Look Right: First impressions of Part III in context
In the few days I was in London I got used to reading reminders for pedestrians to “look right” before crossing the street. This, of course, is because the British (and Australians) drive on the opposite side of the street. P.J., my Australian neighbor, found it hilarious when he realized this was why Americans were so curiously cautious at crossing streets.
Earlier this week, however, I groaned as the Part III orientation speaker fed us the line:
Everybody look left. Look right. These people are the mathematical leaders of your generation. (Loosely paraphrased.)
Aaah!! The corniness almost knocked me over. Inna, a pure mathematician from Harvard, laughed it off later saying that she’s heard that line used before at her previous university.
The other line that they repeated a bit was:
The only difference between those of you who are from Cambridge and those that are from outside of Cambridge is that the ones from Cambridge really believe us when we say that this is a very difficult course.
Well, that kind of gives you a flavor for how the mathematics department here views Part III. As a reminder, Part III is the shorthand for “Part III of the Mathematics Tripos” at Cambridge. The degree is a ‘Certificate of Advanced Study in Mathematics,’ and is the rough equivalent of a 4th year honors or a master’s degree. The program has the distinction of being the oldest such course in mathematics and the international reputation of being very challenging. One’s performance in the course determines whether one is accepted into the CMS for a PhD program, with only about 30% of the students meeting this standard. (On the other hand, 90% of the students do pass.)
Part III has no obligatory lectures, no homework (though suggested problems and problem sessions are arranged), and no end-of-term exam. There is a single high-stakes examination period at the end of the year in which students choose to take exams on approximately five or six of the courses offered. One can additionally offer an essay (at the level of a literature review on current topics) to take the place of one of the exams.
Perhaps the best part of the program are the other students. My college, Trinity, seems to have a plurality of the Part III students, many of whom are international. There’s a good representation of various countries and a much healthier fraction of women than in US math departments. (However, it does seem that the ethnic diversity is as limited as in the states with me as the darkest-skinned student in my classes.) I do agree that there are some very impressive students amongst the group, including a couple of American theoretical physicists that I met during graduate school visits. I hope that we’ll be able to interact with and learn from each other another outside of lecture, as it would otherwise be a shame given the number of young mathematicians (loosely defined) together in one place.
The course offerings span a wide range of pure and applied mathematics (‘maths’). After speaking with the other students following the first two days of lecture, I get the impression that the pure mathematics courses are a bit of a toss up in difficulty. Michaelmas (fall quarter) courses seem to be geared towards a general audience, with those coming from American schools finding some courses ridiculously basic and others much more fast-paced. One has to take into account, however, that many of these students came from institutions where they were able to take graduate level courses… something that the rigidity of the course structure here seems to preclude.
On the applied side, there are courses in subjects such as particle theory (courses in QFT, the standard model, SUSY, bosonic string theory), relativity (GR, cosmology), astrophysics (stellar stuff that I didn’t look too carefully at), fluid mechanics (MHD, a class on how animals swim), and financial math. Focusing only on the physics courses that I’ve sat in on (QFT, cosmology, GR, symmetry and particle physics), I would have to say that the level of these courses are all a bit more basic than what one would expect in similar courses in US graduate schools (and certainly at Stanford). A junior fellow who had just received her PhD from Stanford agreed with me after she sat in on a QFT for condensed matter course in the physics department, which she said was at a much slower and cautious pace given the ‘scary’ reputation of the math and physics programs here. It’s certainly possible that the courses will pick up significantly during the term, but suffice it to say that I’ve written several postcards during hour-long lectures these past couple of days. There’s an algebraic topology course which I’d like to sit in on, but unfortunately it conflicts with the rather slow QFT course that I’d actually like to present for examination… which I’ve found is rather frustrating. I now realize why a previous Marshall scholar had eschewed coursework altogether and spent time doing small research projects with faculty. Though I’m certainly not at that level, I’ve been looking for other students to form a journal club to read review articles and papers. The courses next term will pick up significantly, with Michael Green’s [bosonic] string theory course, a course on supersymmetry and extra dimensions, and a course on the nitty-gritty of the standard model.
At the end of it all, I think the major difference I’ve learned to appreciate is management of time. Unlike students in the US, those taking Part III finish courses in the early afternoon and do not have to worry about the constant assessment of weekly problem sets. There’s a tremendous amount of freedom in how and what one chooses to learn. My major adjustment, then, is not how to turn Part III into an American system where one can pile on as many subjects as one can have forced into one’s brain… but rather to learn within the Cambridge system where there is time provided to do independent readings and explore interesting topics tangential to coursework.
That being said I am guilty of complaining about the pace of the physics courses. My director of studies was very amused that I showed up on the second day of class asking how I could make better use of my time. Because Part III is a one year program it’s not possible to run multiple tracks of courses at different levels, leaving the first term a bit slow.
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