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 Kr graph colored with 2 colors such that there must be a Kn of one color and Km 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.