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Bhaskar Krishnamachari |
At USC, I lead a group of Ph.D. students and researchers exploring a wide range of topics related to next-generation wireless networks.
To stay abreast of the rapidly evolving literature, my group often meets together to read recent technical papers. Typically, none of us have read the material before. We take turns reading a few paragraphs each, stopping periodically to make sure we all fully understand what we have encountered (the description of an algorithm, say, or steps in some mathematical derivation). Whenever someone is puzzled, he or she asks a question. We stop the reading and discuss. The more of us there are in the room, the sooner we figure out the answer. These sessions are always a pleasurable and rewarding experience, and help us bond with each other.
One evening, a few years into my time here, a Ph.D. student remarked after one of our sessions, with a sigh, “I wish my classes were more like this!”
Inspired by his comment, the very next spring, I decided to try out a somewhat more informal approach to teaching. The course was about mathematical techniques for optimization in communication networks. There were a little over a dozen graduate students. We met for about three hours each week. I asked for and got a relatively small room where we could all sit in a circle around a table.
At the beginning of each class, I would present a short tutorial covering requisite mathematical background: how to solve constrained optimization problems in closed form via linear programming, or using convex optimization and Lagrange duality.
For the remainder of the class, we would read aloud in turns a research paper which applied the corresponding mathematical theory to solve an important resource allocation problem in communication networks.
While we read, the students frequently interjected with questions and comments, to clarify doubts, establish connections between the background material and the paper, criticize assumptions, and identify new research problems. I took part eagerly in these exchanges, but not as an authoritative know-it-all. I made it clear to the students that I too was approaching many of these papers with fresh eyes.
By purposely under-preparing in not reading all the papers and in not anticipating their questions in advance, I made myself vulnerable. I do not doubt that my own questions and tentative comments exposed my ignorance from time to time. But whatever I lost in pride, I more than gained back in a closer connection to the students, because this allowed me to have a greater appreciation for the uncertainties and doubts that they were experiencing. And they, in turn, gained a greater degree of freedom and confidence to express their own thoughts and views.
The course got perfect evaluation scores from every student. A couple of the independent projects that students in the class worked on resulted in published papers of their own; several noted in their evaluations or told me in person later that it was one of the best courses they ever took. I myself had never enjoyed teaching a course this much before.
There were many reasons why this course went so well, including the small number of students, the balanced mix of theory and applications, a particularly motivated and articulate set of students, a diverse and interesting selection of material, and the outstanding teaching assistant I had that semester. But I am certain that the biggest factor was the fact that we were, in a very real sense, learning together.
I have warm memories of us all huddled closely around the table in that cozy little room each week, immersed in reading and engaged in passionate conversations late into the spring evenings.
Bhaskar Krishnamachari
Associate Professor and Ming Hsieh Faculty Fellow
Associate Chair, Electrical Engineering-Systems
