The first days.

Monday morning (yesterday) at 8.30 am we had our first lecture, in Riemannian Geometry. The first part of our course is devoted to developing some concepts from Differential Geometry (which is my major field) so it hasn't been so challenging. :)

The thing about his lectures is that he keeps saying these things, which made me think that Riemannian Geometry (or rather Differential Geometry) isn't his actual field. His approach towards proving properties of curves, by finding a frame, was purely analytical and, for me quite strange, because it got rid of almost all geometrical interpretations whatsoever. Curves are not really that interesting to study anyway, but then he went on and said something about that the real point of Differential Geometry was to use the properties of the embedding functions, which is not true at all. From what I know (I don't know anything really about anything, ask me in 10 years and I'll say the same thing) the point of Differential Geometry is just to make way for the Riemannian Geometry (which works for an arbitrary number of dimensions) unless you are in fact interested in studying curves and surfaces in 3 dimensional spaces. The biggest point of Differential Geometry, I would say, is to find that several properties are independent of the embedding in space (the opposite of what he said), like the Gaussian Curvature, and it is in fact these ideas that gave Riemann the idea of developing a Differential Geometry for arbitrary spaces which are purely based on these intrinsic properties that are invariant of the embeddings.

The second lecture I had that day was in Noncommutative Geometry. We started by showing the correspondences between Noncommutative Algebra and Noncommutative Geometry, and then stated that the Noncommutative Geometry is really what justifies the Noncommutative Algebras. The professor is an expert in his field, and seems very intelligent. What is even more impressive is that he doesn't use lecture notes, instead gives theorems and proofs of very abstract concepts just out of his head. That is basicly the level of understanding that I one day hope to achieve.. Even though the course seems very good, it is 2 or 3 years above my level of understanding. But I'm reading a book right now, on Algebras and Categories which might give me the knowledge I need. :)

Since I got the chance of coming here and I really want to learn, I am also sitting and listening to another course, called "Noncommutative Algebraic Geometry" by a professor from Oxford. That course uses a more algebraic approach toward Noncommutative Geometry, and even if it is a bit over my head, like the other course, I'm hoping that some things might stuck, even if the whole picture will elude me for some time in the future.

After that, me and some friends went to Walmart and I bought some Coke to drink while studying and some Shower Gel. After that and after we ate in the cafeteria, I locked myself in my room and started to read some Abstract Algebra.

This morning I woke up, showered, had breakfast and then went to class. It is amazing how much fried food they seem to eat here. Every meal here since Sunday morning has had something fried, eg. Potatoes, Chips, Fries, something that looks like the Swedish "Rösti" etc. Fortunately it is somewhat like a buffet, so there are plenty of different kinds of things to eat, so I have been able to avoid the fried things. Another thing that I noted is that there are always sweets to have as dessert with the meals. I have been avoiding it so far, because that amount of sugar is just not good for you. And most people drink soda with their meals (sometimes I drink the diet Pepsi), but that has to give them a lot of extra sugar.. Well what can you say? North Americans...

Apart from my classes today I have mostly isolated myself in my room to read. I hang out with the people the minutes before and after the lectures and in the dining hall, but apart from that I try to study as much as possible, because well... In a month, I'll most likely never see most of them again, while my knowledge is forever (or until I get senile or die ;) ).