Mathematics Department Colloquium
Latest colloquium information for the 2009-2010 academic year:
Meg Kiessling and Matt Matthews
Department of Mathematics
University of Tennessee at Chattanooga
Friday, November 6, EMCS 422, 2:00-3:00 pm.Computer-Based Homework Trials in MATH 151 and MATH 136
Online homework has become widely available for many disciplines and textbooks, including the texts adopted by the UTC Department of Mathematics for its Calculus and Business Calculus courses. We present our initial classroom experiences with the two different online homework products, MyMathLab (used with MATH 151) and MathZone (used with MATH 136). Data on grades will be presented along with commentary on how students use the systems and how the homework relates to the coursework. The use of MathZone with Math 136 this term provided a unique opportunity to compare students in the same class who did and did not use the online homework program.
Deborah Shepherd
Department of Mathematics
University of Tennessee at Chattanooga
Friday, October 30, EMCS 422, 2:00-3:00 pm.Using Copulas in Quality Control
Multivariate quality control charts and procedures have been developed to monitor processes in which one or more dependent quality characteristics are of concern. There have been several popular methods suggested in order to monitor this type of process. The Hotelling T2 control chart for monitoring the mean vector of the process is one of the most popular methods used when the underlying variables are assumed to have a bivariate normal distribution. Methods for constructing control charts and procedures for monitoring dependent quality characteristics with underlying distributions that are not bivariate normal are not as prevalent in the literature. This talk will present the concept of using copulas to model bivariate processes in which the underlying distribution of the quality characteristics are known but are not normal.
Copulas, first introduced by Sklar in 1956, provide a way to represent the cumulative distribution function of two or more dependent random variables in such a way that the marginal cumulative distribution functions of each of the random variables and the dependence structure may be "separated." This talk will present an overview of copulas and some basic properties of copulas. An example of how copulas may be used to monitor processes will hopefully (still working on it!) be presented.
Students that have taken at least math 151 with an interest in statistics or actuarial science may find this talk of interest.
Francesco Barioli
Department of Mathematics
University of Tennessee at Chattanooga
Friday, October 23, EMCS 422, 2:00-3:00 pm.Delta Conjecture and GCC Conjecture on Minimum Rank Problems
A Minimum Rank Problem asks for the minimum among the ranks of all matrices in a prescribed class. In particular, we will study the Minimum Rank Problem for the class of symmetric matrices and the class of positive semidefinite matrices, under an additional zero-pattern constraint. As the zero-pattern defines in a natural way an undirected graph, we may investigate how graph parameters, like the degree of a vertex, diameter, path cover number and others, may determine lower and upper bounds for the minimum rank.
In this talk I will present an overview on the currently two main conjectures on the topic: the Delta Conjecture, which connects the minimum rank with the minimum degree of a graph, and the Graph Complement Conjecture (GCC) which connects the minimum rank of a graph with the minimum rank of its complement.
Students with some interest in research and no particular background other than Math 212 are strongly encouraged to attend this talk.
Miroslav Bartusek
Department of Mathematics
Masaryk University
Brno, The Czech Republic
Tuesday, October 6, EMCS 422, 3:00-3:50 pm.On Noncontinuable Solutions of Differential Equations with Delays
In this lecture, noncontinuable solutions (i.e., solutions that are defined on a finite interval only and can not be defined for large t) of nth order differential equations with delays are studied. Necessary and sufficient conditions for their existence are presented.
Lingju Kong
Department of Mathematics
University of Tennessee at Chattanooga
Wednesday, September 23, EMCS 211, 2:00-3:00 pmUniqueness and Dependence Results for Second Order Boundary Value Problems
We consider the boundary value problem with nonhomogeneous multi-point boundary condition
A sufficient condition is obtained for the existence and uniqueness of a positive solution. The dependence of the solution on the parameters λ and μ is also studied. Our work complements some recent results in the literature, especially those in our earlier papers [L. Kong, Q. Kong, Second order boundary value problems with nonhomogeneous boundary conditions (I), Math. Nachr. 278 (2005), 173--193; L. Kong, Q. Kong, Second order boundary value problems with nonhomogeneous boundary conditions (II), J. Math. Anal. Appl. 330 (2007), 1393--1411].
This talk is based on some recent joint work with Professor Qingkai Kong from Northern Illinois University.
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