Soggy in Milk

Are all undergraduate students flakes, or just the ones at my institution? Our final is tomorrow, and I've had several students make appointments with me over the last few days -- and show up 15-45 minutes late. Few things in the world irritate me more than missed appointments.

The Proof is in the Pudding

Doesn't that sound like an excuse that a grad student in mathematics might give his or her professor? "I don't have my homework today... the proof is in the pudding."

Finally, after a lot of effort, I proved (I think) that if integer matrices A and B satisfy A^2 = B^2 = -Id, then there is an integer matrix C such that CAC^-1 = B. We went over a similar procedure in class for rational matrices using Module Theory - make Q^2n into a Q[t]-module and jump through some hoops to decompose it as a product of Q[t] / (d1) x ... x Q[t] / (d2n) to come up with a nice basis for the transformation given by A (or B). Of course, the result follows for Q^2n using the Jordan Normal Form of a vector space endomorphism, but the point was we could get at it in a different and more general way using modules.

Meanwhile, preparation for the Algebra qualifier continues in earnest. It's amazing how instructive this preparation is - in looking at past qualifiers, I've run into a number of ideas and problems that I haven't necessarily had to deal with - such as solvable groups and diagram chasing - and so I've been able to expand my horizons as I also become more comfortable with useful tools I've seen before, such as the Sylow theorems and the minimal and characteristic polynomial of a matrix.

I've been thinking a bit today about hypergraphs and how various graph theoretic notions might generalize for them - but I'll post more later when it's percolated more.

Qual and Answer

My first qualifying exam is tomorrow! My chance to prove to the world - er, Northeastern - that I actually know Analysis. And I feel pretty good about it. I've been studying past qualifying exams for the past week with my officemate, Limin, and I've learned lots of little things that simply don't come up during the course itself. Some things I knew, but it didn't strike me how important they were - for instance, the fact that the Fundamental Theorem of Calculus requires that the integrand be continuous (this was inspired by a problem which asked for a function with a discontinuous derivative). At any rate, though I enjoy analysis somewhat, it'll be nice to file it away and focus on the subjects I care more about - primarily algebra and discrete math.

I'll leave you with a theorem whose proof I won't give here:

Euler's Metatheorem:
The concatenation of all of "Euler's Theorems" contains all of mathematics.

Current Events

Currently reading: Zen and the Art of Motorcycle Maintenance. I got this from paperbackswap a while ago and have been meaning to read it; now I've finally started and dug in about 100 pages so far. It's a bit of a head trip, and I'm looking forward to seeing where it'll take me.

Currently playing: Dragon Quest VIII for the PS2 (an excellent game for those of you who love old-school console RPGs); I've also recently started Dragon Quest V for the Super Nintendo (again) on my computer.

Currently playing: Also playing lots of board games. I got Nomeda the Swiss Map expansion for Ticket to Ride: Europe for Christmas, and she got me Bohnanza. Aside from that, we've also been digging into our game library and playing some of our other games while I'm on vacation.

Currently studying: Analysis and Algebra for the qualifying exams in January. I'm not too worried, but I'll still need to study - I've started looking at previous years' qualifying exams.

Currently planning on studying: Algebra 2, Topology 1, and a Graph Theory reading course in the Spring term. Algebra I expect will go quite well, and hopefully it won't be too difficult to keep up with 3 classes and my TA duties.

Currently located: At my in-laws' place for New Years. We'll be venturing out into the mall world this morning so that Nomeda can get a trim and we can have fun otherwise.

Happy New Year's everyone!

My coworkers are lamenting that I will be leaving at the end of July to go back to school and are (jokingly) trying to convince me that I want to stay. Here is an excerpt from my coworker's email to me the other day:

Don’t you know the saying,

Those who cant,

Teach

Those who cant teach teach Gym

Those who cant teach Gym spend endless hours explaining esoteric mathematical theorems to people who in the end are really only pretending to understand and are actually thinking about what they are going to have for dinner.

Fun with Lazorz

I discovered a fun puzzle thanks to puzzlinks.com: http://www.gamingdelight.com/games/laserlogic.php

Each round has a grid with some lasers and targets of various colors, and you have some mirrors, prisms, and filters at your disposal. The goal is to hit each target with the right color(s) of light. I'm currently on puzzle 16, and it's starting to get very interesting. Highly recommended!

Password Rant

Everywhere you go, you read articles about using strong passwords. Make them long; mix numbers, letters, and symbols; avoid dictionary words. I generally abide by this. I use a password scheme that's easy to remember and generates a strong password for each of my many many accounts (while keeping the passwords distinct enough that it's not a simple matter to crack my other passwords based on just one of them).

But sometimes, the website fights your attempt at creating strong passwords by not allowing you to use nonalphanumeric characters. This annoys the snot out of me. As a result, I need to have a slightly altered password scheme for those special sites that won't let me use esoteric characters such as the hypen. What is so hard about allowing symbols? I'm not asking for the ability to make my password šáüê♣τ - but come on people.