Nicole Cunningham - Comparing the Eigenvalues of the Products of Matrices
~~ Undergraduate Research Award ~~
Suppose that A and B are two matrices. Even when both
products AB and BA are defined, it is seldom the case
that these products are equal. In fact, if A in an n x m
matrix and B is an m x n matrix, the products AB and
BA are not even of the same type. In this talk we consider the
eigenvalues of these products and see that the products are not as
dissimilar as they first appear.
Steve Dinda - Watch the Birdie!
The purpose of this work is to explore two diversity indices, the Shannon-Wiener index and
Simpson’s index. These indices are specific sums of the proportion of each biological species
observed and are commonly used by biologists to determine species diversity in ecological studies.
Various properties of these sums are examined in detail. Comparing diversity indices requires a
specialized t-test. Other more commonly used statistics are discussed and compared.
Jeremy Hamilton - Fun with Incircles
~~ Best Talk Award ~~
An interesting property regarding an incircle and
three related circles will be examined. This problem (11046)
was proposed by Christoph Soland in
The American Mathematical Monthly, November 2003.
Theodore T. Stadnik, Jr. - Bivariate Normal Estimation of Digitally Imaged Data
~~ Best Talk Award ~~
Bivariate normal distributions are used to estimate the form of three-dimensional data
collected from a digitally captured photograph. Software is written to collect data and
extract information to calculate parameters for a bivariate normal distribution with dependent
variables. A regression curve is used to compute the major and minor axes of an ellipse. The
software is then run to create a visual and statistical analysis of biological protein gels
captured with digital imaging equipment.
