<p>LoremIpsum wrote:</p>
<p>“I worry, however, about the lack of graduate level courses, especially in math and science, because he can devour new math and science subjects that interest him in pretty much a single pass without repetition or review. He polished off his high school’s entire math curriculum by the end of sophomore year and is taking the last AP science class his third and final year. What does Williams do with a junior or senior who’s ready for graduate level work? Customize independent study projects?”</p>
<p>Greetings, mathematics major at Williams here. Currently a junior. You raise a valid question, though I will note that lack of graduate students does not translate to lack of graduate level courses. The 300-400 level courses tend to cover material seen in the first year of graduate school and follow texts specifically written for “advanced undergraduates or first-year graduate students” (most of them use those words precisely). Here’s the online catalogue of math courses being taught this current semester: [Williams</a> College Catalog](<a href=“MATH Wil Spring 2010-11 – Catalog Archive”>Mathematics Spring 2010-11 – Catalog Archive). So the material covered certainly extends beyond what one would expect from standard, undergraduate courses.</p>
<p>That said, there is certainly a difference between a 300 or 400 level course at Williams and a graduate course at Brown or any other research university, and this has largely to do with the difference between graduate and undergraduate programs. Graduate programs are professional schools, and as a graduate student of mathematics your life essentially revolves around churning out proofs. The courses in a graduate program, from what I can tell, tend to be more accelerated than even the higher level courses at Williams, largely because Williams’ math program is not primarily pre-professional (though it should be noted that we do a pretty good job of sending students to math PhD programs and other careers), as you would expect from a small liberal arts college. What difference does this make? Well, it depends in part on which professor is teaching your course. Some professors will teach in a more accelerated style, and some will teach less so. In both cases, a student will be introduced to graduate level material, but perhaps will cover 60% of a typical first year graduate course in the one as opposed to 40% in the other (I’m generating those numbers based on my personal experience, and they are not scientific figures).</p>
<p>On the other other hand, the work at the 300-400 level will definitely keep you busy, and in my opinion there is no need to turn your college experience into a graduate-level frenzy. And if your son ends up completing work at this level in a timely manner - I have classmates who were doing quite well for themselves at the 400 level in their sophomore year - then he will most likely be primed to pursue a thesis project his senior year and perhaps independent studies his junior year, and those can be at whichever advanced level he can manage to push. Independent studies (semester long courses pursued one one one or two on one with a professor) are not rare or difficult to orchestrate at Williams, which is one advantage of attending an institution where faculty are so present.</p>
<p>I can’t speak to physics or comp sci, but I pass by the physics lounge often around 1 or 2 in the morning and more often than not spy students working out problems on the board at that hour, so I can only assume there is no want for work in that department, either.</p>
<p>I’d also like to direct your attention to SMALL, a summer undergraduate research program hosted by Williams, and the largest such program in the country: [url=<a href=“http://math.williams.edu/small/]Math/Stat[/url”>SMALL – Mathematics & Statistics]Math/Stat[/url</a>].</p>
<p>There’s no doubt that the resources available to math students at Williams are among the best available to any undergraduate anywhere, but I think what really makes Williams stand out is the availability of the faculty and their willingness to be involved in their students’ studies. Sure, you can take a course marked at the graduate level at a research university, but it will be more difficult to access the professor responsible for the course during his or her off hours than it is at Williams. All professors hold official open office hours at least once a week (usually twice), but most are in their offices with their doors open even outside those official hours, and they are always happy to have students come and discuss math. (And make no mistake, they are no strangers to publishing.) I know multiple students who have engineered independent studies, and many students who write theses with a faculty adviser end up publishing their original research. So that’s the flip-side to Williams’ not being primarily a pre-professional program - world-class faculty come to teach at Williams because they have a particular interest in engaging undergraduate students, rather than hiding away and busying themselves day and night with their own research. And this really holds true for all disciplines at Williams. It’s a unique experience, indeed.</p>