Hudson River Undergraduate Mathematics Conference XIII
April 8, 2006
Westfield State College, MA
The following four papers were presented by Canisius College Mathematics Seniors at the 13th Hudson River Undergraduate Mathematics Conference (2006). All papers were vetted through the through the (Canisius College) Department of Mathematics and Statistics “Students’ Seminar Series” during the Spring of 2006. Three of the four talks (as linked below) were based on one-week courses that the students had taken through the programme of New Mathematical Topographies.
Andrew Crossett: “Statistical Analysis of Neuronal Data”
Technical advances in the field of computational neuroscience have given rise to many new and complex situations dealing with neuronal data. Because of the relatively small number of samples that can be taken at any given time, it is important to apply both intuitive and non-intuitive statistical methodology. We will begin by showing that an elementary framework for estimating the firing rate of neurons can be inefficient. Therefore, we will turn our attention to three main points of more non-intuitive methods: the use of maximum likelihood and Bayesian methods to estimate parameters, applying modern nonparametric methods to neuronal data and finally showing that many analyses that are based on Poisson assumptions can be applied to non-Poisson data.
Dave Covert: “Noncommutative Functional Analysis for Undergrads”
This talk will be an introduction to Noncommutative Functional Analysis based on a one-week course given at Canisius College by Dr. David Blecher (University of Houston) in the Fall of 2004. I will start with some key definitions in functional analysis and work my way to the noncommutative world. This talk will conclude with Ruan’s Theorem and how this (fairly) newly-developed field helped solve the Halmos Similarity Problem in Operator Theory.
Greg Knop: “Zebra Mussels and Phosphorous Loading in Lake Erie”
This talk is based on an unpublished paper written by Per Enflo, Robert Heath and Angela Spalsbury. It discusses the following: In the 1970s, new regulations regarding phosphorous loading of Lake Erie were put into place. As a result, certain species of algae that had all but vanished in the 1950s and 1960s returned. In the 1980s, the zebra mussel was accidentally introduced into Lake Erie. This resulted in a reduction of the total amount of algae at first, but then certain species of algae returned to much higher levels (than ever before) several years later. This talk will discuss a mathematical model based on modified Monad Equations (we add nonlinear terms of degree two to Monad-like equations) to study the above scenario.
Phillip Monin: “Zeta Functions of Some Infinite Graphs”
I will open with the definition of the Ihara zeta function on finite graphs and state some of its number-theoretic and spectral properties. Then I will provide an extension of the Ihara zeta function to infinite graphs, which are limits of finite graphs, and present some explicit calculations.