I’m a freshman in high school thinking about my future, and I’m extremely talented at mathematics. I will be taking calculus 1 by sophomore year, calc 2 my junior, and the next level, multivariable calc or something else, my senior year. I am VERY well rounded, do 3 seasons of varsity sports, am in Amnesty International, etc. I am looking at colleges for the future (somewhat for fun). I LOVE liberal arts colleges and everything about them, from size to setting. However, entering college having taken multivariable calc already might be a problem, as will I run out of classes at an LAC like Bowdoin or Williams? Or is a large university like MIT better? I want an answer based on whether or not I will run out of classes, not your personal preference, as I love LACs. Lastly, how is Dartmouth’s math program? Thanks soooo much… I don’t know why my previous post didn’t work… sorry for clogging up the site 
Also, I am exclusively looking in the Northeast, Pennsylvania, New York, and NJ included. Looking for a college close to a rural setting, suburban would be ok. Thx
At the very best math departments, some of which are LACs, the multi variable calculus you would learn in high school, on your own, or a local community college, would most likely be a shadow of rigorous “equivalent” college course. It’s unlikely that you’ll want to skip the college version, and it’s quite unlikely that you’ll be allowed to. There’s much more to math than calculus.
My sense is that you’re ahead of yourself. There is no shortage of very advanced math courses at any of the colleges and universities you’ve mentioned. College course catalogs are online. Check out the offerings for this semester. Wait for a year or two before getting caught up with which college is best.
Thanks, I guess then I’m wondering if a place like Williams will have enough classes if I come in having taken calc 2. I don’t want to be disappointed when I start seriously looking…
There are a number of LACs that allow you to take classes at other universities. Amherst is part of the 5 College Consortium, so you could take advanced classes at UMass. Students at Wellesley can take courses at MIT, Babson, and Olin. Swarthmore, Haverford, and Bryn Mawr students can study at Penn. If you apply to a school that’s part of a consortium, you’re sure to find classes that will suit your mathematics needs.
I know of two Northeastern LACs that have a particularly high percentage of math majors: Williams (13%) and Hamilton (10%). Since you have already gotten some information on Williams, I checked the Hamilton College course catalog. You would have 34 courses to choose from on the 200, 300 or 400 level. These courses are all above the calculus II level, which is a 100 level course.
I don’t think you’d have any problems, especially at elite liberal arts schools. Many, many applicants to such schools arrive on campus taken Calc BC, which is the “equivalent” of Calc I and Calc II, so you really wouldn’t be that far ahead. By a semester, perhaps two, but I can guarantee there will be other people in your situation too. It’s really not that big a deal.
Harvey Mudd does not interest you?
At many of the smaller liberal arts colleges, you may run into a ceiling in that you won’t be able to take graduate level math courses, which is what very advanced math major undergraduates like you would be often do. Also, the junior and senior level math courses that you are likely to start in (e.g. real analysis, abstract algebra) tend to be smaller even at large research universities (but check on-line schedules), so the advantage of a liberal arts college would be less for you in your major than for many other schools.
You may want to investigate liberal arts colleges with convenient cross registration agreements with nearby research universities, so that you can take additional or graduate level math courses if you find the offerings at the liberal arts college to be too limiting.
On-line catalogs and schedules can give you an idea of what is offered at each school, and how frequently (every semester, once per year, once every two years, or even less frequently). Class sizes are often visible in the schedules.
For further reference:
Math SAT scores, 25th-75th percentiles
Williams: 670-770
Hamilton: 660-740
I took the AP Calculus BC exam in my junior year. In my senior year, I took six math courses at a local university. I emailed my favorite LAC to find out about their transfer-credit policies, and they basically told me they wouldn’t transfer any of my credits because my college classes appeared on my high school transcript. (I live in a state where dual-enrollment is free if you take the classes for both high school and college credit. As such, my courses were listed on my high school transcript even though I didn’t use them to meet graduation requirements.)
Going to that LAC would have meant starting at a lower level than I expected. This isn’t necessarily a bad thing. People always try to “get ahead” in math, and it’s all nonsense because math isn’t a race. Your goal is to understand the material at whatever pace is appropriate for you. Your high school calculus classes probably weren’t everything they could have been, and you might benefit from reviewing the material at an LAC. You wouldn’t have trouble getting into graduate school, if that’s what you’re concerned about. Many LACs send their math majors to top graduate schools.
In the end, I chose to attend a university for reasons unrelated to my math classes. They gave me transfer credit for all of my dual-enrollment classes, and I’m glad I’ve been “compensated” for my college work even if it means getting a slightly lesser-quality education. (There are a lot of gaps in my knowledge, and I might have benefited from “starting over” with calculus.) Ultimately, it depends on what you prioritize and value. I want to be an above-average student in an environment that gives me a lot of freedom and options to do whatever I want. Other people want a structured curriculum where the challenges are imposed more directly.
A top student in math should be able to self-study any small gaps that s/he may discover in his/her knowledge. Such gaps would not be unusual with any transfer of credit from another college (or AP), or going to a PhD program at a different school. It is not normally necessary to repeat an entire course to fill in small knowledge gaps*. So fulfilling frosh/soph level courses with transfer credit from college or AP course work taken while in high school can mean having additional schedule space for more interesting electives in or out of one’s major.
- Of course, large gaps may require retaking the course -- examples would be the proof-based "calculus" courses at Harvey Mudd and Caltech, where knowledge of "regular" calculus (from another college or high school) is assumed but not considered equivalent.
You mentioned MIT. By percentage of math majors, here are how a few LACs and universities compare:
Caltech: 13%
Williams: 13%
Hamilton: 10%
Bowdoin: 9%
MIT: 6%
U. of Chicago: 5%
It’s anecdotal, but Reed Hastings, founder of NETFLIX was a math major at Bowdoin.
^ Cofounder of Netflix with Marc Randolph, a Hamilton grad.
If you choose a LAC look for one where you can take grad level courses at a nearby university. The most advanced math majors are taking grad courses by senior year. It also depends on whether you plan to go on for a PhD in math. If you are planning to pursue one in a rigorous grad program, then grad level courses are more important than in other instances.
Smaller LACs will also allow gifted mathematicians to work independently, on their own projects. Even if there don’t appear to be formal classes at the highest level, you could undoubtedly have opportunities for tutorials with professors and possibly design your own Math curriculum as an upperclassman.
Coordinating with the above post, the LAC I researched actually combines an independent project with a formal course titled, “Senior Research.”