Student capstone projects

Fall 2013

Erika Wilson: Investigation of Cepheid Period-Luminosity Relationship
Faculty Sponsor: A. Nanthakumar
This research encompasses the use of many statistical software programs to fit four different copula models on data that measures the Cepheid Period-Luminosity Relation. We first
discuss basic copula theory and its applications. Next, we talk about the techniques of data classification used and the results from this procedure. We then move on to fitting copula models and how to do so. We conclude with a discussion of how we analyzed and proved a suspected break in data at the point of X=1.

Kyle Buscaglia & Sean Crowder: Hidden Markov Chain in Ice-hockey
Faculty Sponsor: A. Nanthakumar
This research focuses at how the concept of Markov Chains and Hidden Markov Chains can be applied in analyzing Ice-hockey games from the videos.

Laura Murtha: Building a Foundation for Calculus
Faculty Sponsor: Terry Tiballi
It took approximately 100 years from the development of Calculus for it to become rigorous and logically sound. Unfortunately, majority of the Calculus students never see the rigor behind it. I will take several facts of Calculus that are taken for granted and prove they are logically sound through Real Analysis. I will walk through a set of problems from the book Real Analysis: A First Course by Russell A. Gordon to shed light on the underlying connections in the proof of major Calculus facts and Theorems.

Nicholas Powers: The Use of Mathematics in Nuclear Physics
Faculty Sponsor: Sue Fettes
Problems in nuclear physics will be discussed and examined from a mathematical standpoint. Specific examples will be looked at in which nuclear physics problems are solved using algebra and calculus. The derivation of certain equations used in nuclear physics will also be briefly examined.

Jacob Gallagher: Linear Fractional Transformations in the Complex Plane
Faculty Sponsor: Terry Tiballi
 I will be talking about what a linear fractional transformation is and the different situations that might arise. I will being giving a few simple examples of some of these situations. Then I will talk about a special case of linear fractional transformation with why and how circles are mapped to circles.