2016-17 August Immersion

Our summer immersion took place Friday, August 12, 8:30am-4:30pm.

2016-17 School-year Program

Tuesday & Saturday, September 20 & 24, 2016

Session Leader: Frank Sottile, Texas A&M
Title: Hyperbolic Footballs

Tuesday & Saturday, October 18 & 22, 2016

Title: I cannot tell a Fibonacci
Abstract: It is well known that rabbits multiply like rabbits. Australia struggled in the 20th century with how to reduce the rabbit population, but Leonardo Bonacci had already considered a different problem in the 13th century: how to *count* them. (This is the difference between applied and pure mathematics.) In this session, we'll discover how to predict, not just how many rabbits there will be 5, 10, or 15 years from now, but even 100, 1000, or 10000 years in the future. The numbers that arise in this way are called Fibonacci numbers, and we'll discover that the very same numbers, and interesting variants, arise in a variety of counting problems that seem to have nothing to do with rabbits, providing us an entree to some exciting algebra and number theory.
Resources

Tuesday & Saturday, November 15 & 19, 2016

Title: A pancake problem, of sorts
The head waiter at the Original Pancake House in Southfield likes to sort the pancakes in each stack (largest on the bottom to smallest on the top) before he delivers them to the hungry customers. This is a little tricky since the only way he can rearrange the pancakes is to stick a spatula somewhere in the stack and flip all of the pancakes above the spatula over, in one move, leaving the pancakes below the spatula alone. Using only this maneuver, can he sort any stack of pancakes? If yes, what is the minimum number of moves that will sort any stack of 10 pancakes? Any stack of 100 pancakes? Any stack of 1000 pancakes? Many mathematicians and computer scientists have worked on different versions of this problem over the past few decades. We will discuss some of the mathematics involved in sorting pancakes as we think about the waiter's problem.
(This MTC was directly inspired by the article "Flipping Pancakes" by Katie Haymaker in MTCircular, Winter/Spring 2016).

Tuesday & Saturday, January 17 & 21, 2017

Title: Stretching Fractions
We'll explore a simple "dynamical system", i.e. we will try to understand the behavior of a repeated process. The particular system we will focus on revolves around stretching and folding a piece of taffy. The participants will be responsible for generating questions, conjectures, and proofs, so who knows what we will learn!
Resources

Tuesday & Saturday, February 21 & 25, 2017

Title: Multiplying Numbers by Flute
We can multiply 8 by 4 to get 32 by counting factors of 2: three factors in 8 plus two factors in 4 gives five factors in 32. But how would we multiply 8 by 10? Hint: 8 * 1024 is close to 8 * 1000. And musical instruments can multiply this way automatically!
Partipants are encouraged to bring their own musical instruments (optional).