__Week 2 __

__AM Mini-Course__: **Combinatorics**

*Jenny McNulty, University of Montana*

__PM Mini-Course__: **Algorithms in
Graph Theory**

*Evan Wantland, Pacific University*

**Variety Sessions**

Monday - TA Panel Discussion

Tuesday - "Apportionment" by Chuck Tiberio

Wednesday - MSLC Tour

Thursday - "Who's a Monkey's Uncle? An Introduction to
Computational Biology" by L. Charles (Chuck) Biehl

**Evening Program**

Monday |
6:45 - 8:00 8:00 - 10:00 |
Open Rec Committee Meetings |

Tuesday |
6:45 - 8:00 8:00 - 10:00 |
Open Rec Bridge Project |

Wednesday |
6:45 - 8:00 8:00 - 10:00 |
Open Rec Serin Observatory |

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

*Monday, July 15
Day 6*

Today was the first day of the second week. We arrived bright and early for the first day of combinatorics. After the morning session we headed off to lunch where the food quality stayed better than anticipated. After lunch it was time for cards and frisbee, then our first session of algorithms in graph theory. Our first lesson was that algorithms are named after an Arabian mathematician whose name we cannot pronounce nor spell. Finally, we went off to dinner, and later had a lively game of volleyball and rec time in the dorms.

*Tuesday, July 16
Day 7*

Man, time flys
by. It's the 2nd week already.

Tuesday
morning is always the same: breakfast, then the morning course with
combinatorics - a fancy word for counting, but with a whole lot more in it. Then
we had lunch, and after
that, we continued with algorithms in graph theory.

Later, we had open
rec and played soccer. The bridge project went well for all of us in the
evening. The scholars split into teams that made their own bridges, and they
came out well.

*Wednesday, July 17
Day 8*

Today was no ordinary day. Instead of doing an extra hour of math, we got a chance to go to Rutgers’ Serin Observatory and see the Moon up close. Before that, we saw liquid nitrogen at 77K (-195°C). The nitrogen froze a rubber tube so that it was easily broken by a hammer. Since it was not dark outside, we couldn’t go on to the observatory for another hour, so the professor that showed us liquid nitrogen gave us a long talk about stars (only Chintan and Garrett seemed to be interested in the speech, while others couldn’t wait till it gets dark enough). Finally, we got upstairs and saw the Moon and Venus through a powerful telescope.

*Thursday, July 18
Day 9*

Morning Class:

Professor McNulty started her lecture with the Pigeonhole
Principle, a simple principle that states the minimum number of pigeons in a
pigeonhole for a given number of pigeons and holes. She continued with the Ramsey Numbers, numbers that give the
minimum K_{r} graph colored with 2 colors such that there must be a K_{n}
of one color and K_{m} of another color. She ended with Schur’s Theorem, which states that if the
natural numbers a colored with any number of colors, there must be 2 numbers of
the same color such that their sum is the same color.

Afternoon Class:

Professor Wantland discussed capacitated networks and flows. Capacitated networks are weighted digraphs similar to a network of one-way pipes each with a certain capacity. A flow is a set of nonnegative numbers for each arc or pipe representing the flow through that pipe such that each number is less than the capacity of the pipe. He then gave an algorithm to find the maximum flow.

Variety Session:

L. Charles Biehl gave a lecture entitled “Who’s A
Monkey’s Uncle” about computational biology.
He discussed how to organize species into evolutionary trees by
characteristics and the how there are many different ways to do so. At the end he gave us four species to organize into an
evolutionary tree and draw their common ancestors.

Evening:

About half of us gathered in Dmitriy’s room to watch * The
Matrix*.

*Friday, July 19
Day 10*

Friday at last! Breakfast as usual, then off to our last combinatorics class. We enjoyed a discussion about Fibonacci and triangular numbers, but the real excitement came when we got to play with blocks to prove some of these numbers’ properties. Then, in the afternoon class, we learned briefly about how a computer handles arithmetic. Then we heard Dr. Wantland’s story about how he solved a tricky math problem, and pushed Professor McNulty (our combinatorics instructor) out of a raft. After that we said our goodbyes once again we are looking forward to a restful weekend.