The Life of a Mathematician

We left for the camping trip on Saturday morning. The drive up there went well; we only took a wrong turn and ended up in Utah once. It took a while to find an unclaimed campsite, but we got a good one. We set up some tents, went for a hike, came back and ate sandwiches, went for another hike, came back and ate stew, started a fire, and made smores.

I didn't borrow a sleeping bag from my dad because people had extras, but I realized that I should have borrowed a foam pad. Sleeping directly on the ground isn't the most comfortable thing in the world. Fortunately I was pretty tired and didn't notice that I was uncomfortable most of the time because I was asleep.

This morning we woke up to lots of rain. Getting the fire going was very challenging but we eventually succeeded. After eating breakfast burritos we broke camp and headed out. We got only a short distance before realizing that one of the cars had a flat tire. Furthermore, it had no spare. Furthermore, neither of the other two cars had compatible tires. Fortunately, there was a repair shop by the visitor center. The rest of the trip home was uneventful.

In other news, Friday's episode of Enterprise was awesome, especially if you know about the episodes of the original series that were alluded to.

I don't appear to have finished my combinatorics homework before noon.

Some of the guys from our college Bible study are going camping at City of Rocks this weekend. I wonder if I can get caught up in all my classes between now and then.

I visited my parents this weekend because my family was celebrating my grandmother's 70th birthday. I was also there for a breakfast Sunday morning, celebrating the church's 9th anniversary. And Saturday was my sister's cat's 4th birthday. So, lots of celebrations. Sunday afternoon we took a drive up into the hills and went for a walk up in the snow. Speaking of snow, it snowed here today. The weather is very unpredictable this time of year. Bible study at my apartment tonight. I'd better read the chapter before then.

Hey, guess what? Today is tax day.

My roommate just got an email from a guy he was at summer camp with, saying that he (the guy, not my roommate) is engaged. The girl that he's engaged to was in my graduating class. Small world, etc.

Okay, so I've kind of been ignoring this. Mostly because I've been doing lots of academics. Let's see if I can remember doing anything besides homework.

I gave the presentation. It went well. There was another student presentation yesterday and there's another one tomorrow. The one tomorrow is on symmetry groups of the icosohedron. I must remember to bring my model to class.

On Friday night we watched Return of the King, extended edition. I can understand why they cut out the final scene with Saruman -- it was long. I liked the Mouth of Sauron. Okay, so in the books he was the Voice of Sauron. But I think this one should be called the Mouth of Sauron. Or maybe just Teeth.

Last night we had a get-together with both the men's and women's Bible studies. We played a memory game called Four on the Couch. Trying to mentally keep track of everything reminded me of playing Clue.

After we got home, my roommate and I played a game of chess. He still hasn't beat me, even though the game lasted until about 22:10.

Problem 5 is done, but I've still got problems 6 and 7. I also need to write up an outline of my presentation for tomorrow.

I've figured out Problem 4 and am working on #5.

Okay, this is weird. Problem 3 on my algebra test has a hint that refers to some theorems from chapter 4. But the problem is identical to the first exercise in the book assigned for chapter 2. So it can be proven using much simpler theorems from that chapter. The proof is very easy, too. I think we even did that problem in a homework assignment last semester. So why is it on a test for this semester?

Okay, let's give this a try. For my representation theory class, I'm doing a presentation on a family of groups. For a positive integer n, the group T4n is defined by:

<a,b a^(2n) = 1, a^n = b^2, aba = b&gt

After playing around with this for a while, I found a convenient way to list the 4n elements for a given n:

1, a, a^2, a^3, ... , a^(2n-1), b, ab, (a^2)b, ... , (a^(2n-1))b

The next step was to find the conjugacy classes. It turns out there are n + 3 of them.

Two have just one element:

{1}, {a^n}

n-1 have two elements:

{a, a^(2n-1)}, {a^2, a^(2n-2)}, ... , {a^(n-1), a^(n+1)}

Two have n elements:

{(a^t)b t is even}, {(a^t)b t is odd}

From there I've managed to find all the one-dimensional representations (there are four of them for any given group), and I know that the remaining n-1 irreducible representations are all two-dimensional. I believe that I know what those representations are, but I haven't proved that they are irreducible yet.

Is there a way to use symbols like "<" and its counterpart without them disappearing?

Sunday School this morning was really interesting. Brad is gone, so he asked David to do a lesson on the history of church music. He had a bunch of CD's with him to give examples of things.

So Enterprise wasn't new like I thought it would be. We watched an episode of the original Star Trek series, Mirror, Mirror, and the second half of The Two Towers, extended edition. Next week we'll probably start Return of the King, which is the one I haven't seen.

The lecture on the Collatz Conjecture was excellent. And the notes are available at www.dougshaw.com/isu.

Only one student in the lab right now, and three tutors. Busy weekend coming up. I've got an Abstract Algebra test, a Representation Theory project, and I should probably be working on the Combinatorics homework. After work I'll go over to the guest lecture, and tonight is Enterprise of course.