On Saturday, Feb. 26, five Arcadia University math majors made individual presentations at the Moravian College Undergraduate Mathematics Conference. Abstracts of their talks are below.
Title: An introduction to sabermatrics
Abstract: Sabermetrics is the application of statistics to baseball. In this talk, we will give examples of this field involving a number of statistical techniques including logistic regression, multiple regression, and the Mann-Whitney –Wilcoxin U-test.
Title: Solving linear differential equations using linear algebra
Abstract: In mathematics, there is a great importance in being able to solve differential equations with speed and accuracy. What I present here, through the work of Luis Verde-Star, is an alternative way of solving these equations by taking advantage of the linear algebra aspects of the problem at hand.
Title: Transfinite bijections
Abstract: In the 19th century, Georg Cantor used power sets to prove that there are infinitely many sizes of infinitely sized sets. This talk will outline an alternative proof of this result, showing how the set of all bijections between any infinite set and itself is always larger than that set.
Title: A recipe for disaster? A marriage of copulas and default correlation
Abstract: This presentation provides a short analysis of David X. Li’s copula model on default correlation. The presenter will discuss Li’s model in detail, including background, mathematical explanation, the model’s advantages and limitations, and a short exploration of the model’s relationship to the 2008 financial crisis.
Title: Satterthwaite versus pooled variance T-Testing
Abstract: When testing the equality of two independent means, statisticians often use either pooled or Sattertwaite T-tests, depending on whether they assume equality of the population variances. Through SAS simulations, we investigate the relative power and Type-I error rates of these two approaches.