Mathematical Content!

While looking into symmetric functions, I came across the Newton-Girard Formulas. That page references Raymond Séroul's "Programming for Mathematicians," which seems to be an incredible resource I will surely borrow from the library more often. However, the proof of these formulas (presented on pages 278-279) is incredibly beautiful.

First, start with a function f(T) = (1-X_1*T)(1-X_2*T)...(1-X_n^T). Now, differentiate in two ways: first by expanding out the polynomial and then differentiating, or by using the product rule directly. The second method results in a summation of functions that can be represented by formal power series. By using the fact that these formulas are equal, we subtract the functions and get that the coefficients of the resulting series are zero. Thus, the formulas are simultaneously proven without induction or any case garbage.

This will be a proof for me to write formally some time and memorize for later use. The technique is so wonderful, it makes me smile.

A Guided Tour

There were a few complaints that the new apartment pictures did not have any people in them, so I decided to fix that tonight. Here is your guided tour. You asked for it.

HI AND WELCOME TO MY APARTMENT! LET ME JUST WIPE MY FEET!

HAVE A SEAT IN OUR SPACIOUS LIVING ROOM WITH TWO FUTONS. CARE TO PLAY SOME VIDEO GAMES?

DON'T MIND ME. I JUST WANTED TO GET SOME AIR ON OUR PATIO! DON'T MAKE TOO MUCH NOISE OR YOU'LL WAKE THE DEAD PEOPLE!

LET ME COOK YOU SOME DINNER IN OUR KITCHEN! I HAVE A PAN!

WHAT A GREAT PLACE TO EAT SUCH A DELICOUS MEAL! YUM!

THIS IS WHERE I AM INCREDIBLY PRODUCTIVE! I NEVER GOOF AROUND ON A COMPUTER!

ALL THAT WORK ENTERTAINING YOU SURE GOT ME SWEATY! I HAVE TO TAKE A SHOWER IN OUR GUEST BATHROOM. THE WOMAN DOESN'T LIKE IT WHEN I STINK UP THE MASTER BATH!

GOODNIGHT! IT IS TIME FOR ME TO RETIRE IN THE GIGANTIC QUEEN SIZE BED WITH CUSTOM-MADE QUILT COVERS!

An Odd Location

Atlantic, Iowa is the least likely place I would expect a bunch of theoretical computer scientists to get together and talk shop, but it happened.

Tidbits on the Morning

This weekend, Katie is out of town. So, I have been staying in the new apartment, finishing some honey-dos and generally fixing what needs to be fixed. A big thanks to Joe for helping me install a rack above the washer.

This morning was way too early to be awake. The sun had not come up, and it is hard to maneuver in a dark place that has boxes and cables strewn about. I stepped on plenty on my way to the light switch.

The number 10 bus route got me to campus in a short, 7-minute ride. Perhaps there just are not enough people commuting at six thirty in the morning.

On the bus, I was reading "Graph Coloring and the Probabilistic Method" when a crucial sentence of a proof included the word "irregardless." This stopped me short and I was unable to finish the sentence by the time the bus got to my stop.

Soon, someone will pick me up so we can drive out to Atlantic, Iowa to talk with a bunch of nerdy people about complexity theory. This is a new thing for me, but it seems it could be fun. Today's topic involves computable analysis, but even though I have a full year of graduate analysis I need to look up some terms before I go. Hopefully, I won't be the only one who needs to play catch-up.

Apartment Pictures

Sorry for the delay. My previous batch of photos were out of focus due to me forgetting to switch the lens from manual to auto. Here are some pictures of our living room, dining room, kitchen, and a couple different views of the disaster that is our office. In one, you can see Katie's bike on the patio.

The Semester is Over

I have just finished grading calc finals, which means my first year in grad school is complete (outside of quals, which are really in the summer). However, I thought I would share some aggravating answers to what should have been a really easy problem.

Here's the setup: Vectors v and w are given, and they already calculated that they are orthogonal. The question is, does there exist a unit vector parallel to w that is perpendicular to v? If so, find it. If not, explain.

Answer: To find the vector, you need to multiply w by the reciprocal of the length of w. This is typical procedure. Since it has the same direction, it is also perpendicular to v.

Here are some "solutions"

• No, because you can't have it both ways. That is absurd.
• No, because you w is already perpendicular to v, so nothing else can be.
• No, because I'm just guessing and if I said "yes" [the professor] would want me to give some kind of bull**** explanation.

Transpositioned Mail

The Mathematical Association of America (MAA) sent out invitations to the graduate students to pay them for membership. The American Mathematical Society gives free memberships, why can't they! Clearly, it is because they need to increase their budget for data entry:

Either Our Apartment is Big, or I'm Suddenly a Midget

Katie and I have been busy filling our new apartment with all sorts of things. However, the place is very big and we are just starting our life together (also, we are waiting for all of you to buy things on our registry).

It turns out, this place is built for tall people. The cabinets go all the way to the ceiling, and the shower heads are six and a half feet off the ground. I was shocked to realize this morning that I did not have to bend my back to rinse my hair.

I hope to have pictures later today, but it is still a work in progress. The office is a disaster, and the bedroom is missing all the furniture except the bed. We have managed to hang some pictures, though. It certainly is beginning to feel like a home.

Note-Books

This year, I experimented with a new style of note taking. Some pads of graph paper were binded into books, and I have used them for notes in class all year. Now that the year is done, I re-bound these books and covered them with old jeans or khakis. Here are some pictures of the end result:




I like the results, and will plan to do this in the future. Now, my notes will sit upon my bookshelf instead of in a 3-ring binder or manila envelope like my old notes. These are compact and impossible to get out of order.

Proof that I am Psychic

As I prepared my breakfast this morning, I poured some juice and thought to myself, "I should make a GraphJam of `mind on my money and money on my mind' from the Gin & Juice song..."

However, I read that somebody beat me to it. Today.