Tag: Mathematics

Title: A mathematical model for the interactions between red blood cells, malaria parasite, and host immune response

Abstract: Malaria infection has been posing a major health threat for hundreds of years in human history, yet no sophisticated mathematical models exist to study its dynamics within an infected host due to complex interactions between the host immune response and the parasite. We propose a new mathematical model, accounting for the dependence of red blood cell Tgcinfectivity on its maturation level and the time delay for the developmental period of the parasite, to investigate the population dynamics of Plasmodium falciparum malaria parasite and its interaction with red blood cells and cells of the immune system. The newly developed model will be applied to study the interplay between the host immune response and the parasite dynamics and investigate crucial experimental parameters for reliable prediction of treatment strategies.

Keywords: red blood cells, parasite, malaria, immune response

 

Title: A lesson in the geometric constructions of the Maya

Abstract: As part of the Math 102 course completed via study abroad in Mexico, I will give students instruction regarding the Maya method of measuring lengths and angles. Using cord purchased prior to our travel to Mexico, students will attempt to create right angles and special-ratio lengths. I will then help students to create the angles and lengths using the method of the Maya, according to Christopher Powell’s dissertation (2010) as found at “http://www.mayaexploration.org/pdf/PowellDissertation2010_MayaGeometry.pdf. This experience will lend itself to a presentation in the Transformational Geometry class on campus at Millersville University, which will benefit the pre-service teachers in that class by introducing them to an interdisciplinary topic that they can use in their future classrooms. It may also be presented at a colloquium for the math departments of Millersville and Franklin &Marshall, and it has the potential to become a regular topic in the Math 102 course at Millersville.

Keywords: Maya, geometry

 

Title: A Sample of the Number Systems of the Indigenous Groups of Patagonia

Abstract: Mathematical ideas and conventions are often based on the idea of interacting with nature through sensory experiences and instinctual reasoning. Although not extensive, some of the indigenous groups of Patagonia had number systems represented orally. The Patagonia region encompasses the vast southernmost tip of South America, shared by Argentina and Chile. There is limited information regarding their cultural forms of number representation as much of this was passed along orally and several of their languages are extinct. Northern regions in South America had an influence on their number systems, and, in spite of the limited resources available there seems to be a number language pattern amongst groups such as Tehuelches, Onas, Alakalufes, Yamanas, Mapuche, Charrúa, Guarani, and Atacameño. I will present and compare several of their number systems and formalize rules to create compound numbers with various examples.

 Keywords:  Patagonia, mathematics, number system, indigenous

Title: The Effect of Within Class Covariance Matrices on Classification using Discriminant Analysis

Abstract: Three classification procedures used with Discriminant Analysis are studied. The procedures are Simple (Fisher) Classification, Mahalanobis Distance Classification and Canonical Function Classification. R code is written to perform each of these classification procedures. A Monte Carlo Simulation Study is performed using two predictor variables and three groups. The Variance/Covariance matrix in each group is the focus of the simulation. By randomly generating multivariate normal data with different variance/covariance matrices we will determine its effect on the percent correct classification using each of the three classification procedures.

Keywords: Discriminant Analysis, Monte Carlo Simulation