Out of town

Hello, faithful CoB readers! I'm comin' to ya this morning from the raininess of Central Georgia, where I'm giving a colloquium talk at Clayton State University, invitation courtesy of my colleague LuAnn. Props, LuAnn! They've been exceptionally kind hosts so far, I've met her Chair, and even her Dean. I almost get the feeling I'm on an interview, I've met so many people. Very hospitable.

Right now I've got an hour or so to kill before my talk, so I thought I'd write a long-postponed update.

I spent several hours yesterday morning poring over the students' first preliminary reports on their research projects. By and large they're solid, and though some can stand a little improvement, all teams appear to be well on the way towards potentially strong final projects.

Today Beatrix is leading class (thanks again, Beatrix!), facilitating as timekeeper while the teams exchange their preliminary reports in order to get a few more sets of eyes to look them over. Once that's done and they've had a chance to absorb the comments I and their peers have left for them, they'll have the opportunity to rewrite and resubmit on Monday, if they so desire. I hope they so desire...not only because they're able to gain a better grade, but because they'll gain the experience stemming from going over their own work once more, with a slightly more critical gaze.

Monday brings Cramer's Rule, and Wednesday brings eigensystems. I've been looking forward to using that 'E' word since the beginning of the semester. I'm excited! It should prove a boon to all of the research teams: the traffic mappers and the Monopoly players can predict long-term behavior in their Markov chains, the rainwater harvesters can decouple any complicated systems of equations that pop up in the course of their analysis, the crystal gazers can determine the directions in which their units cells are perturbed from the norm, and so on. I hope I can help each team incorporate these new ideas into their respective programs.

Under the heading "upcoming events" falls the next exam, on deck for Monday, November 6th. The majority of people seem to favor another take-home exam, but I will give more time for it than was given for the last one, handing this one out on Monday and collecting it on Friday. I plan to have two problems, one of which involves a single overarching idea which will be divided into several stand-alone pieces, and failure to complete any one of them will not affect one's ability to complete the others. I'll let you know more about that once plans are solidified.

Looking back on this past week, I think we've had a strong one. (The week before last, maybe not so much.) On Monday came determinants in the form of cross products and parallelepipeds, and with them cane atomic radii. Wednesday was spent working through the determinant scorecard, a laundry list of determinants which demonstrated explicitly what happens when one modifies matrices in certain ways. The students seemed to like that one. A few said so, and told me that it made more sense to see it in concrete examples than to read through a bunch of notationally dense math that purports to say that row exchange results in a flip of the sign in the determinant. Well said, Studenten! Well met, well played, well well!

I talked for a bit with LuAnn this morning about her guided-discovery combinatorics class down here at CSU, and it sounds like she might be having some of the same ups and downs with her folks as I've had with my own. For her too is the uneasy feeling that comes from using a nontraditional method, the sense you're on a tightrope without a net as you toe-heel-toe-heel-toe-heel your way to the other side. Experiencing class the way we're doing it is something like taking turns driving while out on a family roadtrip across the country. Every now and then I need to take a nap and let the students take the wheel and the navigator's seat. I might doze, but the map's right there in the glovebox (does anyone still keep gloves in those?), if they need to use it. Unfortunately half of the time it looks like it's written in Hmong or Swahili. Nevertheless, the more one drives, the better one drives, and the more one's sense of direction improves. It's good for the mind, good for the soul.

I envy LuAnn's class here; she has only 7 students to my 31. That's not to say that I'd want to lose a single one of my students! But with that small of a class, I'd bet our linear course would be running much more smoothly. As it is, twists and turns aside, we're doing all right. I feel it's going very well for most of us, we're chugging along through the semester like a 300-pound linebacker who's just recovered the other team's fumble and is now on his way to the goal line. But I'm humble enough to admit that I'll do this faaaaaar better the next time I choose to use this style, and I sure as heck won't try it again with a class this size! To my students, yet again, my warmest and sincerest thanks for your hard work and patience as we all learn together. I look forward to working with many of you again next semester in MATH 280 and Number Theory! (And no, I won't be running those in the same way...look forward to my traditional nontraditionalness...those of you who've had me for other classes might know what to expect...)

Please treat Beatrix well today, and have a productive peer review session. Please do let me know how things go by commenting on this post. I'll be back on Monday, when I'll take the wheel again for a little while. Until then, drive safely!