A beautiful description of community

What I saw now was the community imperfect and irresolute but held together by the frayed and always fraying, incomplete and yet ever-holding bonds of the various sorts of affection. There had maybe never been anybody who had not been loved by somebody, who had been loved by somebody else, and so on and on. […] It was a community always disappointed in itself, disappointing its members, always trying to contain its divisions and gentle its meanness, always failing and yet always preserving a sort of will toward goodwill. I knew that, in the midst of all the ignorance and error, this was a membership; it was the membership of Port William and of no other place on earth. My vision gathered the community as it never has been and never will be gathered in this world of time, for the community must always be marred by members who are indifferent to it or against it, who are nonetheless its members and maybe nonetheless essential to it. And yet I saw them all as somehow perfected, beyond time, by one another’s love, compassion, and forgiveness, as it is said we may be perfected by grace.

-p. 205 of Jayber Crow, by Wendell Berry

Exam Results

Two Q’s.

I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!  I PASSED!

WHEEEEEEE!

Now I have to find an advisor/supervisory committee.

Brain-Fried

Well, quals are over for now. The analysis exam was 2:00-6:00PM on Monday and algebra was 2:00-6:00PM yesterday. I think I may not have failed them. I felt better about analysis than I thought I would, and worse about algebra than I thought I would (but only because I had higher expectations for algebra than I had for analysis). But for now, at least, they are past. I should find out by (roughly) the end of the month if I Q’ed them or not. If not, I’ll re-take whatever I didn’t Q in late January. We’ll just hope it doesn’t come to that. Then I get to start thinking about finding an advisor/taking comps next June.Either way, I get a few days off before starting a reading course on algebraic number theory this summer. Also, I will be TA’ing the algebra section of the 2008 IMMERSE program. I’m excited. It should be a great summer!

Chickens don’t clap

About a month ago, I started watching Arrested Development on Hulu.com. I don’t know why I didn’t watch it when it was on, but I’m glad I found it now. Anyway, I finished the show, and found this video yesterday, a compilation of the various Bluth family chicken dances. I love it.

A question

There will be a more substantive post on the goings-on in my life sometime next week, but for now I’ve got a question for the mathy types out there: Given any prime integer p, is p(p^6-1)/7 always an integer? I think the answer is yes, but I don’t know how to show it. Perhaps using finite fields?

  Edit: The answer is yes, and it follows immediately from Fermat’s Little Theorem. It was the punchline to the answer to the question: How many monic irreducible polynomials of degree 7 exist over the finite field with p elements, where p a prime is the characteristic of the field. The answer is p(p^6 – 1)/7.

A Day in Our Office

I was playing with Boinx iStopMotion the other day (which I got as part of the MacHeist 2 software bundle), and this was the result…. Notice how hard we work:

One semester in the books — Off to San Diego!

Well, the first semester of graduate school has come and gone, and I’m still alive to tell the tale. That’s a good sign. My finals week was actually all right, with the exception of the analysis final on Monday. It was awful. It did not go well for anyone, so there’s some solace in that. The thing I hate about analysis is that there can be such tricky problems; my inability to do well had nothing to do with my lack of knowledge, and everything to do well with the tricky kind of problems that he chose. Ah, well. It’s over.

The topology take-home exam was much better. It was difficult, and at times frustrating, but always interesting and occasionally fun. And the algebra exam yesterday was wonderful. It was only over ring theory, which is more my forte–just some basic questions on ideals and some on factorization. Gotta love it! So I think I destroyed that one.

And now I find myself on Christmas break. I am going to my mom’s in Sioux Falls on Sunday. I’ll be around there for a week or so…and then TCX, before heading out to San Diego for the Joint Meetings of the AMS/MAA on January 5. I’ll be there ’til the 9th, when I’ll fly back to Omaha and prepare for the semester. It will be grand.

The Mathletes’ Secret Weapon

No time for a real post right now, but I thought some of y’all would appreciate this. I’m playing on the math grad students co-ed rec flag football team (brilliantly named the Mathletes). We won our first game last night by forfeit, and so we had time for a practice. We designed four basic plays and practiced them several times. We gave them all names: 1, 2, 3, and 4. But someone had the brilliant idea to call them all at the line modulo 4. So it sounds like we’ve got 20 plays, but in fact there are only four.

The best was when we got to the line, Scott called 1, and then audibled to 5.

Math help

If only I could’ve done this on my algebra exam the other day…

Grad school thus far

Well, since Mini insists, I suppose I’ll spare time for an update.

Life in Lincoln has been OK, aside from the random old woman who ran a red light and hit my car last week as I was making a left turn.  The accident was completely her fault, and she acknowledged that, which helps, but doesn’t change the fact that I am currently missing a back bumper and will be without my car for three days next week as it is repaired. It has all contributed to a general feeling of stress, which, truth be told, I do not need more of.

I am now a Mac owner, too. I have been using a sweet black MacBook for a week, and I can’t understand why I never got a Mac before. It’s wonderful. I think Courtney is sick of hearing me gush about it, though. Can’t figure out why….

And now, onto what possibly only two of my readers care about: school. After thinking about it some more, I decided to go with the intro-level graduate algebra survey course (which uses the book by Dummit and Foote). I’m not completely sure I made the right decision in doing so, though. In general, I’m just really bored in the course, probably ’cause I had a great algebra prep at the U-dot (thanks, Jack!). Nevertheless, there are some things on the algebra qual syllabus that I haven’t seen, and it will be nice to be able to ease into graduate school this way, I think. So far, it’s the type of homework I can basically figure out in one setting (always with a problem or two thrown in there that’s just tricky). Analysis is just stupid. We constructed the real numbers in terms of decimal expansions…what the junk? It really was an example of the ugly side of math. Again, it’s been all review so far (and should be for most of the semester). Topology is the one normal course I’m taking that I have very little experience in (most of it came at IMMERSE, too). So far it’s going OK. About half of each of the first two assignments fell together nicely, and the other half presented more problems. But again, it’s wonderful to have other students to talk to to bounce ideas off and work through stickier situations with. The final course was actually just set today–it’s a reading course in commutative algebra and algebraic geometry, using “Introduction to Commutative Algebra and Algebraic Geometry” by Ernst Kunz. It will be neat to be pressing on in commutative algebra while I’m stuck re-learning what a permutation group is. All told, it’s eleven credit hours, and no teaching duties for the first year. School is stressful, for sure, but I’m surviving thus far.

I’ll see you all in five years.