Mathematics Commons^™

Exploring Dynamical Systems: Number Of Cycle And Cycle Lengths, Christine Marcotte

Honors Program Theses and Projects

No abstract provided.

Examples Of Solving The Wave Equation In The Hyperbolic Plane, Cooper Ramsey

Senior Honors Theses

The complex numbers have proven themselves immensely useful in physics, mathematics, and engineering. One useful tool of the complex numbers is the method of conformal mapping which is used to solve various problems in physics and engineering that involved Laplace’s equation. Following the work done by Dr. James Cook, the complex numbers are replaced with associative real algebras. This paper focuses on another algebra, the hyperbolic numbers. A solution method like conformal mapping is developed with solutions to the one-dimensional wave equation. Applications of this solution method revolve around engineering and physics problems involving the propagation of waves. To conclude, …

Numerical Methods For A Two-Species Competition-Diffusion Model With Free Boundaries, Shuang Liu, Xinfeng Liu

Faculty Publications

The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population and with competition of two species. To solve these systems numerically, new numerical challenges arise from the competition of two species due to the interaction of their free boundaries. On the one hand, extremely small time steps are usually needed due to the stiffness of the system. On the other hand, it is always difficult to efficiently and accurately handle the moving boundaries especially with competition of two species. To overcome these numerical difficulties, we introduce …

Mathematical Modelling Of English Coulee: Tanks In Series, Matthew Picklo

Essential Studies UNDergraduate Showcase

In the scope of the College of Arts and Science project: “Coulee Cleanway: Modelling and Analysis of the English Coulee Physiochemical Environment, UND Campus, Grand Forks”, a mathematical model attempting to describe the transportation of dissolved species within the English Coulee was developed based on “Tanks in Series”. By dividing the channel into discrete regions, a governing system of equations derived from conservation of mass equations and well-mixed assumptions is used to describe the spatial and temporal changes in concentration. The resulting system of differential equations was solved by a Runge-Kutta 4 numerical method, which allowed for the addition of …

Creating A Predictive Model For Flowering Of Virginia Orchid, Cypripedium Pubescens, Emily Horton

Undergraduate Theses and Capstone Projects

This research investigates the native Virginia orchid, Cyprepedium pubescens, or the large yellow lady-slipper. Researchers at Lynchburg College, located in central Virginia, collected orchid activity data over the span of nine years from 2006-2014. This data included the following information: when the first sprout appeared, the number of leaves, the number of flowers, and the number of flowers per each plant. Using collected data about nine orchids on the campus of Lynchburg College as a basis, we wanted create a model that would predict when we might see flowering on a yearly basis. Flowering is important because researchers are investigating …

Statistical Modeling Of Financial Time Series, Ranju Karki

Student Theses and Dissertations

This thesis presents a comprehensive report of my research in financial time series analysis from Fall 2017 to Spring 2018. It is focused on two main topics: clustering and modeling of financial time dependent information. The weighted five-day moving arc length is used as a measure of volatility, and we applied self-organizing maps to cluster the subject information. We perform a clustering procedure of financial time dependent information using several lag values, and Apple Incorporation and Google as the leading stocks. As a result, we discovered that there are others financial time dependent information present in the same cluster with …

Rubik’S Cube: The Invisible Solve, Allen Charest

Honors Program Theses and Projects

The Rubik’s Cube is one of the most popular and recognizable puzzles ever made. In this research, we use group theory to identify and analyze the different solutions for the Rubik’s Cube and its variations. Since they cannot be seen on a standard Rubik’s Cube, these different solutions are called invisible solves. But by putting specialized labels on each of the center pieces of a Rubik’s Cube, we are able to track each of the invisible solves and see how they are different from one another. Dependent on the size of the Rubik’s Cube, the number of distinct invisible solves …

Spillover Modes In Multiplex Games: Double-Edged Effects On Cooperation And Their Coevolution, Tommy Khoo, Feng Fu, Scott Pauls

Dartmouth Scholarship

In recent years, there has been growing interest in studying games on multiplex networks that account for interactions across linked social contexts. However, little is known about how potential cross-context interference, or spillover, of individual behavioural strategy impact overall cooperation. We consider three plausible spillover modes, quantifying and comparing their effects on the evolution of cooperation. In our model, social interactions take place on two network layers: repeated interactions with close neighbours in a lattice, and one-shot interactions with random individuals. Spillover can occur during the learning process with accidental cross-layer strategy transfer, or during social interactions with errors in …

Generalized Multiplicities Of Edge Ideals, Alie Alilooee, Ivan Soprunov, Javid Validashti

Mathematics and Statistics Faculty Publications

We explore connections between the generalized multiplicities of square-free monomial ideals and the combinatorial structure of the underlying hypergraphs using methods of commutative algebra and polyhedral geometry. For instance, we show that the j-multiplicity is multiplicative over the connected components of a hypergraph, and we explicitly relate the j-multiplicity of the edge ideal of a properly connected uniform hypergraph to the Hilbert–Samuel multiplicity of its special fiber ring. In addition, we provide general bounds for the generalized multiplicities of the edge ideals and compute these invariants for classes of uniform hypergraphs.

Reflection Functors In The Representation Theory Of Quivers, Danika Van Niel

Renée Crown University Honors Thesis Projects - All

The paper "Coxeter Functors and Gabriel's Theorem" written by I.N. Bernstein, I.M. Gel'fand, and V.A. Ponomarev explores the concept of reflection functors. A thorough proof of several results used by Bernstein et al in their paper is presented. The focus is on the category of representations and reflection functors, both negative and positive. The quadratic form is the bridge between the results on quivers and the techniques of Lie algebras. The Dynkin diagrams mentioned in Gabriel's Theorem are discussed.

Global Stability For A 2n + 1 Dimensional Hiv/Aids Epidemic Model With Treatments, Olusegun Michael Otunuga

Mathematics Faculty Research

In this work, we derive and analyze a 2n + 1-dimensional deterministic differential equation modeling the transmission and treatment of HIV (Human Immunodeficiency Virus) disease. The model is extended to a stochastic differential equation by introducing noise in the transmission rate of the disease. A theoretical treatment strategy of regular HIV testing and immediate treatment with Antiretroviral Therapy (ART) is investigated in the presence and absence of noise. By defining R0, n, Rt, n and Rt,n as the deterministic basic reproduction number in the absence of ART treatments, deterministic basic reproduction number in the presence of …

Projective Geometry Associated To Some Quadratic, Regular Algebras Of Global Dimension Four, Derek C. Tomlin

Mathematics Dissertations - Archive

The attempted classification of regular algebras of global dimension four, so-called quantum P³s, has been a driving force for modern research in noncommutative algebra. Inspired by the work of Artin, Tate, and Van den Bergh, geometric methods via schemes of d-linear modules have been developed by various researchers to further their classification. In this thesis, we compute and analyze the line scheme of two families of algebras -- for both families, almost every algebra can be considered a candidate for a generic quadratic quantum P³. For the first family of algebras, we find that, viewed as a closed subscheme of …

Resistance To Peer Influence Moderates The Relationship Between Perceived (But Not Actual) Peer Norms And Binge Drinking In A College Student Social Network, Graham T. Diguiseppi, Matthew K. Meisel, Sara G. Balestrieri, Miles Q. Ott, Melissa J. Cox, Melissa A. Clark, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

Introduction: Adolescent and young adult binge drinking is strongly associated with perceived social norms and the drinking behavior that occurs within peer networks. The extent to which an individual is influenced by the behavior of others may depend upon that individual’s resistance to peer influence (RPI).

Methods: Students in their first semester of college (N = 1323; 54.7% female, 57% White, 15.1% Hispanic) reported on their own binge drinking, and the perceived binge drinking of up to 10 important peers in the first-year class. Using network autocorrelation models, we investigated cross-sectional relationships between participant’s binge drinking frequency and the perceived …

Relations Between Theta Functions Of Genus One And Two From Geometry, Thomas Hill

Undergraduate Honors Capstone Projects

Genus-two curves with special symmetries are related to pairs of genus-one curves by two and three-sheeted ramified coverings. This classical work dates back to early 20th century and is known as Jacobi and Hermite reduction. Jacobians of genus-two curves can be used to construct complex two-dimensional complex projective manifolds known as Kummer surfaces. On the other hand, the defining coordinates and parameters of both elliptic curves and Kummer surfaces can be related to Riemann Theta functions and Siegel Theta functions, respectively. This result goes back to the seminal work of Mumford in the 1980s. We use the geometric relation between …

Mindset, Attitudes, And Success In Statistics, Matthew Isaac

Undergraduate Honors Capstone Projects

Students in many disciplines are required to take an introductory statistics course while pursuing a college education. Despite the utility of statistical methods in future research and career pursuits, many students have negative views of statistics. We are interested in how students' mindsets and attitudes towards statistics impact their performance in an undergraduate statistics course. We administered a survey to students in several undergraduate statistics courses at Utah State University. This survey included questions addressing mathematics experience, attitudes towards statistics, mindset, and course performance. We observed that the majority of students indicated the presence of a growth mindset and positive …

A Series Of Papers On Detecting Examinees Who Used A Flawed Answer Key, Marcus W. Scott

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

One way that examinees can gain an unfair advantage on a test is by having prior access to the test questions and their answers, known as preknowledge. Determining which examinees had preknowledge can be a difficult task. Sometimes, the compromised test content that examinees use to get preknowledge has mistakes in the answer key. Examinees who had preknowledge can be identified by determining whether they used this flawed answer key. This research consisted of three papers aimed at helping testing programs detect examinees who used a flawed answer key.

The first paper developed three methods for detecting examinees who used …

Three Environmental Fluid Dynamics Papers, Eden Furtak-Cole

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Three papers are presented, applying computational fluid dynamics methods to fluid flows in the geosciences. In the first paper, a numerical method is developed for single phase potential flow in the subsurface. For a class of monotonically advancing flows, the method provides a computational savings as compared to classical methods and can be applied to problems such as forced groundwater recharge. The second paper investigates the shear stress reducing action of an erosion control roughness array. Incompressible Naiver-Stokes simulations are performed for multiple wind angles to understand the changing aerodynamics of individual and grouped roughness elements. In the third paper, …

Supporting English Language Learners Inside The Mathematics Classroom: One Teacher’S Unique Perspective Working With Students During Their First Years In America, Amy Marie Fendrick

Research and Evaluation in Education, Technology, Art, and Design

Reflecting upon my personal experiences teaching mathematics to English Language Learners (ELL) in a public high school in Lincoln, Nebraska, this essay largely focuses on the time I spent as the only Accelerated Math teacher in my school building. From 2012 – 2017, I taught three different subjects at this high school: Advanced Algebra, Algebra, and Accelerated Math. This essay highlights why I chose to become a math and ELL teacher, as well as the challenges, issues, struggles, and successes I experienced during my time teaching. I focus on the challenges I faced teaching students who did not share my …

A Study On The Rotational B-Family Of Equations, Emel Bolat

Mathematics Dissertations - Archive

In this thesis, we study a mathematical model of long-crested water waves propagating in one direction with the effect of Earth's rotation near the equator by following the formal asymptotic procedures. Firstly, we derive a new model equation called the rotational b-family of equations by using the Camassa-Holm approximation of the two-dimensional incompressible and irrotational Euler equations. Secondly,we establish that the local well-posedness of the Cauchy problem for the rotational b-family of equations on the Sobolev space H⁸, for s > 3=2. In addition, we study the effects of the Coriolis force and nonlocal higher nonlinearities on blow-up criteria and wave-breaking …

Asymptotic Properties Of The Deconvolution Kernel Density Estimate Based On 2-Dependent Error Structure With Applications To Remaining Useful Life Problems In Reliability Theory, Geoffrey H. Schuette

Mathematics Dissertations - Archive

This thesis is motivated from an engineering question, which led us to the deconvolution problem with a dependent error structure. We establish a deconvolution kernel density estimator by adapting the methods of kernel density estimates and Fourier Transforms. In this approach, the contaminated data with additive random errors are assumed dependent and satisfying smooth or super smooth conditions. Under both smooth and supper smooth conditions, we derived: 1. optimal rates of convergence in terms of mean integrated squared error for deconvolution kernel density estimator; 2. the limiting distribution of the estimator.

Scattering And Inverse Scattering On The Line For A First-Order System With Energy-Dependent Potentials, Ramazan Ercan

Mathematics Dissertations - Archive

A first-order system of two linear ordinary differential equations is analyzed. The linear system contains a spectral parameter, and it has two coefficients that are functions of the spatial variable ��. Those two functions act as potentials in the linear system and they also linearly contain the spectral parameter λ, and hence they are referred to as energy-dependent potentials. Such a linear system arises in the solution to a pair of integrable nonlinear partial differential equations (known as the derivative nonlinear Schrödinger equations) via the so-called inverse scattering transform method. The direct and inverse problems for the corresponding first-order linear …

Secondary Mathematics Teachers’ Planned Approaches For Teaching Standard Deviation, Maryann E. Huey, Joe Champion, Stephanie Casey, Nicholas H. Wasserman

Mathematics Faculty Publications and Presentations

Research-based guidelines for learning variation exist (e.g., Franklin et al., 2007; Garfield, delMas, & Chance, 2007), but little is known about how teachers plan to teach standard deviation, or how these plans align with recent recommendations. In this article, we survey lesson plans designed by inservice and preservice secondary mathematical teachers. We report on the accuracy, technology usage, and visual representations in the lesson plans. We consider how many elements are used, the level of conceptual development, and the mathematical nature. Findings support differences between preservice and master’s level students in education, as well as a tendency by in-service teachers …

A Logistic Regression Analysis Of First-Time College Students’ Completion Rates At The University Of Southern Mississippi, Jesse Homer Robinson

Honors Theses

The demand for employees with a college degree is steadily on the rise in a plethora of competitive job markets throughout the United States. This increase in demand has aided in the increasing college enrollment rates throughout the country. However, unlike enrollment trends, the rate of college completion has not had the same fortunate rise.

The goal of this study is to research and compare differences among those first-time college students who completed college within four years, six years, or did not complete. The primary source for data in this study was the Office of Institutional Research at USM. Both …

Gravitational-Wave Memory From Black Hole And Neutron Star Mergers, Matthew Karlson

Theses, Dissertations and Culminating Projects

The detection of gravitational waves from binary black hole and binary neutron star mergers has ushered in a new age of observational astronomy. Anticipation of detection from these coalescing compact binaries has led to the development of models for comparison using analytical and numerical techniques. Typically, these methods model gravitational-wave signals as small oscillations that grow over time, reach some maximum value, and eventually decay to zero. However, these models are incomplete: compact binaries can emit gravitational waves that decay to a non-zero value. This phenomenon is known as the gravitational-wave memory. In particular, the signal from compact binaries displays …

The Dispersion Process For Particles On Graphs, Adam Cartisano

Theses, Dissertations and Culminating Projects

In this thesis, we study a process called Dispersion, in which M particles are dispersed among the vertices of a graph G. All particles initially occupy a single vertex called the origin vertex. At each discrete time step, all particles which share a vertex with at least one other, move to a randomly (though not necessarily uniformly) chosen neighbor of the currently occupied vertex. The process ends when each vertex is occupied by at most one particle. We will explore various aspects of the Dispersion process. One of these is the expected time to completion, E[T_Disp] for 3 …

Magic Squares Of Squares Of Order Three Over Finite Fields, Giancarlo Labruna

Theses, Dissertations and Culminating Projects

A magic square M over an integral domain D is a 3 x 3 matrix with entries from D such that the elements from each row, column, and diagonal add to the same sum. If all the entries in M are perfect squares in D, we call M a magic square of squares over D. Martin LaBar raised an open question in 1984, which states, “Is there a magic square of squares over the ring Z of the integers which has all the nine entries distinct?” We approach to answering a similar question in case D is a finite field. …

Nonparametric Estimation Of Time Series Volatility Model Estimation, Teng Tu

Arts & Sciences Graduate Student Theses and Dissertations

In this article we consider two estimation methods of a non-parametric volatility model with autoregressive error of order two. The first estimation method based on the two- lag difference. To get a better result, we consider the second approach based on the general quadratic forms. For illustration, we provided several data sets from different simulation models to support the procedures of both two methods, and prove that the second approach can make a better estimation.

Matrix Methods Of Data Analysis, Kaiye Yu

Renée Crown University Honors Thesis Projects - All

Nowadays, data is playing a bigger part than ever before in the history. In order to get more useful information, methods involving matrix are powerful. There are different algorithms that are able to help one to learn the information they need from data. In this study, there are two main algorithms that I will focus on. One is Pagerank algorithm, a traditional algorithm that was applied to searching engine decades ago in Google. However, Pagerank algorithm has certain limits in providing information like covariance between different factors. Thus, another method is also studied, which is principal component analysis (PCA), while …

Preservice Mathematics Teachers' Conceptions And Enactments Of Modeling Standards, Hyunyi Jung, Jill Newton

Mathematics, Statistics and Computer Science Faculty Research and Publications

Mathematical modeling has been highlighted recently as Common Core State Standards for Mathematics [CCSSM] included Model with Mathematics as one of the Standards for Mathematical Practices [SMP] and a modeling strand in the high school standards. This common aspect of standards across most states in the U.S. intended by CCSSM authors and policy makers seems to mitigate the diverse notions of mathematical modeling. When we observed secondary mathematics preservice teachers [PSTs] who learned about the SMP and used CCSSM modeling standards to plan and enact lessons, however, we noted differences in their interpretations and enactments of the standards, despite their …

Characterizations And Infinite Divisibility Of Certain Recently Introduced Distributions Iv, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Certain characterizations of recently proposed univariate continuous distributions are presented in different directions. This work contains a good number of reintroduced distributions and may serve as a source of preventing the reinvention and/or duplication of the existing distributions in the future.