Pi Mu Epsilon - Mathematical Association of America

Thursday Pi Mu Epsilon Session #3 August 2, 2012
PME Session #3
Room: Meeting Room O
4:00P.M. – 6:15P.M.
4:00–4:15
Low Dimension Lie Algebra Dimension Reduction by Modding by the Center
Nick Benthem
Grand Valley State University
We investigate reducing the order of real low dimensional Lie algebras by modding by the center.
We find the isomorphism between the reduced algebra and one of the non-decomposable Lie algebras
and explain why in certain cases the reduced algebra decomposes.
4:20–4:35
Markov Chains in Literature: Re-Exploring Markovs Original
Applications Using Modern Technology
Anne French
Austin Peay State University
Markov chains have numerous applications throughout mathematics and science, which is something
the creator of the chains never thought was possible. Andrey A. Markov thought that his
chains would only be applicable in the exploration of literature. His love of poetry led him to use
Markov chains to study the alteration of vowels and consonants in Russian literature as a hobby.
This presentation demonstrates how the analysis of literature using Markov chains and computer
programming can be used to reveal the origination of the nonsense texts of the mathematician
Charles Dodson, who is also known as Lewis Carroll.
4:40–4:55
Investigating the Mapping Properties of a Certain Class of Harmonic
Functions on the Unit Disc
Cory Medin
Austin Peay State University
A good departure point for investigating harmonic polynomials is to study certain classes of harmonic
functions. In particular, we compare the mapping properties of a certain family of harmonic
functions with the mapping properties a certain family of Schlicht functions on the unit disc.
5:00–5:15
Benford Melodies: A Senior Thesis on Stochastic Composition
Nathaniel Card
Carthage College
Benfords Law can be applied to many things: addresses, stock prices, and river lengths; however,
in this presentation we will explore using Benfords Law to both analyze and create melodies. The
principal question being thus: do most melodies follow Benfords Law by the very nature of musical
composition and counterpoint, or would composing melodies using Benfords Law create truly
original sounding stochastic music.
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