Now showing items 11-20 of 36
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 ...
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.
Analysis of Combining Musical Scale Vectors
This interdisciplinary project uses mathematics to represent musically significant collections of notes such as scales, chords and intervals as combinations of each other. These note collection were converted into ...
Evaluation of Supplemental Math Intervention in a Montessori Context
Number Rockets is a tutor delivered math intervention program for 1st grade. A randomized control trial of Number Rockets found significant improvements in math computation and concept and application skills for 1st graders. ...
Introduction to D[subscript]8 x D[subscript]8 and its Subgroup Lattice
Let A and B be groups and consider the direct product A x B. In 1889, Edouard Goursat proved a theorem that provides the structure of subgroups in a direct product. The purpose of this study was to improve and make more ...
n-Dimensional Semi-Hypercubes and the Algebras Associated With Their Hasse Graphs
Our goal is to be able to predict how automorphisms of the semihypercubes act using the Hasse graphs of the fixed k-faces to obtain a generating function for the Hasse graph polynomial.
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 ...
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 ...
Ancient Egypt’s Religious Need for Mathematics
Ancient Egyptians are known for their mathematical prowess. To understand what inspired this progress, we must contextualize the mathematical procedures that were developed and used at the time. In ancient Egypt, mathematics ...
An Equivalence Between the Polytabloid Bases and Specht Polynomials For Irreducible Representations of the Symmetric Group
The purpose of this study was to study Young tableaus, which are combinatorial objects useful in the study of representation theory of symmetric groups, using mathematical theory.