Abstract: We will introduce the concept of a random walk, and we will incorporate some ideas from linear algebra, probability theory, and group theory to analyze a few simple random walks. The talk will be accessible to all undergraduates, especially those who have taken a linear algebra course.
Monochromatic Solutions of Linear Equations
Speaker: Mitchel T. Keller (Washington & Lee University) — Pi Mu Epsilon Induction
March 24, 2016 at 3:35 pm in Robinson Hall 105
Followed by refreshments in Robinson Hall foyer
Abstract: A coloring of the positive integers is a function f from the positive integers to some finite set of colors. For example, if the set of colors is {red, green, blue}, we might say that 1 is colored red, 2 is colored blue, 3 is colored blue, 4 is colored blue, ..., 8 is colored green, 9 is colored blue, 10 is colored red, and so on. Given a linear equation with integer coefficients, say x + y - z = 0 or x + y - 3z = 0, a monochromatic solution is a solution to the equation in which all of the values are the same color. For example, although 1 + 2 - 3 = 0,(1,2,3) is not a monochromatic solution to x + y - z = 0 in our coloring above, since we have 1 colored red and 2 colored blue. However, (3,9,4) is a monochromatic solution to x + y - 3z = 0, since 3, 4, and 9 are all colored blue and 3 + 9 - 3(4) = 0. In this talk, we will explore some classical results that help us identify which linear equations with integer coefficients must have a monochromatic solution in every coloring of the positive integers.
Fall 2015
What I Did Last Summer (Parents and Family Weekend Event)
Speakers: W&L Math students Trenten Babcock, Elliot Emadian, Emily Jaekle, Ryan McDonnell, Luke Quigley, and Lewis Sears.
October 2, 2015 at 4:40 pm in Robinson Hall 105
Refreshments at 4:20 pm in Robinson Hall foyer
Abstract: The students will talk about their summer research.
