Discrete Dynamics
Location
ENS 349
Start Date
10-7-2016 4:00 PM
End Date
10-7-2016 5:00 PM
Abstract
We will consider some examples of discrete dynamical systems: repeating a simple procedure over and over (function iteration). Can we predict the long-term behavior of the system? If our dynamical system is supposed to model some real-world situation, we would like it to be stable under small adjustments. Hence, it is natural to ask what effect the initial state may have on the outcome and if small changes in the iterative procedure itself will lead to radically different dynamics. We’ll talk about a still-unsolved problem in mathematics that a 4th grader can understand, how to draw a fern with a photocopier, the difficulty that undergrads (and their professor!) had in proving a simple statement about a boring card game, fractals in the complex plane, what mathematical chaos is about, working in four dimensions, and lessons for our faith when it comes to determinism, and even beauty in God’s mathematical universe.
About the Speaker
Phil Mummert grew up on a dairy farm in Chambersburg, Pennsylvania, and completed his bachelor’s degree in mathematics from Cedarville University in 2001. While at Cedarville, he traveled as a piano player with one of the precursors of HeartSong and also enjoyed singing in the Concert Chorale. Phil’s graduate school experience included a year at Cornell University prior to completing his PhD in mathematics from Purdue University in 2007. His dissertation was in the area of discrete dynamical systems in several complex variables. After seven years as a faculty member at Taylor University, Dr. Mummert returned to West Lafayette, Indiana, as an administrator and teacher in the Purdue math department. He is a member of the Mathematical Association of America’s Classroom Resource Materials editorial board, and his mathematical research interests have taken him to Canada, Sweden, and Korea.
Discrete Dynamics
ENS 349
We will consider some examples of discrete dynamical systems: repeating a simple procedure over and over (function iteration). Can we predict the long-term behavior of the system? If our dynamical system is supposed to model some real-world situation, we would like it to be stable under small adjustments. Hence, it is natural to ask what effect the initial state may have on the outcome and if small changes in the iterative procedure itself will lead to radically different dynamics. We’ll talk about a still-unsolved problem in mathematics that a 4th grader can understand, how to draw a fern with a photocopier, the difficulty that undergrads (and their professor!) had in proving a simple statement about a boring card game, fractals in the complex plane, what mathematical chaos is about, working in four dimensions, and lessons for our faith when it comes to determinism, and even beauty in God’s mathematical universe.
