Browsing Undergraduate Research Scholars Capstone (2006–present) by Department "Mathematics"

Now showing items 1-14 of 14

    • Applications of Neural Architecture Search to Deep Reinforcement Learning Methods 
      Allen, William J; Lindsey, Zachary Peter
      This research aims to investigate the impact of various Neural Architectures (NAs) on the performance of machine learning models in the context of the deterministic game of Othello, with the goal of providing insights into ...
    • Computing Central Values for Elliptic Curve L-functions 
      Shanks, Meghan A
      We give an experimental method for calculating the central values of elliptic curve L-functions. We begin by providing some theoretical analysis of the method, and show that, on average, with appropriate choice of parameters, ...
    • Derangements in a Ferrers Board 
      Linz, William B (2013-09-26)
      The classic derangement question of counting the number of derangements for n objects from some initial permutation of the objects was first considered by de Montfort in 1708. A particular recasting of a permutation allows ...
    • The Frequency and Occurrence of Lyme Disease in Texas 
      Pavey, Juang Mee (2013-02-06)
      This study examines the frequency and spatial occurrence of Lyme Disease (LD) within the state of Texas. According to the CDC, LD is the most prevalent arthropod borne disease in the US with 33,097 cases reported last year ...
    • Geodesic Equivalence in sub-Riemannian Geometry 
      Castillo, Andrew Zane (2013-12-16)
      Sub-Riemannian geometry is an intensively developing field of Mathematics lying at the intersection of Differential Geometry, Control Theory with application to Robotics, Hamil- tonian dynamics and PDEs. Our research is ...
    • The Heteromorphism in Category Theory 
      Williams, Christian Barrett (2017-04-27)
      We explore an alternative interpretation to the abstract mathematical subject of category theory, by examining the role of the heteromorphism, a neglected concept in the field, in elucidating central categorical notions.
    • A Machine Learning Approach to Pitot Static Error Detection and Airspeed Prediction 
      Swischuk, Renee C (2016-08-17)
      Aircraft guidance is dependent on various sensors which provide information on speed, altitude and location with respect to both the ground and the surrounding air. The pitot static system, global positioning system (GPS) ...
    • MathLex: A Web-Based Mathematical Entry System 
      Barry, Matthew (2013-02-01)
      Mathematical formulas are easy to convey in handwritten media, but how should they be represented in electronic format? Unfortunately, mathematical content has not been as well-implemented on the Web as images and video. ...
    • On a Series Involving Euler's Function 
      Frendreiss, William Fortune
      The goal of this thesis is to provide an in-depth analysis and discussion of an equivalence to the Riemann Hypothesis (RH) proven by Jean-Louis Nicolas. Nicolas’ proof relates RH to an inequality of Euler’s totient function ...
    • Quantum Channels and their Minimum Output Entropies 
      Mehlhop, Nathan Alexander; Ogletree, William Travis
      We investigate non-random quantum channels generated from the representation the- ory of orthogonal quantum groups to perform numerical computations for estimates of their minimum output entropies. In doing so, we address ...
    • Representations of the Hecke Group G(2) from Fermionic Modular Categories 
      Matthews, Kevin Michael (2017-04-27)
      This project explores a conjecture which states that groups from the Fermionic Modular Category are finite; specifically representations of the Hecke group G(2) will be explored which are important in number theory. These ...
    • Toward a Classification of the Ranks and Border Ranks of All (3,3,3) Trilinear Forms 
      Allums, Derek (2011-08-08)
      The study of the ranks and border ranks of tensors is an active area of research. By the example of determining the complexity of matrix multiplication I introduce the reader to the notion of the rank and border rank of a ...
    • Uniform Acceleration Radiation 
      Bates, Timothy Gordon Henry
      Radiation of a uniformly accelerating source is an enduring problem in the physics literature that gives rise to multiple apparent paradoxes. Also in the literature there exist several notions for defining radiation. Here ...
    • Uniform Acceleration Radiation 
      Bates, Timothy Gordon Henry
      Radiation of a uniformly accelerating source is an enduring problem in the physics literature that gives rise to multiple apparent paradoxes. Also in the literature there exist several notions for defining radiation. Here ...