Saturday, September 27, 2008


Today the annual Great Eastern Endurance Run was held at Sherando Lake. In fact, it is still being held. With the 6am start time, and a 19 hour time limit for the 100k group, there are likely plenty of runners still out there. I only ran the 50k, so I (thankfully) have been done for a little while.

I've been signed up for this run since sometime in the summer, and it has been my primary training goal since then. What is surprising, to me anyway, is that I don't think I ran too many runs in all that time that were longer than 20 miles. I think no more than 5. I have, though, run every single day for the last 6 weeks (as long as my 2 mile run yesterday counts). I'd like to continue this streak, and run a little tomorrow, but I'm going to see how I feel.

This last week I've been eating lots of pasta, and the last two days several bagels. Yesterday I drank a whole lot of water, and some Gatorade. Also in this past week I watched 'Running on the Sun', a documentary about the Badwater 135 mile ulta-marathon. I think it was a good move (and movie), since it made me much less nervous about my own run. My run seemed entirely reasonable next to those guys.

All the same, last night I was reasonably nervous. It didn't help that it had been raining for two days, and the forecast called for more today. I also wasn't looking forward to the waking up at 3:30 part of the plan. Luckily I got to bed pretty early, and my cats actually let me sleep. At some point a thunderstorm woke me up, so I got to worry about running in one of those. The primary concern there being that the GEER run is out in, and on top of, some of the mountains near the Blue Ridge Parkway. On top of a mountain doesn't sound like the ideal place to be in a thunderstorm.

Waking up early gave me time for a bagel and a banana, and some water. A little after 4 I met with another runner (doing the half marathon) that I was carpooling with, and then we picked up a volunteer for the run on our way out of town. Around 5 we were down at the park, still earlier than many people, which meant we got a good parking space, and getting our packets wasn't too much of a hastle. A couple of trips to the bathroom, a pre-race briefing, and it was go time.

Of course, it was still pretty dark out. Most of the runners had headlamps, and I was running just carrying a flashlight. The first mile or so was on the road, so it wasn't too much of a problem. The next stretch was up a pretty steep trail, but even so, the light wasn't too much of an issue. I was running, at the time, with the one other guy I knew, and we were somewhere in the top 10. Which was a good plan, so we didn't have to worry too much about getting stuck behind people on the relatively narrow trail. Eventually the sun starting coming out, and we were on top of a ridge, running in the fog or clouds or whatever. It was quite nice.

The rest stops all had lots of goodies. I went through handfuls of gummi bears, as well as a few oreos and pretzels, and even a quartered boiled potato. The stops also had bananas, but also other candies, mini chocolate bars, and even twinkies at one point. I had brought along some Clif Shot Blocks, courtesy of my carpooling friend, 3 packets of Gu, and a powerbar. The Shot Blocks and Gu were a huge help, and I never needed the powerbar.

By mile 14 I had moved up to somewhere around 5th place. The way the course is setup, there are two places where you run out and then turn around, and run back. This gives you a good chance to see how many people are ahead of you (if you are keeping track), and gives some indication how far back you are. I was surprised that the first place runner didn't seem much further ahead.

Around mile 20 I took 4th place, and within another 2 miles had passed two more runners on a bit of an uphill. I was quite surprised by all of this, but it made me pretty excited. Surely the top 3 finishers get something cool! Of course, that left me looking over my shoulder for the remaining several miles. Generally in the runs I do I start off far enough back that I spend the entire time passing people, which is a great feeling. Running in the front, all you can do is get passed. That's not as fun.

All the same, I decided I was going to hold on to second place. That (along with all the gummi bears and other goodies) kept me pushing the remaining miles away. My legs had started hurting a bit, and I was worried that my right quad was going to cramp up. It was not appreciating uphills, but luckily the last 7 or so miles are primarily downhill or flat.

I had decided not to run with a watch. This was my first run at this distance, I just wanted to go out and enjoy myself and not stress about my time. At some point about half way through I caught a guy looking at his watch, and got the time from him. I felt a little bad interrupting his run, but it seemed to work out ok. When I'd been thinking about the run, I had hoped to finish in 6 hours. With the weather, I thought 7 might be more reasonable. In the end, I came in just under 5 hours, holding on to second place (just about 4 minutes behind first). Which felt amazing. I'm still pretty excited about it. I got not only a pretty cool jacket (even though it's got a big logo on the back), but also an additional running t-shirt (all runners got 1 for the event).

It's been about 7 hours since I finished running. My legs can definitely tell that they did something this morning, but I feel pretty good. This week one of my professors was talking about how when he goes running he goes for short, hard runs. He wants to get tired as quickly as possible. I told him I'd much rather go and run for a few hours and get tired that way. Today I realized that perhaps part of that is that with a nice long run, you still feel like you did something hours, or even days later. Sure, a half hour hard run will make you tired, but it's not the same tired. Either way though, as long as you enjoy it, that's what counts. Right?

Tuesday, September 23, 2008

Flatland, the Game

I was recently directed to the game here, and thought I'd forward it on to you, devoted reader. It's pretty entertaining, and a great way to think about dimensions. If you haven't read Flatland (wiki), you should probably get on that. After that, you can reward yourself by playing the game.

What happens in the game is two dimensional shapes (letters, numbers, etc) get sliced up into horizontal lines, and all you see is a movie of those horizontal lines. It is then your job to figure out what shape the came from. This is very much like the Sphere passing through the plane in Flatland.

Update 9/24: I was just reminded that Google recently did something where you can embed books. Flatland just happens to be one of them:

Hmm, I seem to not have it right. Suggestions anybody?

Saturday, September 20, 2008

News in Class

I was happy this week about the two new Mersenne primes being found/verified (mathworld). It gave me something outside or the usual calculus material to talk to my class about. Don't get me wrong, the calc is, of course, fascinating. But when you're in the midst of it, day in and day out, a change is welcome, I expect. I feel the same way about my research, incidentally. Looking at it on the broad scale, it's all interesting stuff. In the daily work, it's terribly frustrating. But I digress (seems to be what I do).

So to start class off Friday I mentioned the news. I asked if anybody had heard about it, and can't say I was particularly surprised that nobody had. I talked briefly about GIMPS and about the importance of primes in modern cryptography. I repeated the statements I'd seen in various blogs about the number of digits being vastly larger than the estimated number of atoms in the universe. The students seemed to be enjoying it, for which I was glad.

At some point, one of my students asked "What do you want to do when you grow up?" That may not be an exact quote, but that was the question. This still strikes me as fairly random for the conversation. I guess he was looking at the math I was talking about, perhaps wondering why anybody would care, and if that was the sort of thing I hoped to work on when I was done here. I had to answer honestly that I didn't quite know what I wanted to do, though I do enjoy teaching.

I'd like to continue bringing in math news items for my calc class. I feel fairly well connected online, so that if something I could share were to happen, I'd hear about it. But I'm trying to remember what the last similar sort of math news I could share would be, and it doesn't seem like the sort of thing that happens often. Anybody have any recommendations where I should be looking?

Saturday, September 6, 2008

Techniques of Integration

This semester I'm teaching Calc II from Stewart's text, Calculus. We start in chapter 7, which is about techniques of integration. One of my students made a very good observation early on in the process. We had already covered u-substitution and integration by parts, and were beginning trig integrals (integrating functions that are mostly build up from trig functions, products of sines and cosines and such). He realized that the 'technique' of the section was not, exactly, a new way to integrate. It was really just a way to re-write the integrand so that you could either apply u-substitution or parts. After pointing this out in class, I realized that he was correct, and that for our purposes, there really are only two techniques of integration - u-substitution and integration by parts. Everything past that is algebraic manipulations to change how the integrand 'looks'. That isn't to say the rest of it is easy. There are plenty of strange little tricks that pop up. Odd substitutions, or strange ways to split up the function.

I've made a point of trying to convince my class that they have to go home and do lots of integrals on their own. It won't matter how many examples I do in class (where the time is limited anyway, so we can't do too many). It is always easy to watch somebody doing math and think you understand, but then get completely stuck when you sit down to do similar problems yourself. Certainly there is value in doing examples in class. For example, trig substitutions are not something most people would be likely to come up with on their own. But after an example or two, the idea is something that can be readily used, and should be struggled with individually.

What I've been doing to present examples in class is to have the class guide me, as much as possible, through a problem. I put an integral up on the board and ask for ideas. We might go through a couple of failed u-substitutions or parts attempts before striking on the right way to proceed. But that's all part of the process, and it's good to see what happens when things don't work. After we get going, I try to get the students to tell me about each step. I hope that this keeps the class involved and focused on the problem. This means the examples take more time than if I was just presenting a quick path to the answer. So I'm, perhaps, not getting to as many examples as I could be, but I think I'm happy with how it's going so far.

We've still got partial fractions to go in the chapter. I think I'm happy with how the class is going so far, and hope that feeling continues.