## Saturday, June 07, 2008

### REU 2008 - Week 1

Don't expect an entry for every week of the REU but I figured that the first week was important enough to have its own.

When I first moved into my apartment I was pleasantly surprised by the size. My first impression was that it was way too small for four people to live comfortably. However, after spending some time here I quickly realized that I was mistaken. The roommates are pretty cool, well actually I have only met 2 of them, the last one will be arriving on Monday. The first one I met had just recently returned from Africa where he was helping install water filtration systems in a village. I don't remember the name of the country but it was a French speaking one. The other roommate is a year younger than me and it kind of shows in ways, mainly when we are working in groups (he is a member of my group in addition to being my roommate). The three of us that live here so far are all math majors and the one remaining roommate is an engineering major.

The research is going extremely well. At the beginning we would "play around" with the problems and find a solution. Then our mentors (I can't think of a better term for them, I guess advisers works but that makes it seem like we are PhD students) would present us with a paper which contained the result we had just discovered. You would think that this was disheartening but it actually was not. Having actually come to the conclusion ourselves made reading some of the proofs much easier since we had a better understanding of what they were doing and could relate some of their ideas to our own. However, we have so far have come across a result which we have not been able to find stated in any paper. I guess you could say we have our first theorem, and it's quite a wonderful feeling. We were surprised by the theorem actually. This is because based on the question we were answering one would expect the result to be complicated. However, it is quite the opposite. When we first saw it we were all skeptical and furiously searched for a counterexample but could not find one. After going through it again we were certain that it was correct. All that is left to do for this finding is to actually write up the proof of the theorem and the necessary lemmas.

Well I'll keep this one relatively short and end by saying that it seems like I will be going to the beach quite often (even though we have to climb over a "mountain" to get there). So far this week I have gone three different times.