# Student Research

Ernest James '23Mathematical Models for COVID-19. The COVID-19 Pandemic has been felt across the world. The virus has left us with many questions regarding the effectiveness of social distancing and lockdown orders along with the growth of the virus. Through this project, we attempt to understand these questions in two parts: (1) Develop periodic mathematical models using the data reported in the southeastern region: NC, SC, TN, GA, and FL to determine the effectiveness of social distancing protocols in these states. (2) Create a dynamic mathematical model using the same data to predict the future trends of COVID-19.  The work of this project was presented at the 2020 SURE Conference and 2021 Citadel Student Excellence Day.  Faculty advisor:  Dr. Mei Chen

William Jensen ’22Mathematical Model of the Force Curve of a Soccer Ball and Analysis of Women’s Injuries. This project endeavors to create a mathematical model using regression to illustrate the curve of a soccer ball in the air to then extrapolate the impact forces a soccer ball in the air would have. This project also looks at the relative frequency of injuries on The Citadel’s Women’s Soccer Team compared to the Woman’s Soccer national average relative injury frequency. The work of this project was presented at the 2019 SURE Conference.  Faculty advisor:  Dr. Mei Chen

Skyler Addy ’21 and Zachary Parker ’21 – In 2018 Skyler and Zach jointly worked on an open problem from Math Magazine and submitted the solution and they both received recognition for it. Skyler presented a poster at the MAA Southeast section meeting poster competition in 2019 and received the second-place award for the same. They also presented at the South Carolina Academy of Sciences the same year. Later in 2019 they started working on Lucky Numbers and continued to study properties of lucky numbers until the end of 2020. They presented their research virtually at the Citadel Student Excellence Day in 2020. Recently their work was submitted to peer-reviewed journals for consideration to be published. They worked on their research projects under the guidance of Dr. Swart and Dr. Mukherjee.

Elizabeth Spoehel '20 – Closed Formula for a Problem Involving Lucas and Fibonacci Numbers -- This problem was posed as an open problme in the November 2017 issue of Fibonacci Quarterly.  Advisors: Dr. Flórez, Dr. Mukherjee

Matthew Blair '20 – Worked on research projects in elementary number theory while he was an undergraduate student here, he is particularly interested in Fibonacci sequences. Blair started working on research projects with Dr. Flórez and Dr. Mukherjee as a sophomore. As a junior, he published the paper Matrices in the Hosoya Triangle in The Fibonacci Quarterly (2019). He won the first place Sigma XI award for his poster Matrices in the Hosoya Triangle at the Citadel Research Conference, April 5, 2019.

Blair is exceptionally creative and using his talents to observe patterns he continued to investigate the Hosoya triangle and the determinant Hosoya triangle. This led to his publication Matrices in the determinant Hosoya triangle in The Fibonacci Quarterly in 2020. In another impressive project he undertook as a senior, Blair successfully bridged the combinatorial triangular arrays with graphs and geometric patterns. This project culminated with him giving several presentations and the publication of the paper Geometric Patterns in the Determinant Hosoya Triangle in Integers in 2020. He also submitted an article titled The Wisdom of The Crowd in The Gold Star Journal (published by The Citadel) which was published and later he won the Best Undergraduate Submission award for the same.  Perhaps the most significant achievement for Blair was that he received the Dwight Camper Outstanding Undergraduate Student Research award from the South Carolina Academy of Sciences in April 2020. He also continued working on patterns in the Pascal and the Hosoya Triangle in 2020, and this project is now going to published as an article titled Honeycombs in the Hosoya Triangle in the Math Horizons magazine in early 2022.

Zachary Smith '19 – Mathematical Models of the Impact of the Reintroduction of Wolves in Yellowstone National Park since 1995. This project endeavors to create a mathematical model using systems of nonlinear differential equations to show the effects on multiple populations caused by the reintroduction of wolves into Yellowstone National Park in 1995. The main populations examined for this project are Wolves, Elk, Rabbits, Coyotes, and Beavers.  The results of this project were presented at 2018 Citadel Student Excellence Day as well as at the 2018 SFSSM Banquet.  Faculty advisor: Dr. Mei Chen

Hsin-Yun Ching ’19 – He works research in elementary number theory and is interested in Fibonacci sequences. He solves open problems from Fibonacci Quarterly. His paper Families of Integral Cographs within a Triangular Array is published by Special Matrices Journal. He is working in a second paper related to Fibonacci determinant and prime numbers.  He won the second place Sigma XI award for his poster Matrices in the Hosoya like Triangle at the Citadel Student Excellence Day, April 5, 2019.  Advisors: Dr. Flórez, Dr. Mukherjee

Timothy Clark ‘19 and William Jacobs ’19A New Algorithm for Discriminating Disease Status from Continuous and Binary Factors – This project is developing a new algorithm to adjust the logic regression framework to allow for the inclusion of continuous variables. Advisor: Dr. Nelson

James Andrus ’18Mulitcast Routing using Delay Intervals for Collaborative and Competitive Applications – This project is interdisciplinary between computer science and mathematics. Advisors: Dr. Banik, Dr. Swart, Dr. Verdicchio

Dawson Bolus ’18Style of Partitioning Positive Integers – This project on integer partitions originated as a proposed problem in Mathematical Monthly. Advisors: Dr. Mukherjee, Dr. Trautman

Topper Knutson-Harper ’18Modeling and Optimization for Crop Planning under Limited Groundwater Resources – This project applies mathematics to a real world problem. Advisor: Dr. Zhang

Nathan McAnally, ’17 – Nathan McAnally started working on his undergraduate research projects as a junior. He started his research career with the solution of an advanced problem from Fibonacci Quarterly. Given that the problem was an advanced problem, it was quite hard and McAnally completed the problem and submitted it. He received recognition from the same journal for his solution. He also presented his work at the MAA Southeast Section meeting in 2016 and won the Walt and Susan Patterson award for the best undergraduate research presentation. Nathan continued to work on his research in his senior year when he started on the project titled Identities in Generalized Fibonacci Polynomials. This collaboration with Dr. Flórez, Dr. Mukherjee, and Nathan, led to the discovery of over hundred identities and the eventual publication of an article in INTEGERS journal in 2018. Nathan won first place in the theoretical category for his poster at the Citadel Student Research Conference on the last project.