Tuesday, February 24, 2009


What can intermediate-level math students be expected to get out of a highly technical research seminar?

I'd talked up my out-of-town colleague Seymour's visit quite a bit over the past few days, to both students and colleagues, partly because I knew that if I didn't get the word out, Seymour might end up speaking to an embarrassingly small handful of our strongest students and most devoted faculty members. The last thing I wanted was for a friendly and devoted colleague to drive four and a half hours (both ways, in one day!) to give a talk to a pitiful few. I've given talks to such small groups, and I know how disappointing a small turnout can feel.

As it was eleven of our ever-stalwart students (including five from my Foundations course) came to Seymour's talk this afternoon, and several faculty members rounded the audience out.

As it was I ended up feeling bad not for Seymour, but rather for a few of my students whom I'd strongly encouraged to attend the talk, expecting that though they'd struggle to keep up they'd likely be able to grasp a good bit of the presentation. It turned out that I had a hard time keeping up with the bedazzling details, so I'm certain a number of the students were having a bear of a time.

Nevertheless, by the talk's close I remained convinced of the truth of what I'd told my 280 students in class yesterday: "even if you don't understand every twist and turn of every argument, going to seminar talks early and often prepares you well, as it exposes you to the language, the notation, the terminology, and the conventions of mathematical communication. The earlier you start going to math talks, the quicker they'll start to make sense to you, and the stronger a student you'll be."

To help students get the most out of the talk, I typed up and sent out a "companion piece" indicating to the students who attended what I thought were the important points to keep in mind about the presentation. Leaving aside the technical details of Seymour's highly convoluted argument, I encouraged students to stay focused on the talk's big picture and to try to understand

1. the ways in which Seymour's use of notation for operations in unfamiliar settings suggested analogous, more familiar, mathematical operations;

2. the culture of mathematics evident in Seymour's "humanizing" commentary during his talk, highlighting the importance of collaborative research and the ability to ask good questions as well as answer them; and

3. the mathematician's penchant for ranking, sorting, and ordering that formed the basis for much of Seymour's work.

Intermediate-level students hoping to hone their seminar-watching skills will do well to look for these general "trends" and meanwhile gloss over inconsequential details. Remember that no one should go into a talk expecting to understand every last jot and tittle of the presenter's argument; just because a theorem's proof involves computations you can't possibly understand, not being an expert in a particular field, doesn't mean you're barred from getting a lot out of the talk, provided you know how to take the talk in.

By the way, my thanks go, again, to Seymour, for his unselfish trek up to UNC Asheville this afternoon. I'd also like to give a shout-out to Tomassino, who complained that he hadn't been able to figure out his pseudonym on this here blog. (I've mentioned you before, man, although you'd have to search the blog to find out the context in which your name appeared.)

To be continued, I'm sure!

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