Graduate programs in physics (and other science and engineering disciplines) often have some kind of exam that students have to take on the path to doctoral candidacy. Every place is a bit different. When I was an undergrad there, Princeton had a two-tiered exam system, with "prelims" largely on advanced undergrad level material and "generals" on grad-course-level content. Rice has an oral candidacy exam with subfield-specific expectations laid out in our graduate handbook. Stanford, when I went there in fall of 1993, had a written "qual", two days, six hours each day, ostensibly on advanced undergrad level material.
There are a couple of main reasons for exams like this: (1) Assessment, so that students learn the areas where they need to improve their depth of knowledge; (2) Synthesis - there are very few times in your scientific career when you really have to sit down and look holistically at the discipline. Students really do learn in preparing for such exams.
I've written about this particular exam experience here. Thanks to an old friend whose handwriting decorates some of the pages, here (pdf) is a copy of that exam (without the solutions). Wow. Brings flashbacks.
I recall from your previous post about this exam that there was one particular question with a typo (omega where there should have been an omega_0), which Laughlin thought made the question impossible to solve, but which one Russian conformal field theorist said was indeed solvable, though difficult.
ReplyDeleteIs the typo in question on part #2 of the "Quantum Mechanics - II" section?
Yes. (Added bonus: the rocket equation in the first problem is also wrong.). RBL had a brief moment when he wasn’t sure if the problem was analytically solvable in closed form.
ReplyDeleteGotcha. By the way, for the QM1 question, part 1, were you expected to have a rough idea of the typical radius of the proton and neutron beforehand? Or was there some other way to estimate the characteristic proton-neutron binding distance?
ReplyDeletePPP, IIRC you can assume the proton and neutron are point particles. For order of magnitude, you can treat it as a particle-in-a-3d-box problem, box depth V0, and pick b so that what would be the first excited state has energy 0.
ReplyDeleteIt would not be unusual for each problem to have been crafted by a different member of the faculty (so that Laughlin did not personally have to do all the work of creating the entire exam by himself). I'm not sure if that's the way things were done at Stanford in 1993... but anyway, whichever professor wrote the pot roast question is a kindred spirit.
ReplyDeleteDan, I’d mentioned in my original anecdote about this - Laughlin had gotten annoyed and impatient with his faculty colleagues on the qual committee, and had decided to write most of the exam himself.
ReplyDeleteA follow-up: In the aftermath of this problem of multiple typographical mistakes on the exam, they decided to add a couple of students to the qual committee, whose job it was to check over the problems before the test to make sure it was do-able. I ended up in that role for two years.
You talk about how these high stakes exams help students learn while crash studying for them. But then you talk about "flashbacks" and being sent on wild goose chase on problems with typos, long calculations, etc.
ReplyDeleteSo which one is it?
I also had to pass a rigorous set of exams as a grad student and feel like I learned while studying for them. But I'm not sure I learned more than if that time had been used for more unstructured study. And I'm not sure if the trauma of high stakes exams is healthy for some students.
Grumpy, the two aspects (students learning while preparing for exams + exams serving some useful diagnostic purpose on the one hand; the exam being a stressful experience for the students on the other) are not necessarily mutually exclusive.
ReplyDeleteRegarding learning from unstructured studying: that might work well for some people, though educationally there is some virtue (I think) in fighting the usual doctoral tendency toward very narrow, specialized focus.
I agree that high stakes exams are not necessarily healthy. One reason why I like oral exams more than written quals: Oral exams at least resemble or mimic some aspect of real scientific discourse. In a professional scientific setting, I might actually have to respond to questions and do some calculations or estimates on-the-fly at a chalkboard, and communicate my thinking and the results to someone. In contrast, I've always found timed, closed-book exams to be very artificial instruments that may not be measuring what an evaluator would really want to know.
That was truly the Golden Age of Bob as a personality.
ReplyDeleteQuals for Nuclear Science and Engineering at Michigan in the 60s were 6 hrs of written and a 2hr oral. The challenging part of the written was determining which problem was contributed by Prof Chihiro Kikuchi (ruby maser developer). It would be something he was working on and he was looking for help. You obviously had to attempt it last.
ReplyDelete