We struggle, as a faculty, to come up with the best way of evaluating second-year graduate students as they make the transition into full-fledged researchers. They have to do two things: First, they must demonstrate a sufficiently broad and deep knowledge of the material they need to know to do research on their chosen problem. Second, they have to write and defend an intelligent research proposal, showing that they are familiar with the state of knowledge in their field, that they can identify an important problem, and that they can choose a logical approach to solving that problem; there must also be sufficient preliminary data to convince us that they can carry out the proposed research.
The real problem is the first part -- what, exactly, is "a sufficiently broad and deep knowledge of the material they need to know"? My students need to have strong backgrounds in biology and/or chemistry and/or physics and/or biochemistry and/or biophysics and/or computer programming and/or mathematics and/or ... Hell, they need to know everything I know, and everything I should know but don't!
The really hard part is testing the ability to think. The written qualifier isn't supposed to be a regurgitation, although it almost always contains huge doses of that. It's supposed to demonstrate the student's ability to apply what he/she knows to new problems. But it's really hard to design questions that test that.
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I remember my own written comprehensive exam. It ranged from overly simple to delightfully tough.
The overly simple part was a mechanics question that shouldn't have bothered an undergraduate: a bowling ball is launched with velocity v0 and without rolling, so it slides along the floor; after a while it is rolling without sliding. If there were no loss of kinetic energy due to friction, what would the final velocity be?
The delightful question was: Suppose the electron had spin 3/2. Discuss. (b) Suppose the electron had spin 1. Discuss. I loved this, because I could tackle anything from the structure of stars to the periodic table. I chose the latter and did pretty well, at least on part a. I blew the second part, because I forgot the difference between fermions and bosons. Shouldn't I have failed, just for that?
I had lunch with the usual crowd the day after the exam. John Merrill, a young assistant professor was always part of the group. When I commented that I loved the question, John admitted that he'd written it. I asked him what the answer was, and he said, "I have no idea. I'm looking forward to reading your answer and then trying to figure it out myself."
The exam took two days, if I remember correctly. When I got home after the second day and was relaxing and celebrating that it was over, Eric Jakobsson called me. "Congratulations!!" he said. When I protested that I'd barely finished the exam and didn't yet know the outcome, he said, "Regardless of whether you pass or fail, I'm congratulating you, because right now you know more physics than you ever have or ever will again!"
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