In defence of the PhD prelim exam

In the department of Physics at McGill University, there are a few requirements for graduation in the PhD program. One of these requirements is to pass the preliminary examination, or prelim for short, at the end of the first year¹. This type of examination is becoming rarer across North America. The Physics department has been discussing the modernization of the prelim, either by changing its format or removing it entirely.

In this post, I want to explain what the prelim is and why I think its essence should be preserved.

What is the prelim?

The prelim in its pre-COVID-19 form is a 6h sit-down exam, split in two 3h sessions. It aims to test students’ mastery of Physics concepts at the undergraduate level. At McGill, there are four themes of questions:

1. Classical mechanics and special relativity;
2. Thermodynamics and statistical mechanics;
3. Electromagnetism;
4. Quantum mechanics.

The first 3h session is composed of 16 short questions, 10 of which must be answered. Some of the short questions are conceptual, while other involve a small calculations. Here is an example of a short question from the year I passed the prelim:

Imagine a planet being a long infinite solid cylinder of radius $R$ with a mass per unit length $\Lambda$. The matter is uniformly distributed over its radius. Find the potential and gravitational field everywhere, i.e. inside and outside the cylinder, and sketch the field lines.

The second 3h session is composed of 8 long questions, split evenly among the four themes. Four questions must be answered (no more!), with at least one question from each theme. Here is an example of a long question from the year I passed the prelim:

A simple 1-dimensional model for an ionic crystal (such as NaCl) consists of an array of $N$ point charges in a straight line, alternately $+e$ and $−e$ and each at a distance $a$ from its nearest neighbours. If $N$ is very large, find the potential energy of a charge in the middle of the row and of one at the end of the row in the form $\alpha e^2/(4\pi \epsilon_0 a)$.

I passed the prelim exam in 2018. For the curious, here are all the questions from that year: short (PDF) and long (PDF). The department of Physics also keeps a record of the prelim questions going back to 1996. Senior undergraduates are well-equipped to answer prelim questions. The difficulty comes from the breath of possible questions, as well as the time constraint.

A test of competence

Of course, the prelim is only one of the requirements on the way to earn a doctoral degree. Most importantly, PhD students need to write a dissertation and defend its content in front of a committee of experts. So why have the prelim at all?

The prelim serves as a way to ensure that all PhD students have a certain level of competence in all historical areas of Physics. Evaluating students for admission to the Physics department is inherently hard because it is difficult to compare academic records from different institutions across the world.

Earning a PhD makes you an expert in a narrow subject. Passing the prelim indicates that students have a baseline knowledge across all historical Physics disciplines.

Proposed alternative: the comprehensive examination

Not every department in the McGill Faculty of Science requires PhD students to pass a prelim exam. Another popular alternative, in use in the Chemistry department for example, is the so-called comprehensive examination².

The structure of the comprehensive exam varies across departments, but generally it involves the student writing a multi-page project proposal and defending this proposal in front of a committee of faculty members. In the course of the comprehensive exam, committee members may ask the student any question related to their research topic.

A comprehensive exam has two attractive attributes. First, its scope is closer to students’ area of research. Second, a large part of the comprehensive (the project proposal) can be done offline, without the pressure of being timed.

In defence of the prelim

The prelim is a stressful event. Not everyone is comfortable in a sit-down exam setting. A PhD career can end because someone slept poorly the night before the exam. I support any and all adjustments to the current prelim format to make the experience more accessible in this sense.

My main objection with replacing the prelim with something closer to the comprehensive exam is the functionalization of education. Removing the prelim eliminates the incentive to have a baseline knowledge across Physics. It encourages PhD students to have an even narrower set of skills, making the PhD program more focused around the resulting dissertation.

The comprehensive exam is inherently about making students’ experience more focused on their research area. This is appealing from students point-of-view: why should they have to go out of their way to stay aware about classical mechanics, something which they might never use? The comprehensive exam (in the format that I have described above) streamlines the requirements for graduation.

The graduate student experience is about much more than the resulting dissertation. We want our students to be more than just experts in their narrow fields; we also want them to be ready to contribute to society beyond their immediate expertise. Does the prelim ensure that this is the case? Of course not. But removing the prelim sends the wrong message about what it means to graduate with a PhD.

On a personal note, the prelim made me review all of my undergraduate studies. I purchased the Feynman Lectures on Physics and read all three volumes. With a Masters’ degree under my belt, I was able to appreciate my learnings under a new light, even though I haven’t used most of it since then. While I cannot say that the exam was fun, the studying experience was definitely one of the highlights of my PhD.