Browsing Mathematics by Title
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Applications of Stochastic Processes to Cancer Research
(East Carolina University, 2013)The purpose of this thesis is to implement stochastic models that are currently used to analyze the impact of different drug treatments on cancer and to model drug resistance by cancer cells. Mathematical models are used ... 
COLLEGE ALGEBRA REDESIGN: IMPROVE STUDENT LEARNING AND SUCCESS USING A HYBRID EMPORIUM MODEL
(2015)The purpose of this project is to describe a learningbased college algebra (Math 1065) course redesign at East Carolina University. Historically, East Carolina University’s College Algebra program maintained a high ... 
Diophantine Generation, Galois Theory, and Hilbert's Tenth Problem
(East Carolina University, 2012)Hilbert's Tenth Problem was a question concerning existence of an algorithm to determine if there were integer solutions to arbitrary polynomial equations over the integers. Building on the work by Martin Davis, Hilary ... 
Economic Design of CUSUM Control Charts
(East Carolina University, 2014)In statistical process control, control charts are one tool for monitoring the control status of a process. One such type of chart is the cumulative sum (CUSUM) chart which has advantages over other styles of control chart. ... 
The Effect of the Mathematics of Finance on the Dynamics of a Credit Economy
(East Carolina University, 2012)The general equilibrium theory of J.M. Keynes was developed in the 1930's to help explain the great depression and prevent future economic downturns. Out of this came the ISLM (investment saving/liquid money) model, ... 
Eigenvalues for Sums of Hermitian Matrices
(East Carolina University, 2015)In this thesis we explore how the eigenvalues of nxn Hermitian matrices A,B relate to the eigenvalues of their sum C=A+B. We mainly focus on inequalities bounding sums of r eigenvalues for C by sums of r eigenvalues for A ... 
ESTIMATION OF THE PROBABILITY A BROWNIAN BRIDGE CROSSES A CONCAVE BOUNDARY
(East Carolina University, 2010)This thesis studies a new method to estimate the probability that a Brownian bridge crosses a concave boundary. We show that a Brownian bridge crosses a concave boundary if and only if its least concave majorant crosses ... 
AN EXPOSITION OF THE RIEMANN ZETA FUNCTION
(East Carolina University, 2014)This thesis is an exposition of the Riemann zeta function. Included are techniques of analytic continuation and relationships to special functions. Some generalizations of the Riemann zeta function are outlined, as well ... 
Financial Market Analysis Using a Kinetics Model
(East Carolina University, 2013)Over the past several decades physicists have used models and techniques that were developed in the sciences in order to analyze the price and volume behavior of financial markets. These models and techniques ... 
First Order Definition of Rings Using Group of Units
(East Carolina University, 20230503)We discuss the technical background and relevant research regarding the undecidability of $O_{\mathbb{Q}^{\text{ab}}}$. Given an algebraic extension $K/\mathbb{Q}$, we consider the subring defined by $$R_K=\{x\in O_K\,\,\forall ... 
Fourier Analysis on SU(2)
(East Carolina University, 2012)The set SU(2) of 2x2 unitary matrices with determinant one forms a compact nonabelian Lie group diffeomorphic to the three dimensional sphere. This thesis surveys general theory concerning analysis on compact Lie groups ... 
Idempotents in Cyclic Codes
(East Carolina University, 2012)Cyclic codes give us the most probable method by which we may detect and correct data transmission errors. These codes depend on the development of advanced mathematical concepts. It is shown that cyclic codes, when viewed ... 
IDENTIFYING SUBJECTIVE VALUE IN WOMEN’S COLLEGE GOLF RECRUITING REGARDLESS OF SOCIOECONOMIC CLASS
(East Carolina University, 20180503)College athletics have grown into a major industry and athletic departments are pushing coaches to recruit the top talent. To recruit golfers, college coaches depend on multiple ranking systems. These systems are bias ... 
Improved Tsunami Modeling Via qAdvanced Special Functions
(East Carolina University, 2013)This thesis studies qadvanced functions that are used as forcing terms in the forced wave equation and the Kortewegde Vries equation in modeling tsunamis. The model improves existing tsunami models and is compared to ... 
Inferences Over Fields: A Preliminary Investigation into the Deductive Capabilities of FieldTheoretically Defined Logical Connectives
(East Carolina University, 20230503)In this paper, we will be concerned with developing an inferential structure over the field with four elements in characteristic $2$. We begin by discussing the historical context in which this research occurs. In subsequent ... 
Irredundant and Mixed Ramsey Numbers
(East Carolina University, 2013)The irredundant Ramsey number, s(m,n), is the smallest p such that in every twocoloring of the edges of K[subscript]p using colors red (R) and blue (B), either the blue subgraph contains an melement irredundant set or ...