Mathematics

The Math Club gives students an opportunity to discuss and investigate mathematics outside of the classroom. 

The current leadership of the club:

• President: Sarah Netchert
• Vice President: Julia Schneider
• Treasurer: Lindsay Kane
• Secretary: Kaitlyn Bigos

Recent and ongoing research projects include: 

• Tara Koskulitz and Mike Gottstein were awarded a Summer 2016 stipend research on the game KAMI and its relationship to graph theory
• Taylor Rupp, Mike Gottstein, and Craig Siekierka are some of the previous Summer stipend recipients.

Other projects include:

• Fundraising for the club and for local charities
• A series of tutorial videos (posted to youtube) designed to help lower level mathematics students at the university
• A meal paid for and delivered by the club to a needy family at Thanksgiving

From the Mountain Top Eagle -

Misericordia University Teacher Education and Math Club students offered lessons on sorting, patterns, symmetry and fractions during a fun and entertaining Math Day at St. Jude School in Mountain Top. More than 30 Misericordia students provided fun and engaging ways for 200 students in pre-k through 8th grades at St. Jude to learn about and appreciate mathematics. 

Steven Tedford, Ph. D., of Mountaintop, associate professor of mathematics at Misericordia University, and his wife, Veronica, a former collegiate professor of mathematics, coordinated the program. 

The Department of Mathematics at Misericordia University hosted the 9^th annual Luzerne and Lackawanna Counties Mathematics Symposium on Saturday, October 6, 2018. 

The symposium began at 8:15 am with a continental breakfast. Talks began at 9:00 am and continued until 2:00 pm.

List of Speakers and Talks:

1. Dr. Tania Hazra (Misericordia University)

Title: A super-Gaussian Poisson-Boltzmann model for electrostatic solvation energy calculation: smooth dielectric distribution for protein cavities and in both water and vacuum states

Abstract: Calculations of electrostatic potential and solvation energy of macromolecules are essential for understanding the mechanism of many biological processes. In the classical implicit solvent Poisson-Boltzmann (PB) model, the calculation becomes challenging for the dielectric property across the solute-solvent boundary and interior cavities. To overcome these experimental challenges, a novel super-Gaussian dielectric PB model is presented in this work. Mathematically, an effective dielectric constant (EDC) analysis is introduced in this effort to benchmark the dielectric model and select optimal parameter values. Computationally, a pseudo-time alternative direction implicit (ADI) algorithm is utilized for solving the super-Gaussian PB equation, which is found to be unconditionally stable in a smooth dielectric setting. Solvation free energy calculation of a Kirkwood sphere and various proteins is carried out to validate the super-Gaussian model and ADI algorithm. One macromolecule with both cavity-fluids and empty cavities are employed to demonstrate how the cavity uncertainty in protein structure can be bypassed through dielectric modeling in a biomolecular electrostatic analysis.

2. Dr. Jennifer Vasquez (University of Scranton)

Title: Entanglement: Topological and Quantum

Abstract: We will begin by discussing topological notions of entanglement such as braids and linking of knots. This will be followed by a discussion of quantum entanglement. Finally, time permitting, we will describe possible connections of different types of entanglement.

3. Dr. Soumyadip (Dip) Acharyya (Embry-Riddle Aeronautical University)

Title: To be Announced

Abstract: To be Announced

4. Lindsay Kane (Misericordia University)

Title: An Introduction to Fibonacci Graphs

Abstract: The Fibonacci numbers have been studied for centuries by many people using a large variety of techniques. When considered combinatorially, these numbers can be translated into graphs. We introduce these graphs and discuss some of the basic properties of them, which arise from this combinatorial interpretation of the Fibonacci numbers.

5. Dr. Steven Tedford (Misericordia University)

Title: Fibonacci Graphs continued.

Abstract: We will continue the introduction to Fibonacci graphs given by Lindsay. In particular, we will look at some structural results for these graphs as well as an infinite graph that represents the entire Fibonacci Sequence. Finally, we will consider similar graphic structures for additional combinatorial number sequences.

6. Dr. Michael Floren (Misericordia University)

Title: What works best? The practical effects of model misspecification in determining statistical significance.

Abstract: This talk will discuss a medical research example where model specification played a key role in determining (or not determining) treatment differences.

7. Dr. Karen McCready (King’s College)

Title: Properties of edge-colored 2-connected graphs

Abstract: An edge-colored path is properly colored if adjacent edges receive distinct colors. An edge- colored graph is properly connected if each pair of vertices in the graph is connected by at least one properly colored path. In such a graph we extend the idea of diameter to that of proper diameter, a function of both the graph and its coloring, which is defi to be the maximum length of a shortest properly colored path between any two vertices in the graph. We will explore the relationship between the diameter and proper diameter of certain graph classes and consider how proper diameter values relate to the vertex connectivity of a graph.