# Spring 2013 Sessions

## Week 1 – January 22, 2013

Host: Dr. Maria Wesslén

Topic: Fun with Numbers

The first week of the semester we will tackle some number puzzles, riddles and more. I will try to prove that 1 = 0 …. Let’s see if you believe me!

## Week 2 – January 29, 2013

Host: Dr. Maria Wesslén

Topic: Commutative and Associative Operators

We will start with a seemingly simple problem, which turns out to be more difficult than you might think. This will lead to definitions of Commutative and Associative Operators and we will go from there to explore the background of abstract algebra.

## Week 3 – February 5, 2013

Host: Dr. Kristin Shaw

Topic: A Threesome of Triangles

Dr. Kristin Shaw will help us explore triangles in ways you never thought possible! Depending on the surface they are drawn on, some very interesting things can happen….

## Week 4 – February 12, 2013

Host: Dr. Maria Wesslén

A Mad Veterinarian has invented some very interesting machines which we will explore.

## Week 5 – February 19, 2013

Topic: The Pigeonhole Principle

Here is a problem for you to try:

Write 7 distinct integers on the board. Can you find a pair of numbers (among the 7 numbers) so that either their sum or their difference is divisible by 10?

Try this with other sets of 7 distinct integers. Try to find a set of 7 distinct integers so that none of their pair wise sums or differences is divisible by 10. Is this possible?

The famous Pigeonhole Principle will help us with this and many other problems.

## Week 6 – February 26, 2013

Host: Andrew Petersen

Topic: Fractals

We will go to the computer lab and do some programming to explore this fascinating topic. (We will still meet in the regular room at first.)

## Week 7 – March 5, 2013

Host: Dr. Gerhard Trippen

Topic: More Programming

This time we will try to program our way out of a very tricky situation, and attempt to beat the rest of the group in the process.

12 March is March Break, so there is no Math Circle this week.

## Week 8 – March 19, 2013

Host: Dr. Maria Wesslén

Topic: Inversion in the Plane

This is a method that can help solve geometric problems. Problems that may seem impossibly difficult at first, can become very simple after performing a geometric inversion.

## Week 9 – March 26, 2013

Host: Dr. Jaimal Thind

Topic: 50-50 odds and Permutations

People often like to say things along the lines of "Well, we're either gonna win the game, or we're not. So I'd say the odds are fifty-fifty." This is, of course, rarely the case. We will look at some problems and try to determine what the odds really are.

Consider the following problem. A plane has 100 seats and 100 passengers. They enter the plane, one-by-one, in order. The first passenger is lazy and selfish, and picks a random seat to sit in. The rest of the passengers try to sit in their assigned seats, but if they find another passenger there, they chose another seat at random. What are the odds that the last passenger sits in their assigned seat?

To solve this problem, we will introduce the idea of permutations. Along the way, we will learn some basic facts about permutations. (No prior knowledge of permutations will be assumed.)

## Week 10 – April 2, 2013

Host: Dr. Maria Wesslén

Topic: Games and Graphs