Spring 2023 Directed Reading Program Symposium
The Spring 2023 Directed Reading Program (DRP) Symposium event will be held on Thursday, May 4th from 5:30 - 7:30 pm in Avery Hall 19. The DRP pairs undergraduate students with graduate student mentors to dive into an interesting mathematical topic not typically covered by coursework.
Undergraduate DRP students from this semester will give 20-minute presentations on their projects during the DRP Symposium event. Here is a list of the students giving presentations, the titles of their presentations, and abstracts of their presentations:
Presenter: Dakota Andrews
Title: Smooth Manifolds
Abstract: Most are familiar with the mechanics of calculus in the conventional Euclidean space, but what does calculus look like in spaces that aren't Euclidean? This presentation will introduce smooth manifolds as a space with the least amount of structure needed to perform calculus.
Presenter: Caitlin Murphy
Title: Introduction to Control Theory
Abstract: Control theory is a field of applied mathematics which focuses on governing the behavior of linear systems via their inputs. In this talk, we will explore the mathematics behind determining whether a system is controllable and illustrate with an example.
Presenter: Kolton O'Neal
Title: Hom-Tensor Adjunction
Abstract: This talk involves R-modules and category theory. In this talk, we will see that there is a close relationship (adjunction) between two notions in homological algebra. One is the set of homomorphisms from a particular R-module, which itself forms an R-module. The other is the tensor product, which turns R-bilinear maps into R-linear maps.
Presenter: Sara Vance
Title: Bifurcations and the Qualitative Behavior of Ordinary Differential Equations
Abstract: This presentation will contain a brief overview of methods to solve ordinary differential equations and systems of ordinary differential equations. Then, it will cover the qualitative behavior of systems of ODEs, including bifurcations.
Presenter: Elizabeth Weber
Title: An Introduction to the Kalman Filter
Abstract: The Kalman filter is a method of data assimilation and seeks to combine observations with models to form predictions. This talk with go over the Kalman filter and it’s uses as well as talk about other variations of the Kalman filter.
Presenter: Nick White
Title: Solving 1D Differential Equations with Finite Element Analysis
Abstract: The Finite Element method is one of the most common methods of numerically solving differential equations. In this talk we will describe some of the theoretical background behind the method, as well as seeing an example of it implemented in MATLAB code and the error of the approximate solution.
Pizza will be provided!