<p>I know it's good, but are there enough options if you've already done a lot of the basic math (calc I/multi/linalg/diffeq) and are a prospective math major? I'm generally a fan of smaller schools, but worry more about academic options for them than for larger ones.</p>
<p>Williams has a <em>lot</em> of math classes for a small school. You might want to take a look at the math section of the course catalog:
<a href="http://www.williams.edu/admin/registrar/catalog/coi0708.pdf%5B/url%5D">http://www.williams.edu/admin/registrar/catalog/coi0708.pdf</a></p>
<p>and at past courses taught:
<a href="http://www.williams.edu/Mathematics/adv_courses.htm%5B/url%5D">http://www.williams.edu/Mathematics/adv_courses.htm</a></p>
<p>Hmm, from that I see...</p>
<p>only 1 sem Real Analysis, offered every year I assume
1 sem Algebra</p>
<p>Most things in (pure) math beyond that (Topology, Differential Geometry, Complex Analysis...) offered every other year =/</p>
<p>The argument for small schools usually goes that there are more opportunities for professor interaction and things like directed reading for classes that aren't offered regularly...maybe that would help fill the gaps in a given year?</p>
<p>I'd be sort of concerned about running out of courses, especially without other schools nearby like many of the other LACs.</p>
<p>(Note--I'm not trying to be annoying here, I'm genuinely curious. Clearly LACs don't do too shabby in math grad school placement, etc, so I'm just wondering about opportunities for "advanced," for lack of a better word, work, formal courses being somewhat sparser than usual).</p>
<p>With Williams tutorial system you could find like minded students and take a tutorial for higher math topics.</p>
<p>Just one possibility. Clearly, a university will have more courses.</p>
<p>I don't know how you would run out of courses, unless you chose to take all your four classes in mathematics (and even then, you'd have to take other classes for the distribution requirements)</p>
<p>I can see Geometric Group Theory, Algebraic Number Theory, Matrix Groups, Groups and Characters, Real Analysis, Chaos and Fractals and Abstract Algebra in the realm of pure math. (and Intro to Number Theory, but if you've taken that much math you're probably pretty well acquainted with number theory) That's 7 courses, and it's just for this year. For 08 they'll have more.</p>
<p>Yeah, and keep in mind that the major only requires nine classes. There are quite a bit more than that being taught this year - the seven that apathy mentioned plus game theory, probability, discrete, measure theory, topology, "the big questions" senior seminar, etc. Add all the courses not being taught this year along with a senior thesis/independent study and I doubt you'd run out of classes unless you <em>really</em> want to specialize.</p>
<p>Keep in mind also that Williams doesn't allow freshmen to take more than two courses with the same prefix in a year, and sophomores are limited to three (the so-called "early concentration rule"), so you'd have a hard time even approaching the limits of what's being offered. If you want to take nothing but math classes for four years, then Williams probably isn't the right place for you. But if you want a top-notch, well-rounded education that includes a lot of personal contact with superb math faculty, then we're probably about as good as it gets.</p>
<p>I'd suggest you contact the Math/Stats Dept. Tell them what you've taken, what your interests are, and what your concerns are.</p>
<p>How about applied math courses?..</p>
<p>Just a suggestion.. caltech will offer all the math courses that you need?.. Williams will offer more that math tho</p>
<p>*more than</p>
<p>an interesting statistic about Williams: about 10% of the student body majors in math, a number that's freakishly high for a liberal arts college (the national average of math majors is less than 1%). That should tell you something about the caliber of the math profs here. Another sidenote: two of them made a living during grad school as comedy writers.</p>