All Abstracts

Random matrix theory is a major branch of contemporary mathematics. With origins in nuclear physics and statistics, random matrices have numerous applications in areas as diverse as real-time signal processing, civil engineering, combinatorics and number theory. The notion of rigid motion in Euclide...

Graph theory is the study of connections. There are many applications of graph theory to other fields. In this project, we analyze different properties of graphs that imply the existence of certain sets of cycles in graphs. In particular, we investigate pairs of subgraphs that must be forbidden to i...

According to the Center of Disease Control, there were over 1,500,00 cases of chlamydia reported in the United States in 2016. Is this figure in line with the recent past or does it represent a rise on the incidence chlamydia? This project's aim is to look at the trend of chlamydia rates within the ...

Within this research, Computational Commutative Algebra was used to solve a common Graph Theory problem known as three colorability. A special kind of generator for the ideals of a polynomial ring in n-variables R[x1, x2, ... , xn] were studied. These generators are called Gröbner bases, which are ...

Through the course of this research, we utilized the geometric mean to discover how it differs from the arithmetic mean. The geometric mean is found by taking the n-th root of the product of n numbers. The geometric mean can be used to determine growth rates, portfolio returns, and stock indices. ...

For decades HIV and AIDS have remained a public health problem for the United States and many other countries. While great progress has been made in preventing and treating HIV, there is still much to do. Considering that the HIV virus can lead to Acquired Immunodeficiency Syndrome (AIDS) if not tr...

Graph theory is the study of connections. There are many applications of graph theory to other fields. In this project, we analyze different properties of graphs that imply the existence of certain sets of cycles in graphs. In particular, we investigate the pairs of subgraphs we must forbid to imply...

Previous research indicates that executive functioning, the ability to manipulate information through the use of focused attention, is an important predictor of math achievement. Some studies report that the direct effects of executive functioning seem especially strong for mathematics. The present ...

In 1202, Fibonacci, an Italian mathematician, created a mathematical sequence to model the reproduction of rabbits. Fibonacci used his sequence to explore patterns found in multiple areas outside of mathematics such as: nature, art, and architecture. Additionally, the Fibonacci sequence can be found...