__Week 1 __

__AM Mini-Course__: **General Mathematics
Background**

*Michael O'Nan, Rutgers University*

__PM Mini-Course__: **Graphs and Their
Applications**

*Deborah Bergstrand, Swarthmore College*

**Variety Sessions**

Monday - Recreation ID and Campus Tour

Tuesday - Ropes Course

Wednesday - "Piles of Tiles" by Joseph G. Rosenstein, Rutgers University

Thursday - "Careers in Mathematics" by Tony Chiappetta, Rutgers University
Career Services

**Evening Program**

Monday |
6:45 - 8:00 8:30 - 9:00 9:00 - 10:00 |
Open Recreation In-Hall Time to Unpack Community Standards, Ice Cream Social |

Tuesday |
6:30 - 8:00 8:00 - 10:00 |
Open Recreation Committee Meetings, Open Door Night |

Wednesday |
6:45 - 8:00 8:00 - 10:00 |
Open Recreation Board Games |

Thursday |
6:45 - 8:00 8:00 - 10:00 |
Open Recreation Movie Night |

*Monday, July 8
Day 1*

On our first day of math camp we arrived bright and early, ready and eager to learn discrete math. We walked to our first class at 8:45 to learn about logical connectives. After that, we went to lunch where many of us were pleasantly surprised by the cafeteria food. In the afternoon we started our mini-course on graph theory. After that session, we got a campus tour and a guidelines talk. Today was an overall excellent first day of the program.

*Tuesday, July 9
Day 2*

Today is the second day of math camp. After yesterday's self-introduction,
people are starting to know each other. Everyone is making friends quickly and
we are all impressed by the maturity level of all of our classmates. It's nice
to know there are people really like us in the world.

At morning, we had our breakfast. The meal was very good, there were lots of
combinations of food & fruit. After that, we had our morning lesson on basic
logic, and a bit of proving. Then, it's lunch, and the afternoon course: basic
concepts of graph theory. After that we had dinner.

If you read the schedule, then I bet you are wondering what is a "Ropes
Course". Well, it's a kind of mathematical problem in real life. Not just
math, also there is also science involved in it. Further, we had a committee
meeting, and an "Open Door Night", where one can go to others' suites
and chat with each other and play games

Oh, 11 o'clock already. OK, Lights out.

What a day!

*Wednesday, July 10
Day 3*

This is the third day we are here, but we already know each other pretty well. Today professor Rosenstein introduced the "piles of tiles" to us. He promised a $10 prize to the person who finds and explains the solution to this problem, so everyone wants to solve it. I doubt that everypone will get the answer, but if the prize was $100 or so, we would try harder to find the solution. In the evening we played board games. I won against Garrett in Monopoly, while other played the game of "Life."

*Thursday, July 11
Day 4*

Morning Class:

Professor O' Nan gave a lecture beginning with a solution to the one of the camp qualifying test questions about the number of queens necessary to attack an 6x6 chessboard. He showed that at most n-2 queens are necessary to an nxn board. Next he used the queens to attack certain rows and columns of the board, and then attacked the remaining squares diagonally. He used this method to show that 3 queens are sufficient to attack a 6x6 board, and 2 queens are insufficient. He also discussed factorials, Pascal's triangle, and binomial coefficients.

Afternoon Class:

Professor Bergstrand started the class by discussing the Art Gallery Theorem. This theorem answers the question of how many cameras are necessary to completely monitor a polygonal closed art gallery if the cameras are placed only at the art gallery. The theorem states that at most n/3 cameras are necessary where n is the number of vertices of the gallery. She proved it by triangulating the art gallery, coloring the vertices with three different colors, and placing cameras at the vertices of one color.

She also discussed Ramsey numbers. She asked, "Suppose you want to have a party where you are sure there are at least 3 people who are mutually acquainted or at least three people who are mutually strangers. She proceeded to prove 6 people are necessary. Next she discussed Ramsey numbers. These numbers are denoted r(x, y). r(x,y)=n, where Kn is the smallest K graph with the edges colored red or blue where there must be either a red Kx or a blue Ky.

Variety Session:

Tony Chiappetta discussed various careers in mathematics, and described the career services program, a program at most colleges that help students make decisions about their careers.

Evening:

The evening began with a barbeque outside the athletics center, followed by games of football and volleyball. Later in the evening, we watched the movie "A Beautiful Mind."

*Friday, July 12
Day 5*

In our morning class today, we had the first round of the Tour d' Euler, a
competition between our four teams to answer math questions as quickly as possible.
In our afternoon class Professor Bergstrand taught us about Eulerian, Hamilton,
directed, and pseudo graphs. (Very Interesting!) Afterwards we all said our
goodbyes and left for home for the weekend.