Tuesday, November 28, 2006

Hello, hello!


I've not been as regular a poster as I c/should be lately! Yes, it's here, folks: that dreaded End o' the Semester Crunch. It's biting down hard on everybody, including yours truly. I didn't managed to finish quite as many of the tasks I'd hoped to cap off over the oh-so-short Thanksgiving Break we had last week, so this week's found me in the midst of a dizzying whirlwind of activity.

Strangely enough, though, things are starting to come together.

Linear-wise, we're a little over a week out from our Symposium. I've just made up flyers...ooo! That reminds me, I should post them on the website!

That's right, at 3:00 next Wednesday afternoon, we'll be gathering in Room 105 of Rhoades Hall to regale each other with traveler's tales of linear algebra applications to everything from wastewater management to computer graphics. I'm looking forward to it. Today alone I helped one group to use wavelets to generate computer music; another to come up with a reasonable model for their traffic transition matrix, given the observed data they'd gleaned from an hour's worth of counting cars in downtown Asheville (photos forthcoming!); and third to sort out a pretty complicated model for the flow of water through a conservation-conscious household. Busy day in Linearland.

Regarding the upcoming third exam, I floated the idea of an in-class exam, figuring that might help unburden these horrifically busy students a wee bit by freeing up some out-of-class time...but ALL but one person (and I've heard from well over half of the class) is looking for another take-home exam. I guess I'll get to work on that one!

What else? Hmmm...one stalwart and studious person showed up to last night's Problem Session, to match the one who showed up to the previous one, just prior to Thanksgiving Break. Not once have I been totally stood up! And tonight's session promises to be well-attended, I've already had several folks RSVP.

I'd best be off now, after this relatively short missive; there's a bit to be done before today's final Senior Seminar presentations, coming up in about half an hour!

Ta-ta for now...

Sunday, November 19, 2006

...Sunday night!

Well, it's over and done with.

The Harvard talk seemed to go over very well. It was an interested audience to which I spoke, a small group of preceptors and graduate students in the Harvard Department of Mathematics. They asked good questions, and they most definitely kept me on my toes.

After we got the ball rolling with the Markov Dance, I described the basic philosophy of the course, and then got into the nitty-gritty details of the way the course is put together. Much of the time we had a hearty dialogue going, in which we engaged in a discussion of the course and its design. They were really interested in finding out more about the team quizzes, the nature of the worksheets we work through, the source of our applications, the dynamics of the group work we've encountered, and how the size of the class has affected the way it's been run. I gave honest answers, often aided by the 11 pages of comments (from which I quoted heavily) you all gave me in your last journal entries. (Thank you all, thank you, thank you, thank you!)

I had a much-needed rest on Saturday, hanging out with Bedelia and her honey, Eugenia, and their beautiful daughter, Isadora. We hung out in their Somerville apartment, ate crepes, and joined them in a walk to the Cambridge Public Library. Good times!

I'm tired. Very tired.

I hope that all went well with all of you this week, and that you've had a chance to look over each others' preliminary reports before revamping them along lines penciled in lightly by your colleagues. We'll all be back together again tomorrow afternoon, when we'll consider Fibonacci-like applications that arose in my own research this past spring, and are arising again as a consequence of the conversations I had with my colleagues in Tennessee this past week.

To be continued!...

Friday, November 17, 2006

Live, from Harvard Square, it's...

Hey, folks!

It's been a busy few days, and I really am a little bit homesick and missing the green, green grass of UNCA as I pass the midpoint of my whirlwind tour of...well, two schools. I don't know how rock stars do it. (Anyone familiar with the song "Math Prof Rock Star," by Jim's Big Ego?)

I had a pleasant (however brief) stay in Murfreesboro, TN, where, on Wednesday last, I gave a research talk in graph theory to a crowd of folks from Middle Tennessee State University. I followed this talk with a very fruitful two-hour discussion with the couple of colleagues who'd invited me out to speak (props, Xavier! Thanks much, Caspar!). I look forward to working with them closely in the next few months.

Meanwhile, I'm sure you're all interested in knowing how the deal at Harvard is going. I haven't given my talk yet, but I had lunch with the principal pointy-heads, and they seem open to learning all about what we've been doing for the past several weeks. I'm going to open things up by asking them to do the Markov Dance; we'll see how well they perform those steps! From there we'll discuss the structure of the course, its planning, its successes and failures, its pitfalls and its triumphs. I'll be sure to post the PowerPoint slides on the course website when I get back (please remind me to do so if it slips my mind!).

I will also be sure to share your comments with them as well; I've created a digest of your feedback through the latest journal entry (the one asking, "whaddaya wanna say to this Harvard folks?") to share at relevant points in our discussion this afternoon.

Oh, and to those who had asked: yes, I have taken and will continue to take some pictures. I hate to disappoint you, Farina, but the folks up here in Cambridge don't look all that different from the faculty and students at UNCA.

Only, we're prettier!

On that note, I'll end for now. I'll try to post again this evening and let you know how things went.

Take care, and...oh!...have fun in class in a few minutes (those of you who are taking part in the optional peer review session)!

Thursday, November 09, 2006

It's that time again

Judging by my relative reticence lately, you've probably come to the correct conclusion that things have been


around here the past week or so. The next time I agree to give three talks in three weeks, please shoot me. Although I'm excited about my travels, I'm not looking forward to the busy-ness next week will bring (how do my soccer students do it?): Wednesday sees me heading out to Murfreesboro, Tennessee to give a research talk in the colloquium series at Middle Tennessee State University, and after driving home on Thursday morning, we find ourselves (me 'n' the missus) flying up to Boston on Thursday night so's I can hit the folks at Harvard with the 411 on how our class is run. Many thanks go to...oh, what name have I given you in past posts?...let's just say many thanks go to Bedelia, one of my bestest friends and my host while up in Cambridge.

I asked the 365 folks to use their most recent journal entries to let me know anything they'd like me to pass on to the Harvard audience, beginning with the prompt, "As you all know, I will be traveling to Boston in a week and a half to speak on the style of study we have undertaken in this class. Please include in your journals anything about this class (good, bad, ugly, or beautiful) you would like the folks up at Harvard to hear about." The responses have been, as far as I can tell, honest and heartfelt. It warms me to know that these hard-working people feel comfortable expressing not just the good but also the bad. I hope to put together a packet of all of their comments (unabridged, unexpurgated) to share with interested parties in Cambridge.

I've also decided how I'm going to begin my presentation at Harvard...but to make sure Bedelia doesn't spill the beans (she reads this blog semiregularly, I believe), I'm not going to say anything about it...

Meanwhile, the course moves onward apace. We've spent several classes now on eigenvalues and eigenvectors, since these are by far my favorite concepts in linear algebra, and, I believe, among the most useful. We've looked at eigenstuff from a number of points of view, including computational, geometric, and algebraic. We've looked at applications to win/loss records, traffic flow, crystal structure, and, most recently, heat flow. Tomorrow we'll work at diagonalizing a discrete time model for heat transfer in a one-dimensional rod. (Doncha wish you were in this class?)

On Monday I handed out the second take-home exam. I underwent a protracted internal deliberation regarding the format of this second exam, and though at one time I considered making this second exam in-class, when I found that the overwhelming portion of the class preferred to see another out-of-class exam, provided they were given a bit more time, I went with another take-home test. (I feel such tests are substantially more appropriate for our course, anyway.) I feel this exam is a good deal easier than the last in a number of ways: although it's probably longer than the first, it involves more straightforward computation, and is less "theoretical." Already I've noticed fewer tears (on the students' parts as well as my own) and less stress. I think we'll make it through this one okay.

Alas, I must now away and come up with some cool big numbers with which to entertain the Super Saturday kiddies this weekend as we learn to count to infinity...

Thursday, November 02, 2006


It's been a little while since I've posted, this week's been slamming.

I do have a lot to say, a lot I've been thinking about as my Hahvahd trip nears and I have to say something about IBL in the context of our 365 course. I want to write a bit more later in reflection on my goals for the course, and how well we're meeting them right now (in particular as regards the learning goals I'd set out in the syllabus).

I've still got some fun course materials to type up, though, so I'll be brief at present.

For the time being, I hope that the inventors won't mind me sharing with my readership the following linear algebra drinking game, made up this past weekend:

Equipment: TI-81-or-later calculators, one per person. Drink (non-alcoholic, of course!).

Object of game: players compete by constructing 6x6 matrices on their calculators, and then computing the determinants. The first to obtain a matrix with determinant lying between 10 and 20 takes a swig. Repeat as desired.

Change of Basis reminds you to drink responsibly.