09-02-09 This blog may as well be called math and vegetarianism.

No pictures today. As a consolation prize, writing! (heh)

I have learned (and am learning) my lesson about starting the wash anytime anyone might be sleeping. I would probably stop it now if I was sure I knew how to do so. The washing machine in my apartment consists of a metal cylinder suspended in the square body such that its faces are perpendicular to the left and right sides. It then spins like you would spin if you were facing it as if to load and then did a summersault. There is a curved metal lid which fits onto an opening on this cylinder through which you load clothes. It is an interesting design, although it would seem to me that lifting wet clothes out of the water at any point must take a stronger motor than just rotating them in the water like ours do at home. (That is, like mine does at home, I guess the ones in the UPS dorm loaded through the face of a cylinder on its side.) There is a clothesline suspended in the bathroom for drying.

Today was an excellent day. I have the applications I need in motion at home, classes began, and I found my hat. (The hat I accidentally left in the desk of a lecture hall last week. I walked all the way to school on Saturday to retrieve it, only to find that the school was locked. The result of this little adventure, beside my frustration, is the picture of the school in the previous entry.)

I only had one class today. I do not really think I have a choice about taking advanced abstract algebra; any subject which gives me the capacity to pay attention to two forty five minutes of lecture separated by a ten minute break (the Hungarian standard) I simply should not pass up. It is going to be a challenge though. It was hard to gauge the class, because the material we covered today I had seen before. We’ll see.

We also had the Classical Algebra seminar, which is a three week course to ensure there are not certain holes in the education of students coming to the program. (That is, material a Hungarian college student would know, but most American college students don’t.) It is taught by an American professor who is here for the purpose. He is retired and likes the opportunity to hang out in Budapest. It is useful, but not nearly as interesting as the other class I attended today. Although, any class which does not give grades can not be particularly demanding.

I need to learn how to eat here. At UPS, I was always bad at breakfast. I compensated for this with bread and coffee, and always had a huge lunch at our vegetarian friendly cafeteria. Here, I still do not like breakfast but there is no easy lunch about. I definitely felt how much I had been neglecting my stomach when I left class at about 4:00. Thank you, leftovers.

Restaurants in Hungary, paired with the exchange rate, have been quite good. There is an excellent hummus bar, which will serve you a plate loaded with hummus and falafel for about four dollars. This was more than I could eat, even after not eating very much the day we went. There is also a vegetarian restaurant which is excellent. That meal, and leftovers which made another full dinner, cost about seven dollars.

I am getting to the point where my kitchen is stocked enough to cook. (This has taken about four grocery trips and a hundred or so dollars worth of food. At home, it would be fewer trips but twice the cost at least.) There are many pedestrians who carry groceries home on a regular basis, so there is a long line at the store right as businesses and schools close. The store itself closes at six, which is a bit of a pain sometimes. However, in the winter, it gets dark early and pedestrians, at least, do not want to be out.

Walking home from class and the store, just as the light was shifting was an excellent experience. Lighting determines the mood of a city. Seeing different streets with different light, culminating in a last glimpse behind the park on my walk home made me realize how much I am enjoying my time here. It is a subtlety beautiful city. I have my own place in it, and I am beginning to understand its relation to other places. I am starting to feel like I live in Budapest.

Math Fact of the Day: (anyone else excited? Save it for when I have too many and not too few; today was mostly review anyway.)

Let G be a group acting on a set A. Fix a \in A. We can use the orbit stabilizer lemma to determine the order of G in the following way.

1) Determine how many orbits of a there are.
2) Call the subgroup of G which stabilizes a G_a.
3) We know |G|=|O_a| |G_a|
4) Fix b \neq a in A. Determine the orbits of b in G_a
5) Call the subgroup of G_a which stabilizes b (G_a)_b
6) Then |G_a|=|O_b| ||(G_a)_b|

Repeat repeat…

(There is a bit of sloppiness going on with the naming of the orbits, but you get the idea.)

This is pretty intuitive, but it is a nifty way to determine the size of a group acting on a set. (graph automorphisms?!?)