The Haar wavelet was one of the first wavelet bases that was developed by Alfred Haar in 1909. Haar used these functions to give an example of an orthonormal system for the space of square-integrable functions on the unit interval [0;1]. We will furth . . .

The additivity of crossing numbers over a composition of links has been an open problem for over one hundred years. It has been proved that the crossing number over alternating links is additive independently in 1987 by Louis Kauffman, Kunio Murasugi, . . .

We will examine how we can use Caputo’s definition of a fractional derivative to develop a method to numerically evaluate a fractional derivative of a function at a point. A fractional derivative can be thought as an instantaneous fractional average. . . .

In this paper we propose a procedure to obtain an optimal clustering solution for a given set of data. The main idea that runs through this thesis is the clustering of a data set with the consideration of multiple clustering solutions. This is achieve . . .

The effect of time delay on the control of a single and two coupled torsion bar structures is explored using analytical expressions solved numerically and numerical simulations of the response of the systems. The maximum gain for stability is determin . . .

In this paper we will modify the classic Suscptible-Infected-Recovered (S-I-R) model to include a fourth Envirnoment (E) class in order to model the dynamics of the waterborne illness Cholera. In this model we are now able to consider the interactions . . .

Sets of data used for business and research are rapidly increasing in size. The problem of analysis on big data has becoming a pressing concern for the statistician. In this thesis, I compare different methods for performing least squares linear regre . . .

We investigate the shape of color space data for Young Stellar Objects cataloged in the NASA archive MIRES using Computational Topology. Mapper was used to construct graphical summaries of the 6-dimensional and 21-dimensional color space data for all . . .

Factor analysis is a multivariate statistical tool that is used in the development, refinement and evaluation of tests and measures of data that can be used in clinical and educational contexts by an analyst. This thesis will focus on a brief understa . . .

The goal of this discussion is to determine the Schnirelmann density of the deficient numbers, which is not currently known. The Schnirelmann density for deficient numbers is defined as the infimum of the set of densities of deficient numbers up to n. . . .

This study addresses the phenomenon of students taking longer than 6 years to complete a bachelor’s degree in mathematics. More specifically the goal was to identify and describe contributors to academic path elongation and the formation of mathematic . . .

This paper investigates the relationship between the spectrum of a Toeplitz operator and the spectra of its approximating Toeplitz matrices. The main tool in this investigation is the concept of epsilon-pseudo-eigenvalues introduced by Reichel and Tre . . .

Buckling restrained braces (BRB) have recently been incorporated in standard seismic design practices. Common BRB systems have incorporated a steel core with either a concrete or mortar as a bracing element. This treatise will model a novel BRB system . . .

In this paper the linear complementarity problem (LCP) is discussed. The focus is on the types of solutions the problem can produce. Theory about the solution structure is discussed through the use of cones and complementary matrices. This theory is u . . .

“I’m not good at math” and “I hate math” are common reactions teachers hear from their students. Increasing student motivation and achievement in the classroom is a challenge teachers are faced with. This research project studied the effects that GeoG . . .

In this thesis we will investigate how a species that is being afflicted with an SIR disease reacts when another species is introduced into the system that has a symbiotic relationship with the diseased species. First we will introduce the classical S . . .

This paper surveys the Mapper technique introduced by Singh, Memoli, and Carlsson for summarizing features of the shape of a high-dimensional data set with a 1-complex [1]. After a brief explanation of geometric and abstract simplicial complexes, the . . .

We will examine the ruler sequence and its relation to the discrete logarithm, prim­itive roots modulo powers of a prime, p-adic ordinals, odd perfect numbers, and the 3n + 1 problem. Emphasis is placed on the multiplicative order of an integer modulo . . .

The objective of this thesis is to find the transition probability functions of a Markov process with jump sizes of 1 and 2. When all of the transition rates are equal in the process, results are found analytically by randomization, the dual of the sy . . .