I am very highly interested in mathematics, but I am also considering the liberal arts college experience. What liberal arts colleges are at the top of the top in terms of their math departments? Are there any that come close to, are the equivalent of, or even surpass the likes of MIT and Princeton at the undergraduate level? From my own low-level research, I've heard a lot about Williams, Swarthmore, Reed and Pomona. Should anything be added or taken away from this list?
I'm especially interested in the liberal arts colleges that have a focus in mathematics. On this note, I've heard the name Harvey Mudd tossed around. Are there similarly focused schools, and how does this one compare to top universities and other top LACs?
To make more specific what I am asking, I'm looking essentially for the following characteristics:
- High selectivity (I like being regularly intellectually challenged by my peers)
- Large math course selection (I expect to move through classes quite fast (I've done Real Analysis, etc. already), and I don't want to run out of options)
- Qualified math professors (in terms of recognition among both the mathematics and teaching community)
- Opportunities for research (I want to be a qualified applicant for top graduate schools; also, research is fun)
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