Have fun and turn left (St. Mary's Feast)

(Results) Usually, when someone says "tank top" in a running context, they are wrong, and should be saying "singlet." In this race I had the unusual experience of the opposite: They advertised that you could choose between a race T-shirt and singlet, but in reality, it was unequivocally a tank top. Alan and I both chose the tank top option, and now we both look like matching hicks.

The race information was unclear on where to go to register for this race, so we followed the time-honored strategy of getting near the start and then looking for people in singlets. Without the nice man in the singlet, we never would have found it, because it was in the basement of a small building hidden behind lots of food vendors in the festival!

Funny things heard while sitting inside in the air conditioning before warming up:

"Do we have to put money down on this race?" It would be awesome if you could just ask them to deduct the entry fee from your future winnings. But no, you have to cover your bets in road racing.

"Do I have to put down my real age? I'm just going to subtract 10 years and be 43." And she did, too.

Anyway, the race. We lined up and the only runner I recognized was JoAnn. "Have fun and turn left," I joked to the woman next to me. "Oh, do we turn left?" she asked. I explained that in fact, the course did turn left, but it is usually a track racing joke.

The gun went off and she and I ran together. It soon became clear that this was a two-woman race for the win. We hit the mile in 6:05. I was breathing easily, but so was this other woman! Who was she? I became concerned that she might be this Irish Olympian from CT that I've seen in race results but never met. I asked the woman if she was from CT. Nope, from RI. Really, there is a woman in RI who can jog along at 6-minute pace and I don't know her? I was shocked.

(I asked because if she were the Irish Olympian, I might have slowed down and just raced for second place, because she would probably beat me anyway, and I wanted to conserve energy for the next morning's 5k, where more money was on the line.)

After about 1.5 miles, I detected a slight increase in her breathing: it was getting harder for her, but not for me (yet). So I took the opportunity to surge. I put a few meters between us, and also passed this guy who had been running right ahead of us. He and I went back and forth a few times, but in the race for first female, that was it. I didn't have a very big gap, but I did keep it for the rest of the race.

Lots of people were out on their steps, or lining the roads, cheering for us! That was nice. Some were even spraying the runners with their garden hoses. This race is called the Summer Sizzler, and for good reason; it is almost always over 90° (it is in the evening). We lucked out this year, as it was only in the mid-70s.

The spectators helped me, because I didn't want to look back to see where the closest female was (because that shows weakness), but I did want to know. So when a spectator cheered for me, I counted breaths until they cheered for the next runner. In the second half of the race, it was consistently 12-15 seconds. Of course, there was no way of knowing if the next runner was female or male. (It turns out it was a male, though the females were not far behind.)

After the race, I caught up with the second-place woman, Renae, and we exchanged contact info so we could run together sometime. New running buddy!

Alan also won his race, so at the awards we were both happy to win $150. I also got a gift certificate for a large pizza; he got one for a wash, cut and style at a hair salon. And they gave me a big bouquet of flowers:

My first time winning flowers in a race!

And then we went home to eat, sleep and recover for the next race, just 16 hours after the first.

Finished on the 50 (Harvard Pilgrim 10k at Patriot Place)

(Results) I had heard of this race for a few years (especially since two of my Williams teammates went 1-2 in it a few years ago), and I wanted to do it, but I didn't want to pay $50 for the privilege. Happily, I did a photo shoot for DMSE, and in return they gave me a free entry to any of their races, so I was able to do this one. (I would rather have done Mount Washington, but I was in Utah on race day.)

 The race was in the evening, so it was hot. Alan and I warmed up by running around the parking lots for the football stadium. There were about 7,000 people in the 10k and 5k races combined. I saw Bill Rogers on the starting line!

I also saw a BAA runner (Lisa) who I knew had run under 3:00 at the Providence Marathon, so I knew she was very fast. I figured she would be my main competition, and I was nervous. There was also a very skinny high school girl listening to music, but I was not concerned about her.

Rightly so. When the gun went off, the skinny high schooler sprinted to the lead -- of the entire race, ahead of everyone in both the 5k and 10k, including all the men. That didn't last very long. I passed her, and then waited for another woman to catch up to me. Where were they? I wondered. I didn't feel like I was going that fast.

A BAA guy passed me and I asked him where Lisa was. He told me she was planning to run 6:20 for the first mile. Just then, we hit the mile mark. 5:45! Hoo boy, that's a little quick. That's my cool evening track 10,000m pace, not my hot summer road 10k pace.

To make a long story short, that was it for the racing. I had maybe 20 seconds on the second female at that point, and I would extend it to about a minute by the end of the race, despite slowing down to a more reasonable pace. In the second mile, I passed a guy in red (Breno), and he immediately surged to pass me again, so I decided not to play that game, and instead just stuck behind him for the rest of the race. I was afraid that Lisa's race plan was some sort of cat-and-mouse deal where she would start slow and then chase me down (which is why I ended up with more than a minute lead; I didn't want to slow down too much just in case), but it didn't happen.

As we neared the stadium, I got a biker! This guy biked next to me and radioed back to the finish line about my number and what I was wearing. Also, I passed a guy, still on his way out of the stadium, who was walking with bare feet. Imagine paying an entry fee to walk a 10k barefoot on hot pavement! Not my idea of fun.

My idea of fun was to run into a dark, humid tunnel, and then emerge out of a giant helmet onto the football field.

I ran out of the big helmet!

I had this grand idea that when I emerged onto the field, there would be the 50-yard line and I would cross it -- you know, "Finish On The Fifty." But it was like a beach at high tide, people everywhere. The announcer pointed out that the first female had entered the stadium, and instinctively I put up my arm, to identify myself -- with the idea that anyone who paying attention to the announcer might need help trying to pick me out of the mob.

Only after I finished the race did I remember that no one really listens to the announcer, except to hear their own name. So the waving probably came off as self-promoting. But seriously, my cognition is severely impaired when I'm running (remember, I can't even subtract). I was just trying to help people.

Anyway, I finished! On the 50! And I ran 38:29. The last time I ran 10k on a hot day, I also ran 38:29, and it almost killed me. This time, I was just bopping along. I think that's a great sign!

Miss Massachusetts is holding the finish tape! 

Maybe a Patriots football player is holding the other end, but we'll never know for sure.

The post-race refreshments were good; I had a nice time talking with Lisa and Breno; I briefly met Dave McGillivray himself; and I was happily surprised to win a nice gift bag with socks, a hat, a shirt, an American flag, algae bits, $25 to the adjacent mall, and an overnight stay at the adjacent hotel!

Teaching the teachers

Last week, I taught at the Exeter math conference for high school teachers. The teachers come for a week and take two courses, which each meet for two hours per day, on subjects such as using technology in the classroom, creative ways to teach math, and learning new mathematics.

My courses fell into the latter category. I taught one section of the Exeter math curriculum course, which someone else designed years ago, and then I created my own course, "Greatest Hits of Higher Mathematics." It was the first time I'd ever created my own course, and it was quite successful. In this post, I'll reflect on things that went well and things I'd like to change for next year.

The goal of the course was to introduce the teachers (hereafter, "students") to the college math major or graduate school math curriculum: specifically, analysis, algebra, topology and number theory. I chose these topics because the first three are standard core curriculum, and number theory seemed like the most compelling other topic (rather than algebraic geometry, partial differential equations, etc.).

When I chose the course materials and the exercises to assign, I had no idea what the participants' level would be. I was afraid that they would not be able to understand the textbooks that I used as an undergraduate, because they would only have one night to read it, and concepts like an "open ball" took me weeks to fully understand. Thus, I paired each textbook reading with an essay by Stephen Strogatz, which presented similar material in a way aimed at the general public.

I structured each class so that we spent the first half going over the previous night's homework, then had a short break, and then had an introduction to the next topic. This way, they were introduced to the ideas before doing the reading on their own.

As it turned out, the participants were really sharp. (This is probably because of the selection bias for people who sign up for a course on higher mathematics.) They understood the textbook readings and delved into the homework problems. Because I didn't want them to have no idea how to do the homework, I had assigned mostly easy problems, even some that were just repetition of examples from the text, such as proving that the fourth root of 2 is irrational after seeing the proof for the square root. I wish I had assigned some that were more difficult, because they could totally have handled it.

Here are my reflections on the individual topics.

Real analysis: This went well. On the first day of class, I asked them to prove (as a group) that the square root of 2 is irrational. Most of them had seen the proof before, but all had forgotten the details, so this was a good exercise in constructing a proof, and also in having a group discussion. Then we talked about open and closed sets (as intervals on the real line). Is the union of two open sets always open? How about the intersection? How about for closed sets? Can the infinite intersection of a collection of open sets be closed? Can the infinite union of a collection of closed sets be open? They loved thinking about these problems and were very engaged.

The homework also consisted of compelling problems, including some that were too hard for them to do for homework. We spent most of the class period going over solutions, and by the end we were able to solve even the hardest one (my favorite concept, "dense"). That was a good class.

Topology: I had trouble finding a good book to use. Everything I found started by talking about sets. I wanted something that talked about shapes and fundamental groups. I ended up using just the first chapter of a book on intuitive topology, which had a series of exercises that were pictures of knotted-up shapes that asked students to figure out how to unknot them.

My goal for the topology section was for the students to learn to imagine the shapes in their head, and to not use any numbers, equations or writing. This was successful, and we again spent most of the class period working on the hardest exercise, this time in small groups. However, it took the groups a very long time to untangle the object, and I was afraid that it wasn't the best use of time. But I decided that as long as they were thinking hard about math, it was a fine use of time.

Next time, I think I would actually do point-set topology, defining a topology and talking about the topology of various spaces with their open sets defined in various ways. I actually think the students might prefer that.

Algebra: My preview for algebra was to define a group, and then give a proof that the identity is unique. I didn't even have to give it, as someone told me what to write as I was writing it. The book I chose ended up being perfect for this course, as it was full of interesting exercises that were easy to state. I only photocopied small sections of the book, but I should have copied more, as some of the exercises I didn't assign referred to sections I hadn't included, so the students couldn't try them (because, for instance, they didn't know the definition of U(12).)

We went over the homework exercises quickly, and then spent the rest of the class period working on more problems in small groups. Algebra really is fun, especially at the beginning. This topic went well.

Number Theory: This was the weakest topic. I was using a book that explained the major theorems well, but lacked compelling exercises. I recently heard someone say that the exercises you choose make the course, and that was definitely true here. The homework exercises were not proofs, just verifications like showing that a whole bunch of even numbers could indeed be written as the sum of two primes, so we went over the solutions quickly in class and then had 90 minutes left without much to do. I will definitely choose next year's book based on the exercises.

Choice topic: Since the four topics I chose just scratched the surface of higher mathematics, on the last day I asked each student to pick a topic in higher mathematics and then give a 10-minute presentation telling the class what it is about, and maybe doing an example of the sort of problem the field looks at. I brought lots of books, and the students borrowed them throughout the week. They were also welcome to use other resources like the Internet, of course.

My hope was that we would see presentations on things like knot theory, graph theory, the real analysis behind calculus, and point-set topology. In fact, the presentations were about the game Nim, RSA cryptography, the math behind the win/loss predictor in baseball, the Euclidean algorithm, and subgroups. They were getting tired and overworked by the end of the week, and in any case, the presentations were good.

I'm looking forward to offering this course again next year, and I hope people sign up!

Tri-color champion(ships)

(Results) On Sunday, the USATF New England outdoor track championships took place at Regis College. Let me just take this opportunity to opine that Regis College's track facility is extremely nice. There are signs telling you where to go, and the throwing area is on the far side of the track.

The only weird thing about it was that the steeple pit was just past the finish line, so they had to start the steeple 200m around the track from where it usually starts, and it ended at the 200m mark instead of at the finish line (so they were hand-timed). That's okay, though.

I wanted to run the 10k, because I wanted to be the New England 10k Champion. Unfortunately, no one else shared my sentiment, so it was cancelled a few days in advance (there were only two entrants, me and a guy, for this mixed race).

(I also wanted to run another track 10k. I consider the 10k to be my best event, so I am sad that there is only one track 10k per year that I can do. Perhaps next year I will fly to California.)

Luckily, I had also signed up for the 5k and the 3k. Onwards to the 5k. What with my altitude training and all, I thought I might be able to run under 17:00, so I got on the pace train with Kyle and her pace-setting fiancé. I valiantly ran 2k of the 5k at 17:00 pace, and then I fell off the train. Precipitously. 2k later, Aly passed me. Bye, Aly!

I managed to finish up the race with a surprisingly respectable time of 17:32. Crazy, to have such a bad day and still run 17:32. My 1600m times were something like 5:24, 5:40, 5:52. Not the best way to run a race, but hey! You can't run under 17:00 unless you run 2k under 6:48, and that I did.

Bronze medal!

Then I sat in my car for a while to get out of the sun. I emerged a few hours later for the all-important task of informing my teammates that we would be running the 4x400. (My attempt to field a 4x100 team was stymied by our only having two people present; the others were coming later.) Why? So that there would be more than one team in the race! It's just embarrassing to sit there and watch the GBTC slurp up 5 uncontested points.

Much less embarrassing, of course, to lead off the relay with a 70-second quarter and pass off the baton literally 50 meters behind the other team.

Silver medal!

That left the 3k as my last opportunity to become the New England Champion. The 3k started approximately 5 minutes after the conclusion of the 4x400. There were two entrants, myself and a high schooler. I unashamedly asked her what she was hoping to run (10:20). I told her I was trying to equal my 3k split from my 5k (10:18).

The starter stood about 10 feet away from us. When he fired the gun, I literally heard my left ear go quiet. It hurt. And the starter wasn't wearing ear protection. Even now, a few days later, my left ear hurts occasionally. That wasn't cool.

I fell in behind as we went through 200m in 40 seconds, just a bit fast. Then she started sprinting! She came through 400m in 78, me at 82. I was pretty confident that dropping me by 4 seconds in the first lap of the race was going to come back to bite her, so I continued with my race plan of running 82 seconds per lap. Honestly, my legs were totally tired and it was still pretty hard. I came through 1600m in 5:28, the product of four perfect 82s, and only two seconds behind.

Over the next 200m I caught up, and just tucked in behind and jogged. We ran that lap in 85. She slowly moved out, so she was running next to me, and then moved behind me, so I was in the lead without having to pass her. That was surprising. We ran another 85.

With 600 meters to go, my only goal was to be New England Champion. I suddenly realized that I had perfectly executed my strategy up to this point, but now I had no plan. Kick 600 meters out? Or wait? So I went with the old standby: Kick at the bell and then sprint all-out from 200 meters. And it worked. Whew. I was second-to-last, but it was enough.

Gold medal!

Someday, this meet will be well-attended, and then it will be more difficult to win. But as I like to say -- "the key to winning races is choosing your races wisely."