A Weekly Dose of Bollobás



A Weekly Dose of Bollobás: The Mathematics Directed Reading Program




Mathematics is taught in different ways. Some people prefer the large lecture format, others the small seminar, and still others that venerable Harvard institution, the long night alone with a textbook and a problem set. This year, while promoting all of these, the mathematics department is trying something different. I was privileged enough to secure a spot in their inaugural Directed Reading Program.

The DRP, as those in the know call it, works by pairing up a graduate student with an undergraduate. They then work together to read through an advanced textbook or set of papers, in preparation for an upcoming extravaganza in early December when the undergraduates will present for ten minutes each on what they have learned. Beyond that, there are neither rules nor regulations. My advisor and I meet for about an hour each week, having both read a chapter of Bollobás’s Modern Graph Theory; the other pairs are encouraged to meet once a week, but the time, duration, and topics are up to them.

For those wondering why I need a graduate student to help me through a textbook, math textbooks are different to those in other fields. More than any other academic discipline, mathematics prizes compactness and elegance over easy readability, to the point where it often takes professional mathematicians serious work with a pen and paper to figure out exactly what other professional mathematicians are writing about. This leads to esoteric notation and strange definitions (“collapsed adjacency matrix”, anyone?), as well as regular use of a large and complex mathematical canon of standard proofs, techniques, and theorems that we are mostly expected to either understand or look up on our own. In most subjects, understanding the context is necessary for understanding what the author was really trying to say; in mathematics, it’s necessary for understanding whether or not what the author wrote actually consists of valid sentences.

So far, the project seems to have been a qualified success. My supervisor and I are certainly enjoying the work, and there have been no emails from supervisor Dusty Grundmeier and the DRP team shutting the whole project down after a disaster of some sort. However, it has mostly failed to create any sort of wider DRP community. As part of the program, the mathematics department hosts periodic social events, in which people are supposed to get together and chat about life in general and their projects in particular; at the most recent one I attended, I was the only undergraduate. I certainly hope that this will change during the end-of-semester presentations, but for now the outlook in this direction does not seem good.

This is something of a shame, given the effort the department put into the idea. The committee found the money to buy every pair a copy of the book they planned to read, and recommended we pick a hardback for posterity. Modern Graph Theory has no hardback edition, and my supervisor probably needs our copy more than I do, so I may or may not get such a souvenir, but the thought is there. From my limited perspective, despite its issues, the DRP is a functional and interesting new way of teaching mathematics. British colleges already do something similar (at Cambridge, it’s called a supervision, at Oxford, a tutorial), and it is pleasing to see it make its way to the USA.


Michael Kielstra ’22 (pmkielstra@college.harvard.edu) doesn’t want to admit how much he could use more direction in his life.