A Study of PhD completion rates in the Mathematical Sciences

When talented undergraduate students ponder graduate school, an important factor in their decision is the PhD completion rate of the program they are applying to. That is, in our definition, the percentage of graduate students who start a graduate program with the declared intention of earning a PhD, and some years later (typically 5 or 6 years), finish with a PhD. Low completion rates can occur when departments ask too much from their teaching fellows through onerous work loads, or when departments filter too much through difficult exams, or when advising and mentorship is poor. Of course it happens that graduate students declare their intentions for a PhD program, receive fellowships and support, yet quite happily leave after having earned an MA. This phenomenon, however, is common to all PhD programs, and we feel that when completion rates are low over many years, it shows that a department, at the very least, is not doing a good job choosing graduate students who fit the department's profile and ambitions

PhD completion rates are notoriously difficult to obtain, and when present, are frequently unreliable. There are data available at PhD.org, who, in turn, has obtained its data from the National Research Council's Survey. But the completion data refer only to one year (2005), and on close examination show many contradictions. For example, Colorado State's math department reports a completion rate within 6 years of over 60%, but also notes that the median time to completion 6.7 years, an obvious contradiction. In another example, the math department of Rutgers University is assigned a completion rate of only 36%, when our data show that the true completion rate is close to 80%.

We have collected data on PhD programs in the mathematical sciences from publications from the American Mathematical Society (AMS) over a period from 1991 to 2012 in an attempt to improve on these data*. It has to be said that these publications also exhibit contradictions and missing values, due to the self-reporting nature of the data collection. However, the fact that we have data spanning over 20 years allows us to impute values when they are missing, detect errors, and estimate with some confidence the true average completion rates, as well as trends in those rates.

When estimating the number of doctoral students we usually use, as proxy, the number of full-time funded students. Likewise, beginning doctoral students are usually identified with full-time funded first-year students. This identification is based on the fact that many, if not most, PhD-programs only fund students who are accepted into their doctoral program and are full-time. Conversely, the need for teaching assistants in mathematics is so great, that few PhD-students in the mathematical sciences need to fund their studies themselves.

There are exceptions, of course. Some programs, like Ohio State, do fund some students admitted to special Master's programs. In other programs, especially in statistics or applied mathematics, some PhD-students have external funding. Both exceptions can throw off our estimates by quite a bit. Please keep that in mind. Feedback from those who have more inside knowledge than us is always welcome.

*data compiled from the annual survey Assistantships and Graduate Fellowships in the Mathematical Sciences. (AMS) and Notices (AMS) (usually the February edition, supplemented by an August listing)

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This is rather time-consuming work, and since this is not our primary research, we are publishing our analysis case-by-case. If a visitor to this site is particularly interested in a program that is not yet analyzed, or thinks that some existing numbers are wrong, please drop us a note at klaus.volpert@villanova.edu and we will do our best to come up with an analysis within a short period of time. Otherwise we are adding our analyses as time allows.

On this page we list the names of the program, the overall completion rate based on 1994-2011, and a trend if discernible.