Wednesday April 23, at 3:45 pm in Roop 103; tea at 3:30


STUDENT TALKS
Honors Theses and Independent Research

TITLE:  Minimizing the Expected Value of the Variance of the X-Interpcept in LS Regression.

         Mr. Andrew Chang, advised by Drs. Hasan Hamdan and JL Leary (chemistry)

ABSTRACT: Chemists are usually interested in using the best spacing of concentrations of selenium, Se-78, Centrum Silver or tellurium-125, X, on the instrument response, Y, in minimizing the variability of the X-intercept around 0.5. In this talk, we derive an approximation of this variance. The formula has a complicated form that depends on the poulation intercept, the slope and the X-value.

TITLE: Cantor Set Construction and Cardinal Invariants

         Mr. Jorge Bruno, advised by Dr. E. T. Brown

ABSTRACT:  This paper focuses, mainly, on two issues. The first deals with the mathematical analysis of C[0; 1] and R; entailing the construction of Cantor sets. The second one is concerned with the notion of Sacks forcing; general and applied to C[0, 1]. Necessary background and fundamental concepts are briefly sumarized before a more rigourus discussion of the previously mentioned topics is undertaken.

TITLE:  Using UNMIX in Estimating Bivariate Scale Mixtures of Normals in Stock Models
 
          Ms Victoria Ellison, advised by Dr. Hasan Hamdan

ABSTRACT: In this paper, a new method for estimating multivariate scale mixtures of normals is proposed and evaluated. The method extends the techniques used in the univariate UNMIX method of scale mixtures of normals. In particular, UNMIX is used in estimating the marginal parameters for the multivariate random variable, then these are used to estimate the remaining unknown parameters for the multivariate normal mixture components. The method is applied to the bivariate estimation of continuously compounded stock returns. This method offers an alternative way of estimating scale mixtures of normals, rather than by approximating a univariate slice of the multivariate curve and then performing a uniform rotation of the slice to attain the desired estimate. This method shows promise for bivariate data sets that are highly correlated.

TITLE:  Rhetoric and Mathematics: Reviving the Exploration of a Transdisciplinary Bridge

          Mr. Brandon Strawn, advised by Dr. Elisabeth Gumnior (Writing and Rhetoric Studies)

  In my unique perspective as an undergraduate student of rhetoric and mathematics, I have stumbled upon a secret: these two subjects, often billed as two of the most polarized realms of academia, are not as mutually exclusive as many claim them to be. Following this impulse, I learned that while their antithetical nature is often argued outside both disciplines, most rhetoricians and mathematicians are not surprised by the comparison.  Furthermore, there has been some research in the area, the most noteworthy of which, though, was more than twenty years ago.  Determined to correct this misconception, renew the study of their comparison, and present a more accurate general portrayal of both subjects for the laypeople, I set about rebuild the bridge between rhetoric and mathematics.  I learned that rhetoric can be studied and utilized mathematically both correctly and incorrectly, and that mathematics is rhetorical not only with regards to the communication thereof, but deep within its foundation as well.