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.
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.
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
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.
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.