This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.

I have challenged myself to learn Python. I did this because I wanted to improve myself and my mindset around coding. My view on coding has changed immensely. I was intimidated by the social stigmas around coding, but I have become more comfortable with it. There were times when I thought that I would never understand something, but it became familiar. Through constant exposure, such as completing modules in DataCamp and Kaggle, I better understood the basics and uses of different models. The concepts I had learned before became clearer by completing a project I was genuinely interested in. I could search for a solution or ask my thesis director if I had an error. I enjoyed working with my thesis professor and failing many times. I have learned that I do not have to be a master within the year but must remain consistent with my practice. I will continue to practice and learn more about coding now with more confidence.

Studying the effects of viruses and toxins on honey bees is important in order to understand the danger these important pollinators are exposed to. Hives exist in various environments, and different colonies are exposed to varying environmental conditions and dangers. To properly study the changes and effects of seasonality and pesticides on the population dynamics of honey bees, the presence of each of these threats must be considered. This study aims to analyze how infected colonies grapple more deeply with changing, seasonal environments, and how toxins in pesticides affect population dynamics. Thus, it addresses the following questions: How do viruses within a colony affect honey bee population dynamics when the environment is seasonal? How can the effects of pesticides be modeled to better understand the spread of toxins? This project is a continuation of my own undergraduate work in a previous class, MAT 350: Techniques and Applications of Applied Mathematics, with Dr. Yun Kang, and also utilizes previous research conducted by graduate students. Original research focused on the population dynamics of honey bee disease interactions (without considering seasonality), and a mathematical modeling approach to analyze the effects of pesticides on honey bees. In order to pursue answers to the main research questions, the model for honey bee virus interaction was adapted to account for seasonality. The adaptation of this model allowed the new model to account for the effects of seasonality on infected colony population dynamics. After adapting the model, simulations with arbitrary data were run using RStudio in order to gain insight into the specific ways in which seasonality affected the interaction between a honey bee colony and viruses. The second portion of this project examines a system of ordinary differential equations that represent the effect of pesticides on honey bee population dynamics, and explores the process of this model’s formulation. Both systems of equations used as the basis for each model’s research question are from previous research reports. This project aims to further that research, and explore the applications of applied mathematics to biological issues.