Spring 2005 GSS Schedule

Organizers: John Chrispell and Todd Michel

Date Speaker Topic Abstract
February 21 Tim Flowers A Funny Thing Happened on the Way to the Binomial Coefficient* The basic combinatorics of the binomial coefficients are well known. In this talk we will give a basic introduction to the $q$ generalizations of several familiar topics related to binomial coefficients. Topics will include $q$ generalizations and combinatorial interpretations of the following: $n!\,$, multinomial coefficients, binomial identities, and the binomial theorem.

*Well, actually the Binomial Coefficient came first. -Tim
February 28 Todd Michel The Meaning of Life I will discuss basic coding theory and introduce Algebraic Geometry Codes and how they are constructed using function fields.
March 7 John Chrispell An Introduction to LaTeX TeX created by Donald E. Knuth, is a high quality way of typesetting mathematical notation, and ordinary text. LaTeX documents are created using a markup language much like html. In this talk I will start from scratch, and show how to create a document using TeXnicCenter. Potential talk topics will include:
  1. Environments
  2. Mathematical Tables and Arrays
  3. Including Figures and Listings
  4. Slide Presentations
  5. Tricks for Large Documents: Citations, Bibliographies, Table of Contents
Other topics may be covered as time permits.

Some files used in this talk can be found at my LaTeX page.
March 14 Jason Howell Applying a Defect Correction Method to Viscoelastic Fluid Flow In this talk we discuss approaches to simulating fluid flow and the differences between Newtonian and viscoelastic fluids. We will focus on the numerical simulation of viscoelastic fluid flow, which becomes more difficult as a physical parameter, the Weissenberg number, increases beyond a critical value. We will then discuss a defect correction method that allows us to overcome some of the difficulties in simulating viscoelastic fluid flow at values larger than the critical value.
March 21 Spring Break
April 4 Sarah Graham Approaches to Decoding for Two-Point Codes Reliable data transmission is vital in a technological society. Error-correcting coding theory is a branch of information theory that has developed over the last century to produce codes with encoding and decoding algorithms to correct errors that occur during data transmission. Algebraic geometry techniques can be used to create error-correcting codes and algorithms. This talk will discuss one method for decoding two-point algebraic geometry codes.
April 11 Christine Kraft Predicting Course Enrollment: A More Complete Model Predicting student course enrollment is an innately difficult problem because of changes in student retention, admission policies, and curriculum requirements at Clemson University. Current course enrollment models rely heavily on historical enrollment rates. Until recently there was insufficient data available to identify groups of students whose course enrollment rates are significantly higher than the rest of the university population. Prior to this information, there were also no means to examine groups of students whose enrollment behavior seemed to be different, such as new first time students and transfer students. With the availability of these data, which include student enrollment status, major, and information on previous course enrollment, it was possible to construct a set of generic course enrollment models. This talk specifically focuses on mathematical sciences course enrollment for two highly populated lower level courses to build the procedure, create the models, and test the results. Despite the challenges that the enrollment problem presents, the models created and presented in this talk are validated and can be extended to other courses within the mathematical sciences department, as well as throughout the university.
April 18 ADM Colloquium
April 25 Robert Beeler Automorphic Decompositions of Graphs Given a graphs $H$ and $G=$, we say that $H$ has a $G$-Decomposition if we are to partition the edge set of $H$ so that for each part $P$ of the partition, the subgraph of $H$ induced by $P$ is isomorphic to $G$. Let $I(\mathcal{D})$ be the intersection generated by such a decomposition. We say that $\mathcal{D}$ is an autopmorphic decomposition of $H$ with respect to $G$ if $I(\mathcal{D}) \cong H$. In this talk we will give necessary conditions for the existence of an automorphic decomposition, as well as give several examples of automorphic decompositions.