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
Topic: The Mad Veterinarian
A Mad Veterinarian has invented some very interesting machines which we will explore.
Week 5 – February 19, 2013
Host: Dr. Marina Tvalavadze
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
We will start with a two-player game which will lead to some interesting insights about graphs and graph theory.
Regular participants will also receive certificates for participating in Math Circles.