but as an institution and academic experience mirrors Boston College better than any of the schools you are deciding from).</p>
<p>I would treat those presumptions that your academic experience at Boston College will not be as strong as (UVA, UC, etc.). Honestly, as an exchange student, the difference will be negligible. Unless you are taking a small, upper-division courses at UC-Berkeley where you benefit from the high-caliber of students in the classrooms (a bit of a rarity at CAL-Berkeley), then intellectual experience will not be drastically different in your courses at Miami-Ohio, Boston College, UVA, UNC, etc (that’s a dangerous presumption that the public often makes). </p>
<p>Putting locations and campus life briefly aside, you should sit down and inquire what you have interest in taking; that will inform whether you will have a strong academic experience. From one mathematics student to another, of the American schools, you should really sit down and look at what each school has to offer. If you’re interested in something else for a change, that matters. UC-Berkeley has the most rigorous undergraduate mathematics program (CAL-Math) out the schools you listed hands down; take thought-provoking courses probing questions about society, politics, economics, life, etc. in a lecture setting that encourages critical thinking and active dialogue between the professor and your peers…I’d say a year at UC or Penn-State undergraduate is going end up leaving you short (those classrooms experience that are the hallmark of colleges like Brown, BC, Amherst, Stanford, Georgetown). At a number of the research universities you’ve chosen, you may equally if not more brilliant and fascinating professor, yet the extent to which you’ll benefit from their scholarship will be significantly less).</p>
<p>If you could give me an idea, of what your looking to get out of the experience abroad academically (type of courses, interests, math-only, etc), I could be of better use. If I had to select from the information you have given me, I would take Boston College followed by University of Virginia as second choice, with University of Miami-Ohio and UC-lottery tied at a distant third.</p>
<p>The only three I would definitely scratch off would be SUNY-Albany, UMass-Amherst, UofAlabama, since being at those institutions will cost you a lot location-wise, and the quality of the academic experience is not one I could assure you will be worth the cost of not being near a big city (Albany will put you to sleep faster than any of the UCs).</p>