Article By: Brian Pigott

Each year senior undergraduates in the Math Specialist program at the University of Toronto take a seminar course taught by a senior faculty member. A glance at the course calendar provides almost no information about the course, with the exception of the phrase “Student presentations will be required.”

During the 2009-2010 term, this course was taught by Professor P. Milman who took the presentations to a new level using a new Departmental Wiki page to showcase these innovations. When asked about the purpose of the course Professor Milman said “I wanted to force them to prepare good talks that the other students could absorb.”

Students were required to prepare notes on a topic approved by Professor Milman using Beamer, a LaTeX document class used for preparing slides for presentations. These slides would then be distributed to the audience to be used as an aid for following the seminar. Professor Milman reviewed the notes ahead of time to make sure they were succinctly brief so as not to be read like a book during presentations. This brevity meant that questions played an integral role in the seminars with Professor Milman assigning participation marks to the students based on their level of engagement in the presentations. “If you want to be a mathematician, you have to learn to ask questions,” he said.

The presentation topics themselves were diverse, covering major theorems from differential topology, algebraic geometry, resolution of singularities, and others. For many of the students, this was their first time reading research articles or advanced textbooks. From the perspective of the students, the workload was enormous. Will Pazner, a third-year undergraduate who was registered in the course, said, “I have never worked that hard on a single project before, especially leading up to the presentation date.”

That hard work paid out in the end, though. Janet Li, a fourth-year student in the course, said that she took away a confidence in her ability to prepare and deliver a good presentation. “(Professor) Milman’s dedication really motivated us,” she said. According to Paul Harrison, a fourth-year undergraduate, “It gave me a whole new appreciation for how much work the professors put into preparing lectures.”

Professor Milman put in his share of hours as well, from spending six hours on the phone on a Sunday with Janet Li, to what Will Pazner figured to be twenty hours in his office answering questions. Paul Harrison said that he felt more like a collaborator than a student with Professor Milman.

Altogether there were fifteen presentations given in the course, with one talk being given by a student who wasn’t officially part of the course but who wanted to participate nonetheless.

At the end of the course, each student received a gift from Professor Milman: a CD with a class photo, preliminary materials prepared by Professor Milman, and the slides from each of the presentations.

When asked what it was that he hoped students took away from the course, Professor Milman replied, “I wanted them to see mathematics as a whole (though none of the students chose a topic in analysis) and to experience at least some aspects of the working life of a mathematician.”

For more information or to see the slides from the presentations, please visit the official Wiki page for the course:
http://wiki.math.toronto.edu/TorontoMathWiki/index.php/2009-2010_MAT477_Seminar