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Student Talk Abstracts

Lucas Acosta-Morales, DeSales University
Solving Double Choco Puzzles Through Computing

Puzzles and games often provide unique opportunities for studying mathematical patterns. Games that are meant to test human reasoning provide interesting challenges and insights when subjected to non-human computation and analysis. This project explores the Japanese Double Choco Puzzle and the possible ways to train a computer to solve it.


Clare Bolin, The Catholic University of America
Time Series Forecasting: Discrete Fourier Transforms and Discrete Wavelet Transforms

In an expansion of a project completed in a mathematical modeling course, student Clare Bolin worked with Dr. Prasad Senesi to research time series forecasting methods. Discrete Fourier Transforms and Discrete Wavelet Transforms were explored as possible optimization techniques for a discrete data set of warehouse inventory.


Benjamin Brindle, Lehigh University
Bifurcation Analysis in a Mathematical Model for Red Blood Cell Dynamics

A system of nonlinear, deterministic, ordinary differential equations is used to model loss of red blood cells. Numerical methods are used to display bifurcation diagrams and transient dynamics. Methods of mathematical analysis such as nondimensionalization and proofs of invariance, positivity, boundedness, and uniqueness for arbitrary functions are given.


Jack DeGroot and Heather Kwolek, Marywood University
A Mathematical Model for Forecasting the Spread of Covid-19 in Pennsylvania

Our team created a SIR mathematical model that utilizes calculus and a 3 x 3 system of first-order differential equations. We then used an iterative numerical ode solver to forecast the number of Covid-19 cases within a certain time period t within a set population in Pennsylvania.


Breille Duncan, Cedar Crest College
Exceptional Totient Numbers

Let us denote the set of positive integers less than n and relatively prime to n as R(n).  If R(n) can be partitioned into two sets that have equal sums, n is called super totient.  We will discuss exceptional totient numbers, which are defined similarly, and provide a classification for them.


Lucy Martinez, Stockton University
Minimum Rank of Regular Bipartite Graphs

The rank of a graph G is defined as the rank of its adjacency matrix A. The smallest rank among all the matrices with the same pattern of non-zeros entries as A, over the field F, is called the minimum rank of A over F. The smallest among all the minimum ranks of A (considering all the fields) is called the minimum rank of G. In this work, we study regular bipartite graphs. Specifically, we used linear recursions with linear complexity 2 and zero forcing sets to prove that the minimum rank of a (n − 1)-regular bipartite graph, with n vertices on each side, is 4. The matrix that attains the minimum rank of G is an extended parity check matrix for the graph code of G, which has the highest dimension possible (depending on the component code to be used).


Emma Miller, Paige Beidelman, John Moore, and Johnna Farnham, Moravian College REU
Strong Proper Connection

The strong proper connection number of a graph is the smallest number of colors required to edge color the graph such that there exists at least one properly colored shortest path between each pair of vertices in the graph. We will present results for amalgamations of cycles, paths, and complete graphs, and graph operations including join, corona product, and box product. All graphs in this presentation can be assumed to be simple.