July 5 2004
Great Day to say the least. Despite the early rising and silent marches today was very fun. Through the first two lectures no one really spoke. Other than me. Or maybe I just dont listen to others enough.
The food was not un-delicious, to say the least. The lectures were informative, I enjoyed them. The whole experience was made a lot easier by the ice-breaker activity. After that the whole evening livened up a lot. Definitely looking forward to the rest. I just realized it has only been one day. One very long day. That is all.
-Saurya

July 6 2004
8:35 AM- We presented the overhead from the previous night.
10:05 AM-After learning about quantifiersand reviewing some of our recently learned logic. We are given classwork.
11:45 AM-We find out what problem we have assigned for the next day we collaborate and work in groups.
1:15 PM-After a time at luch we have our photo taken for IDS.
3:00 PM-We learned about planes,graphs, and worked with proving graphs to be planar.
4:35 PM-We finish working on our group problems.
5:45 PM-Finish Piles of Tiles.
8:00 PM-Volleyball!
-George

July 7 2004
Today we learned about number systems and mathematical induction in our morning session. Induction is like toppling a stack of dominoes. First prove P(1) is true, and then prove that P(n) implies P(n+1). During the break, Professor O'Nan told us about rings and fields, which we will cover in two weeks as a small segment of number theory. I still havent solved Professor Rosenstein's problem, but I think I am close. After lunch, we continued with graph theory and elementary topology. The main topic was an informal proof of the Five Color Theorem using Kempe-chain argument.
Possibly the best part of the day was the TA panel discussion. The TAs and Mr.Tiberio talked about what motivated them to enter the field of mathematics,opportunities for careers and particular areas of interest. Scott, a math and philosophy major at Boston College, spoke about Godel's Incompleteness Theorem, which informally states that one cannot prove that the axioms of number theory are consistent. My friend and I had written a paper on math and philosophy, a large portion of which had focused on the theorem. Later, when Dhaval took us to the Computer lab, I found that Gerhard Genteen proved that transfinite induction could be used to prove the consistency of arithmetic. Although Godel's theorem applies to math, its philosophical equivalent is intriguing.
-Vikram

July 8 2004
We awoke in the early morning with exitement, this being the first barbecue and movie night. Breakfast as usual, and class was as usual also. Today was tedious: nine proofs by induction and binomial expansion, in the morning, and another afternoon dose of graph theory. Finally variety session with Chuck teacing us the many solutions to a problem pertaining to dividing a fixed number proportionally among groups of different size. Oh, and there was the bug that was eating the finfly on the hallway window that we saw during break.
What followed class was a disappointment, no barbecue, because of warnings of inclement weather. Then there was free time, which I spent back at the lounge with Jonathan and Vikram. The second game of scrabble we played was so hilarious, we had to photograph the board. Vikram has the details and we may post them here.
Finally there was the movie Bring it on Again. Stupid funny, in my opinion. Most of us watched. Some of us studied. A few played pool.
That's how we come to this hours, 11:49 at night. We've been back in our suites for about half an hour, after putting away everything in the lounge. Good night. Time to look forward to going home on friday.