Now showing items 11-20 of 23
Classification of Rational Lemniscates in the Complex Plane
Generalizing the work of Ebenfelt, Khavinson, and Shapiro, this study sought to find a means of classifying shapes in the complex plane by using "fingerprints" of shapes. These fingerprints are constructed to have useful ...
Graph Theoretic Models for RNA Secondary Structure
RNA forms bonds with itself and partially determines how the RNA functions. We investigate some models for this RNA secondary structure using a mathematical object called a matching. Some bonds are more likely than others ...
Bayesian Inferential Statistics Implemented in R
Conventional frequentist statistics taught in undergraduate courses are obviously better than nothing, yet suffer from systematic failures that allow for easy p-hacking and consistent over-estimation of significance and ...
Math 380: Research Methods in Mathematics
Math 380: Research Methods was developed for Fall semester of 2015 by Dr. Dandrielle Lewis, Dr. Carolyn Otto, and three undergraduate mentors. The main premise of this course is to instruct future mathematicians on ...
Study of Least Absolute Deviation Methods
In the context of finding the "best" predictive model, this research project focuses on assessing and fitting models with least-absolute-deviation techniques.
New Methods of Constructing 4-dimensional Tops
The mathematical field of mirror symmetry seeks to understand the geometric correspondences between paired Calabi-Yau varieties.
Embedding Properties in Central Products
In group theory, we study ways to get new groups from old groups, and we study properties of subgroups and further characterizations of subgroups in various groups. Edouard Goursat determined a method to characterize the ...
Minimal Complexity C-complexes for Colored Links
In this project, we study the analogous measure of complexity given by a generalization of a surface called a C-complex.
Mirror Symmetry in Reflexive Polytopes
There are always two Calabi-Yau varieties that produce a particular physical model. In mathematics we call this phenomenon mirror symmetry, the purpose of this study.
Mirror Symmetry from Reflexive Polytopes
There are two main theories used by physicists to explain the inner workings of the universe. General relativity is used to describe the very large, while quantum mechanics describes the very small. For decades, physicists ...