Paris!

Paris is such an incredible city! Todd and I have been walking around most of the city, and just taking in a lot of the sites. No matter where in Paris, there is always amazing buildings and beautiful scenery. We went to the Louvre and the Orsay museums, which were really cool. Although we didn't get too close to the Mona Lisa because it was so crowded, we got to see a lot of very famous artworks. The Orsay Museum was definitely my favorite, though. We also saw the eiffel tower and spent a lot of time underneath it. Its actually a lot bigger than I imagined, and every half hour they have a light show on the tower. I got a video of it, which I'll upload as soon as I can. Everyone in France has been really nice to us so far, also, despite the rumors that they're snobby and what-not. They are by far more helpful and courteous that the Italians I met in Rome.

I wish I could write more, but I'm almost out of time, and internet here is twice as expensive as in Rome. Leave it to the French to find a way to package the internet and make it more expensive. I'm going to spend new years under the eiffel tower, so expect some fun pictures. All for now, ciao!

Roma

Hey I've been in Rome for a couple days now. We saw a lot of the Roman ruins like the Forum and the Colloseum, and walked around much of the city. We're staying at a really cheap hostel by a fish market so it smells like old fish all the time. Im having a lot of fun, but this city is really expensive. Its almost impossible to find lunch for under 10 euros (which is like 15 USD), and dinner is much, much worse. Also, restaurants here charge for ridiculous things like bread, water, and sometimes even sitting down to eat. The food isn't as incredible as people make it to be, though. Definitely not 40 euros incredible, which is how much I spent on a pasta and a piece of chicken for dinner last night.

Im going to try to get on skype on christmas day, even though I dont know if any shops will be open, so leave your skypes on and Ill try to swing by to say "hi". Im using internet cafes right now, so internet time is pretty pricey.

I dont know if Ill be able to last through paris right now, which is going to be even more expensive. Hopefully Todd's friend comes through, and we can crash on his floor and save hostel fees. Otherwise, its going to be about 30 euros a night to stay in a cheap hostel on top of food and other touristy costs.

My favorite thing so far is the Italian people. They are absolutely hilarious--yelling out of cars, arguing in the streets and using very animated hand gestures. A lot of people here speak english, which is nice. Im going to check out the vatican today, probably since its almost xmas.

All for now, ciao

Leaving Tomorrow for Rome

I have my last final tomorrow morning. I think I've done pretty well so far, we'll see how the grades turn out. I know I got an A in algebra, which was my hardest class by far. But, I may have spent too much time on it, which could have caused my other grades to suffer. Anyway, this is my itinerary for the trip:

Rome, Paris, London, Amsterdam, Greece, Turkey, Israel, Egypt

After my final tomorrow, I'm packing up my computer. I don't know how much internet access I'll have while I'm traveling, but if I find some place, I'll drop a line to let you know I'm still alive.

Thanks for reading, I've had a fun semester!

Last Week

I haven't posted in a long time, sorry about that. It's dead week, which means that the semester is officially over one week from today. I'm excited for my trip, but I'm also going to miss my friends who are leaving for the states.

Europe is funny, because everything is so close. My friend Todd lives in Denmark right now, and even though he's countries away he doesn't feel distant at all. If I wanted to, I could buy a plane ticket for less than 100 dollars, and in a couple hours I could see him. On the other hand, the US is so big, that unless someone lives in a neighboring state, they might as well be on another planet. And I don't have a rocket ship. Not that I would know how to fly a rocket ship if I had one anyway. The point is, that I may never see a lot of these people again.

I haven't updated since before the putnam exam, so I haven't told anyone how I think I did. I'm pretty sure I got two problems correct, and part of another one. I'm pretty content with my performance for now, but I have big expectations for next year.

Also, my camera is broken. The flash stopped working, and it won't take pictures without the flash. So, I'm sorry for not uploading pictures.

I'm going to get back to preparing for finals, but I'll leave you with a little thing to think about. We proved this in Conjecture and Proof, and it's called the Banach-Tarski Paradox. It uses something called the "axiom of choice", and because its such a strange result, some people believe that the axiom of choice must not be assumed. Most mathematicians accept the axiom, though, but just think that this result just shows how funny math can be.

If you have a sphere, then it IS possible to turn it into two equal copies of itself (which doubles the volume).