B is for Breadth – or Burden?

In an earlier post, I mentioned two proposals from the departmental graduate committee and explained what I thought about the first one. The second one was discussed briefly at a faculty meeting last semester and tabled for now, but will likely be considered again in the future. The proposal is as follows:

We propose a 2-course (6-credit) ceiling on the number of “reading courses” that a student can count in the 30 credits for her/his degree. This change would encourage students to take regular lecture courses and thus gain breadth in their training. (There would be no limit on the number of reading courses a student could enrol in and enjoy. The proposal is simply that the student must present 24 or more credits earned through some other activity in order to earn an advanced degree. This change would be most relevant at the Master’s level, because we count credits earned in MSc studies toward the doctorate. So most doctoral students have completed most of the 30 credits they need before they even enter the PhD program.)

That last statement is a bit misleading. At the same faculty meeting, we were told that the department would aim to increase the number of candidates admitted directly to the Ph.D. program (skipping Master’s). The new rule would certainly affect them.

In my experience, most students want to take regularly scheduled courses. They enjoy the regular contact with faculty, the company of other students, and the feeling that they’re accomplishing something. That’s also what the students’ advisors want them to do. If that’s not enough, instructors do not get teaching credit for reading courses and will not offer one without a good reason.

Consider the following two scenarios. In each case, the student has just entered graduate school and has chosen a field of study, but her knowledge of that field is mostly limited to undergraduate material.

  1. The student takes several regularly scheduled courses in her field of study. She gets to know the faculty in this field and has frequent contact with them. She gains a reasonably broad and thorough knowledge of the area. She practices problem solving and gets feedback on her work from the instructors. Once she has acquired sufficient background in the area, her advisor suggests a research project.
  2. The student learns the basics of her field of study through reading courses. Her advisor has to meet with her frequently, once a week if possible, to suggest the literature, answer questions and check on her progress. These individual tutorials are in addition to his regular workload and he gets no teaching credit for them, so he can’t afford to see her more often than once a week. The student is largely on her own. Her command of the background will likely be a little bit erratic. Both she and her advisor may well be burned out before she even starts a thesis project.

Guess what. It’s not very often that either the student or the advisor would choose willingly the second option over the first one.

In reality, most of us are somewhere in between. That doesn’t mean, however, that both options are available equally to everybody.

If you’re a probabilist at UBC, the world is your oyster. There are several graduate courses in probability every year, sometimes as many as six if you include summer schools, ranging from the basics to advanced research topics. You never have to stray far from Option 1 if you don’t want to.

But if you’re an analyst at UBC, that’s a very different story. The basic courses in analysis are traditionally taught at a very low level. The material they cover is irrelevant to current research topics. There have been only 3 advanced courses since I was hired in 2000.

There will be a separate post sometime about this state of affairs. For now, I’d like to note a couple of consequences.

If you wish to supervise graduate students in analysis at UBC, it’s Option 2 most of the way. It’s a rather significant workload for both the student and the advisor before they even get around to talking about research.

But that’s just one part of the problem. If the student signs up for 2 basic courses in analysis (she may be familiar with much of this material already, but never mind), and if one advanced course will be offered in the 2 years in which the student is expected to complete her coursework, it only adds up to 9 credits. Assuming that the new initiative passes, she can earn no more than 6 credits for reading courses. That leaves 15 credits, or a year’s worth, of additional work that will not necessarily have anything to do with her research.

Should the student sign up for advanced courses in areas that she will not specialize in? Y’know, breadth and all that?

In my opinion – she shouldn’t have to.

A few graduate courses in related areas – such as PDE, differential geometry, number theory, combinatorics – can be interesting and useful to an analysis student. Most courses, however, are aimed specifically at students working in their subject areas. They’re much too specialized for the rest of us.

Which is how it should be.

I’m all in favour of a well-rounded general mathematical education at the Master’s level, or in the first year of the Ph.D. program for those students who skip Master’s. That can be done for example through a system of first-year “core” courses and comprehensive qualifying exams at a graduate level, especially if the latter are coordinated with the former. In terms of breadth, it works much better than forcing students to take research-level courses that they’re not interested in. It also forces all students to get a broader education, not only those in analysis or whichever other area happens to be underrepresented. Unfortunately, UBC Math took a pass there.

A Ph.D. program, however, is all about specialization. You focus on a specific area of research, study it in depth, commit months and eventually years of your time and effort to your chosen research problems, write a Ph.D. thesis. Actually, if you want to have a succesful career in research, you have to do more than that. Write several papers. Publish them in good journals. Expand gradually your range of specialization.

I’m sorry but that purpose is not being served when you continue to spend your time instead on coursework in unrelated areas.

The graduate committee’s main concern should be creating conditions where students are able to write and succesfully defend a Ph.D. thesis. As opposed to throwing obstacles in their way.

Bottom line? Most students should earn most of their credits for regularly scheduled courses, just like they do now, but there has to be room for exceptions. For example, when there is a shortage of appropriate courses in the student’s area, or when an international student comes from a country where the same material is already covered in undergraduate courses.

Independently of that, the department should take a good look at its course offerings and make sure that they are a little bit more evenly distributed across different fields. The graduate committee has in fact promised to do it; unfortunately, I’m less than confident about the results. The smaller groups – i.e. those of us who really have a problem – are not represented on the committee, and so far I don’t see the committee going out of its way to consult us. Let’s hope that they will.

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