I've been in Ames, Iowa, for 2 weeks now, taking part in Iowa State University's Math Research Experience for Undergraduates (ISU Math REU) sponsored by the National Science Foundation. It's been great, quite relaxing and yet busy enough to keep my mind off the return from Budapest. It's a very different lifestyle from that of 2-3 weeks ago, though, and also different from my usual routine in Claremont.
My life is now occupied with: combinatorial matrix theory, running, lifting, frisbee, meals, doing things with REU friends.
Combinatorial matrix theory is an interesting subject. It's a cross between graph theory and linear algebra, but I've come to find out (to slight disappointment, after my great Graph Theory class in Budapest) that we're working mostly with linear algebra. I have one undergraduate partner, Sean, of Mary Washington College and Virginia, and together we work with our faculty mentor Leslie and grad students Rana and Olga. We meet as a group for about an hour each day, discussing what we've been working on and what to do next, and for the other 4-5 hours of the working day Sean and I work together in our office (yes, we have an office) on the problems posed for us.
This paragraph should be skipped unless you care about linear algebra. Maybe even if you do.
So here's what I've been working on: we represent a graph (vertices and edges) as a symmetric matrix, where if i and j are vertices, then there is a nonzero value at (i,j) and (j,i) in the matrix if and only if there is an edge between i and j in the graph. The specific problem we're working with is the "minimum rank" problem: if we can assign arbitrary nonzero values to these entries in the matrix, and any values to the diagonal entries, then what is the minimum rank (number of independent columns or rows) of the matrix? It's been solved for some graphs, like trees, complete graphs, paths, etc. So far, we have extended the result for trees to any field, have answered the question for cycles, and are working on showing that minimum rank = 2 => the graph is a path (the opposite implication is known to be true).
We already have about 4-5 pages of a paper that will be completed by the end of July, and we're planning on sending it to the Electronic Journal of Linear Algebra to be published, which is pretty exciting! We're quite a bit ahead of the other people in our REU group, and I feel quite comfortable with the pace at which we've been going through the material.
My other "job" this summer is to train for my last season of CMS cross country. I'm going for 650 miles again across the summer, like I did the past two years. Surprisingly, the running has been going very well despite 5 months in Budapest when I was running 1-2 times a week. I haven't gotten my average distance up to par yet (about 5-5.5 mi a day instead of my goal of 7) but my paces have been as fast as my runs at the end of last summer. Perhaps I can attribute this to my decrease in days of sleep deprivation while in Budapest (maybe 1 day a week instead of 3-5).
So yeah, running takes a lot of time and effort. But it feels great to be back into it, I almost feel like an athlete again. I've also been lifting at ISU's rec center 3 times a week, and playing a lot of Ultimate Frisbee and other games with my REU friends.
Speaking of which, I'm happy to say that my ISU Math REU group is really cool. There are about 12 of us, which (unlike the BSM group) is small enough that we can do a lot of things together: walking to class in the morning, going to lunch at an ISU dining option each day, playing Ultimate/basketball/volleyball, etc. Some of the highlights have been a day boating on Big Creek Lake last weekend organized by the REU mentors, and a potluck we organized among ourselves in our apartments on Friday (I made fajitas…mmm). Most nights, to stave off boredom, people have gotten together to go to a movie, toss the frisbee, play a computer game on the LAN (hopefully not the first step of getting re-addicted to Quake III Arena), etc.
Oh, I guess I forgot to mention…I got a new computer! It's a white MacBook, and I got it with a free iPod nano and free printer…gotta love Apple education rebates. With the great convenience of finally once again having a PC of my own, I've also resurrected the issues of having such a convenience…there are times when I'm staring at my screen, trying to find something to do, and I often boot up the internet browser, play a video/TV show, or start a game…not to mention that I check my email about 50 times a day. My mission this summer, in spite of the free time I have, is to turn these wasted moments into doing something more productive, namely, reading a book or thinking about math. It would be great for me to accomplish this, one and for all.
All right. That about wraps up the general description of my life here in exciting Ames. I'll try to keep further posts more specific, for interest's sake.
Hope that everyone who reads this is having an excellent summer so far!! I'd love to hear from anyone about what they're up to.
Basketball outside our apartment building
Most of the REU group at a late night party in our apartments
Hydro-biking on Big Creek Lake, with Mike (from Pomona!)
Informal Ultimate game that we organized vs. the Computational Chemistry and SPIRE (whatever that means) REU groups. They beat us 10-8, but we were down two players. Mathematicians rule.
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