What is exactly the purpose of graduate course work ?
Post-graduate education, in just about every university system, places most of its emphasis on research over course work, for very good reasons. Much like knowing the recipe by heart does not make one able to cook a sophisticated dish, re-hashing for years textbook material and solving countless exercises of ungodly difficulty (physics graduate students reading this will immediately think of our nemesis) does not enable one to do science. The one and only way to learn how to do research, is doing research.
(The following discussion is centered on my own discipline, namely physics. I am curious to know whether some of it may apply, or have any relevance to other fields as well).
I myself did my undergraduate work in Italy and my PhD in the US, and favor graduate curricula in which the amount of required course work is minimum (as in, zero). My observation is that a) a solid undergraduate background is all that it takes for a motivated graduate student to plunge into research right away; b) the effectiveness of course work drops dramatically, as the material to be learned becomes more and more advanced.
This is very much the philosophy underlying most graduate education in Europe, where seldom are students required to take courses. Typically, the few that are taught are highly specialized, and students take them voluntarily (whether they actually learn anything by taking them, is a different story).
In the North American system on the other hand, a significant fraction of the total amount of time that a student spends in graduate school is devoted to course work, for the most part required. In some cases the requirement is explicit, in others indirectly enforced, through the administration of a comprehensive exam, for which students prepare by taking courses. This can occupy the better part of the first twelve to eighteen months, and is perhaps the main reason why the duration of the program of study is five years or more, significantly longer than for a graduate student based in Europe, for example.
But what is really the point of graduate course requirements ?
One of the “canonical” arguments invokes the (supposedly) higher level and greater rigor of undergraduate education overseas; graduate students in America need the course work in order to “catch up” with their European or Asian peers. I myself have long thought that that was the case, but after teaching first year graduate courses in North America for over a decade, to students from all over the world, I am not sure that I believe that anymore. My observation is that while, e.g., European undergraduate curricula may impart a stronger foundation in some of the more “formal” aspects (e.g., mathematics), in practice reasonably prepared American students perform equally well in graduate courses.
Moreover, it is my impression that the level at which required, foundation graduate courses are taught is often only slightly above that of the corresponding undergraduate ones , suggesting that the goal has tacitly become not that of enhancing, but rather filling gaps in one’s undergraduate background, by covering material that should have been learned at the undergraduate level but was not, for one reason or another (obviously to no fault of the students, who simply did what they were told to do).
But if graduate courses end up serving the purpose of “remedial study”, why not simply send those students whose background is somewhat deficient (as assessed by means of an entrance exam, for example), to take the undergraduate courses instead ? This would not only avoid duplication of teaching effort, pernicious at a time of stretched departmental resources, but also would spare graduate students whose background is adequate to sit through entire semesters of unneeded repetition.
Then there is the so-called “breadth” argument. This may not have the same emphasis in other fields, but in physics it has been traditionally felt that, while graduate students specialize in specific areas, the underlying intellectual unity of the discipline, and intrinsic interconnectedness of all subjects that it encompasses, demand that a physicist be a bit of a “renaissance man”, reasonably knowledgeable of current research themes and issues across different areas, and capable of relating to colleagues working in relatively distant sub-fields.
Now, in principle there is no argument, here. There is no question that possessing a broad background is a huge asset. After all, most physics graduates will eventually switch to a different subject than the one of their doctoral research, whether they continue in academia or move to industry. Moreover, being able to see the connections between subjects in seemingly unrelated areas, is often what allows a scientist to make progress on a specific problem, or think of a new one .
But when it comes to the actual implementation of this principle, by way of designing a graduate curriculum, seemingly insurmountable problems immediately arise. What is the core set of topics that every respectable physicist needs to know ? Can we get any two of us to agree on it ? I do not think so. If you are a physics faculty, postdoc or graduate student, try it for yourself and ask ten of your colleagues.
There is enough for a student to be taking courses forever, let alone two years. Classical Mechanics, Quantum Mechanics, Quantum Field Theory, Thermodynamics, Statistical Mechanics, Electrodynamics, Relativity, but also Non-linear Dynamics, Hydrodynamics, Numerical Analysis, Computational Physics, Condensed Matter Physics (both “hard” and “soft”, of course), Nuclear Physics, High Energy Physics, Biophysics, Astrophysics, Cosmology, Atomic and Molecular Physics, Chemical Physics, Optics, methods of Experimental Physics… where should the line be drawn ? Nobody can possibly be expected to know everything; but then, how does anyone go about picking any subject as being “more important” or “fundamental” than others ? Physics has become a very diverse discipline over the past two decades, and the notion that its practitioners can be broadly classified in few, rigidly defined categories is increasingly out of touch with reality [2,3].
Furthermore, is it really a useful intellectual exercise for anyone to sit through a series of lectures, work on some assignments, possibly get a grade, and then forget everything in a few months (as it invariably happens to all of us, if the subject is not one with which we practice regularly) ? To say nothing of the fact that, for such a course to be suitable for students with very diverse backgrounds, it likely means being taught at a very basic level, so that only the surface is skimmed.
The way I see things evolving, I believe that in the long run graduate courses will be elective only, and focus on topics of direct relevance to student research. The person in the best position to make a recommendation to a student, regarding courses to take (both to shore up a student’s shaky background, as well as to become familiar with the terminology and research issues in a given area of research), is the student’s major professor. This person was hired as a faculty precisely because (s)he is presumed to be able to make this type of determination, and should be trusted to be competent.
Ultimately, the goal of broadening one’s background rests with the person, and is very much an individual effort, that requires setting time aside to study. The duty of a department and/or graduate program is to offer students opportunities to hear about a lot of different topics, mostly through seminars and colloquia.
 Textbook comparison is quite telling. Consider, for instance, Quantum Mechanics. Widely adopted textbooks in North America are Shankar’s at the graduate level, and Griffith’s at the undergraduate one. While the first undoubtedly covers a wider range of topics, and in slightly greater depth, I think most colleagues of mine would agree that a student having gone through the second book knows all that (s)he needs to get started with research work. Conversations with colleagues have led me to believe that a similar argument can be made about Electricity and Magnetism as well.
 I confess to be jealous and in awe, when reading blogs such as Doug Natelson’s or Zapperz’, at the ability of their authors to stay abreast of developments in areas very different than theirs, speaking knowledgeably about topics that require a non-trivial amount of reading and thinking even on the part of specialists.
 If you think that there are a few subjects deemed “fundamental”, not renounceable (e.g., Quantum Mechanics) by simply every physicist, theorist or experimentalist, “pure” or “applied” (whatever that means), in condensed matter or particle physics… well, all I can say is — you are in for a big surprise.
 Naturally, there is much room for disagreement even on the content of the individual courses.