Throughout my undergraduate years at the University of Central Florida, I worked on two research projects as a part of the Honors Undergraduate Thesis (HUT) program and the Research and Mentoring Program (RAMP). I will list the names of both projects below, alongside a brief description.
Modeling and Analysis of COVID-19
I've started to work on this project with the goal to study the mathematics behind the COVID-19 propagation and understand the parameters that contribute to its accelerating spread the most. My research was built upon the preexisting models in dynamical systems and other takes on COVID-19 modeling. The result was a rather accurate model, provided that the predictions were short-term. Furthermore, a lot of insight was gathered on which parameters are the most vital ones in decelerating the spread of the virus.
Modified Truncated Cone Resistor
The students passionate about physics and mathematics can face very cool and fascinating problems, even in introductory physics classes. However, the expected solutions discussed in classes often hide the more intriguing parts of the problem and are sometimes even inaccurate when analyzed carefully. Nonetheless, this characteristic of omitting the truth at early stages is purposeful and standard in education as not all students are ready for a harsher challenge. Nevertheless, it remains that the deeper, more elegant stuff gets easily overlooked. As you could have guessed by now, this paper covers one such scenario involving a problem with a conical resistor where its solution is obtained using advanced mathematical techniques revealing beauty and complexity otherwise hidden.