Mathematics Commons^™

Inference For Multiple Utility In Time-Dependent Choice Pairs Under Copula-Based Models, Sasanka Adikari

Mathematics & Statistics Theses & Dissertations

Models for discrete choice experiments (DCE) are frequently used to analyze consumer choices about products and services. A family of DCE, best-worst scaling experiments, offers more in-depth insights into consumer preferences by eliciting a best and worst choice from a set of options, rather than just a single preference. Traditional approaches often assume that choices are mutually exclusive over time, which may not always be the case. This dissertation proposes a novel model for DCE that takes into account the changing nature of consumer choices over time and the priority constraint of transition probabilities. The model introduces a copula combination …

Cohen-Macaulay Properties Of Closed Neighborhood Ideals, Jackson Leaman

All Theses

This thesis investigates Cohen-Macaulay properties of squarefree monomial ideals, which is an important line of inquiry in the field of combinatorial commutative algebra. A famous example of this is Villareal’s edge ideal [11]: given a finite simple graph G with vertices x1, . . . , xn, the edge ideal of G is generated by all the monomials of the form xixj where xi and xj are adjacent in G. Villareal’s characterization of Cohen-Macaulay edge ideals associated to trees is an often-cited result in the literature. This was extended to chordal and bipartite graphs by Herzog, Hibi, and Zheng in …

Tribute To Gene Chase, Calvin Jongsma

Faculty Work Comprehensive List

Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

Faculty Work Comprehensive List

Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

The Development Of Sociomathematical Norms In The Transition To Tertiary Exam-Oriented Individualistic Mathematics Education In An East Asian Context, Woong Lim, Hyunkyoung Yoon, Younggon Bae, Oh Nam Kwon

School of Mathematical & Statistical Sciences Faculty Publications

This study investigates social, mathematical, and sociomathematical norms perceived by college students in an engineering mathematics course and examines the students’ sense of mathematics as signals of individual merit. Data sources include a survey and one-on-one interviews with 38 students. The findings help illustrate student perceptions of academic social norms in a large-lecture course represented by the acquisition model of learning in college, detached from communal and collaborative disciplinary practices. Findings provide insights into the local educational context of an East Asian country as a case study when exam-oriented mathematics is institutionalized as normalcy.

An Investigative Study Of Potential Factors That Contribute To High Under-Five Mortality Rate In Africa, David Banahene

Theses and Dissertations

Under-Five Mortality remains a significant challenge in developing countries, especially in Africa. The United Nations has implemented various measures, such as the Millennium Development Goals (MDGs) and Sustainable Development Goals (SDGs), to combat this issue. However, the success of these initiatives is uncertain. Our study investigates the social, economic, and environmental factors contributing to high Under-Five Mortality rates in African countries, using data from 1985 to 2020.We analyzed 53 African countries, partitioning them into training (45 countries) and testing data (8 countries). We conducted Multiple Linear Regression analysis and assessed the model performance using R-squared values and Root-Mean-Squared-Error (RMSE) values. …

Effects Of Missing Data Imputation Methods On Univariate Time Series Forecasting With Arima And Lstm, Nicholas Niako

Theses and Dissertations

Missing data are common in real-life studies and missing observations within the univariate time series cause analytical problems in the flow of the analysis. Imputation of missing values is an inevitable step in the analysis of every incomplete univariate time series data. The reviewed literature has shown that the focus of existing studies is on comparing the distribution of imputed data. There is a gap of knowledge on how different imputation methods for univariate time series data affect the fit and prediction performance of time series models. In this work, we evaluated the predictive performance of autoregressive integrated moving average …

Uniform Distributions On Curves And Quantization, Joseph Rosenblatt, Mrinal Kanti Roychowdhury

School of Mathematical & Statistical Sciences Faculty Publications

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n -means and the n th quantization errors for different …

Propuesta De Un Modelo De Enseñanza En Las Matemáticas Enfocado En La Solución De Problemas En El Nivel Secundario En Puerto Rico, Carlos J. Colon Rivera

Theses and Dissertations

El propósito del estudio fue proponer un modelo educativo enfocado en la solución de problemas matemáticos en el nivel secundario, y se realizó la revisión sistemática para evaluarlo. El marco teórico incluyó teorías heurísticas y modelos educativos. La metodología de seis fases que se empleó en este estudio, incluyendo la formulación de preguntas investigativas, búsqueda de literatura, selección de investigaciones, levantamiento de información, análisis y resumen de resultados y exposición y discusión de estos. Se siguieron guías para revisiones sistemáticas y criterios de inclusión y exclusión para evaluar la efectividad de modelos didácticos en la disciplina de matemáticas con énfasis …

The Sharp Bounds Of A Quasi-Isometry Of P-Adic Numbers In A Subset Real Plane, Kathleen Zopff

Undergraduate Theses

P-adic numbers are numbers valued by their divisibility by high powers of some prime, p. These numbers are an important concept in number theory that are used in major ideas such as the Reimann Hypothesis and Andrew Wiles’ proof of Fermat’s last theorem, and also have applications in cryptography. In this project, we will explore various visualizations of p-adic numbers. In particular, we will look at a mapping of p-adic numbers into the real plane which constructs a fractal similar to a Sierpinski p-gon. We discuss the properties of this map and give formulas for the sharp bounds of its …

Multiple Solutions Of P-Fractional Schrödinger-Choquard-Kirchhoff Equations With Hardy-Littlewood-Sobolev Critical Exponents, Xiaolu Lin, Shenzhou Zheng, Zhaosheng Feng

School of Mathematical & Statistical Sciences Faculty Publications

In this article, we are concerned with multiple solutions of Schrödinger-Choquard-Kirchhoff equations involving the fractional p -Laplacian and Hardy-Littlewood-Sobolev critical exponents in R N . We classify the multiplicity of the solutions in accordance with the Kirchhoff term M ( ⋅ ) and different ranges of q shown in the nonlinearity f ( x , ⋅ ) by means of the variational methods and Krasnoselskii’s genus theory. As an immediate consequence, some recent related results have been improved and extended.

Theory Of Invariant Manifold And Foliation And Uniqueness Of Center Manifold Dynamics, Bo Deng

Department of Mathematics: Faculty Publications

Here we prove that the dynamics on any two center-manifolds of a fixed point of any C^k,1 dynamical system of finite dimension with k ≥ 1 are C^k-conjugate to each other. For pedagogical purpose, we also extend Perron’s method for differential equations to diffeomorphisms to construct the theory of invariant manifolds and invariant foliations at fixed points of dynamical systems of finite dimensions.

The 2015 Ncaa Cost-Of-Attendance Stipend And Its Effects On Institutional Financial Aid Packages, Sara Greene

Honors Theses

In 2015, the National Collegiate Athletic Association (NCAA) allowed “Cost of Attendance” (COA) stipends to be offered to athletic recruits for Division I schools. These stipends are intended to allow schools to grant aid to student-athletes beyond a full-ride scholarship to cover additional costs imposed on student-athletes. These stipends created an opportunity for the “Autonomy” Power 5 programs to utilize a competitive tactic to try to win over the top recruits. There is evidence that these COA stipends have caused an increase in the estimated cost of attendance reported by the university. This paper examines if the COA stipends have …

The Parental Labor Gap: The Impact Of Daycare Access On The Parental Labor Force During The Covid-19 Pandemic, Acacia Wyckoff

Honors Theses

In the two years since the COVID-19 pandemic began, the landscape for work has shifted dramatically. Many companies and employers switched to telework when the pandemic hit, and many still do not require workers to come into the office. Research suggests these COVID-induced changes have led to a closing of the gap in childcare duties between men and women in households. Comparing parents in positions with telework eligibility versus in-person positions, Heggeness and Suri (2022) found that while telework improved the labor participation rate of mothers slightly, there was still a major gap in labor force participation between mothers and …

Brill--Noether Theory Via K3 Surfaces, Richard Haburcak

Dartmouth College Ph.D Dissertations

Brill--Noether theory studies the different projective embeddings that an algebraic curve admits. For a curve with a given projective embedding, we study the question of what other projective embeddings the curve can admit. Our techniques use curves on K3 surfaces. Lazarsfeld's proof of the Gieseker--Petri theorem solidified the role of K3 surfaces in the Brill--Noether theory of curves. In this thesis, we further the study of the Brill--Noether theory of curves on K3 surfaces.

We prove results concerning lifting line bundles from curves to K3 surfaces. Via an analysis of the stability of Lazarsfeld--Mukai bundles, we deduce a bounded version …

Total Dominator Coloring On The Queen's Graph, Fiona Smith

Celebrating Scholarship and Creativity Day (2018-)

A chess board of size m x n can be translated to a Queen's graph in which vertices are adjacent if their squares on the board are in the same row, column, or diagonal. In this research, the total dominator coloring of a Queen's graph is explored, yielding a conjecture for the general m x n case.

Employee Attrition: Analyzing Factors Influencing Job Satisfaction Of Ibm Data Scientists, Graham Nash

Symposium of Student Scholars

Employee attrition is a relevant issue that every business employer must consider when gauging the effectiveness of their employees. Whether or not an employee chooses to leave their job can come from a multitude of factors. As a result, employers need to develop methods in which they can measure attrition by calculating the several qualities of their employees. Factors like their age, years with the company, which department they work in, their level of education, their job role, and even their marital status are all considered by employers to assist in predicting employee attrition. This project will be analyzing a …

Analysis Of The Discrete Cosine Transform Coefficients, Dillon C. Mckinley

ATU Scholars Symposium

No abstract provided.

Symmetric Functions Algebras (Sfa) Ii: Induced Matrices, Philip Feinsilver

Journal of Stochastic Analysis

No abstract provided.

Defining Characteristics That Lead To Cost-Efficient Veteran Nba Free Agent Signings, David Mccain

Honors Projects in Mathematics

Throughout the history of the NBA, decisions regarding the signing of free agents have been riddled with complexity. Franchises are tasked with finding out what players will serve as optimal free agent signings prior to seeing them perform within the framework of their team. This study hypothesizes that the adequacy of an NBA free agent signing can be modeled and predicted through the implementation of a machine learning model. The model will learn the necessary information using training and testing data sets that include various player biometrics, game statistics, and financial information. The application of this machine learning model will …

Using A Distributive Approach To Model Insurance Loss, Kayla Kippes

Departmental Honors & Graduate Capstone Projects

Insurance loss is an unpredicted event that stands at the forefront of the insurance industry. Loss in insurance represents the costs or expenses incurred due to a claim. An insurance claim is a request for the insurance company to pay for damage caused to an individual’s property. Loss can be measured by how much money (the dollar amount) has been paid out by the insurance company to repair the damage or it can be measured by the number of claims (claim count) made to the insurance company. Insured events include property damage due to fire, theft, flood, a car accident, …

The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak

Honors Projects

So often in the education of Mathematics does instruction solely consist of the lecture. While this can be an effective method of communicating the ideas of math, it leaves much to be desired in gathering the interest and intrigue of those who have not dedicated their lives to the study of the subject. Theatre, by contrast, is a tool that has been used in the past as means of teaching complicated and difficult to understand moral and emotional subjects. While Theatre and Mathematics have been used in combination many times in the past, it is most often done in the …

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

A Growth Mindset: Fostering Resilience And Success In The Middle School Mathematics Classroom, Mary Jicha

Liberty University Research Week

Undergraduate

Applied

Analysis Of An Seir Model With Non-Constant Population, Kylar Byrd, Tess Tracy, Sunil Giri, Swarup Ghosh

Student Research

Analysis of an SEIR model with Non-Constant Population
by Kylar Byrd and Tess Tracy, with Dr. Sunil Giri and Dr. Swarup Ghosh.

Mathematical modeling can be useful in helping us to understand disease dynamics. Epidemiological models consist of differential equations with variables and parameters defined to portray these dynamics. We will be presenting the mathematics involved in formulating and analyzing a model for a disease such as influenza. We will first explain a simple SIR model, and then we will introduce our model. We will be looking at an SEIR model that incorporates the use of an exposed class as …

A Discrete Morse Approach For Computing Homotopy Types: An Exploration Of The Morse, Generalized Morse, Matching, And Independence Complexes, Connor Donovan

Mathematics Honors Papers

In this thesis, we study possible homotopy types of four families of simplicial complexes–the Morse complex, the generalized Morse complex, the matching complex, and the independence complex–using discrete Morse theory. Given a simplicial complex, K, we can construct its Morse complex from all possible discrete gradient vector fields on K. A similar construction will allow us to build the generalized Morse complex while considering edges and vertices will allow us to construct the matching complex and independence complex. In Chapter 3, we use the Cluster Lemma and the notion of star clusters to apply matchings to families of Morse, generalized …

Mean Value Theorems For Analytic Functions, Lubomir Markov

Mathematics Colloquium Series

Questions related to the location of zeros and critical points of classes of functions (polynomial, entire, analytic in a certain domain, etc.) are fundamentally important in Analysis. In this talk, he will examine some interesting mean value theorems concerning real and complex analytic functions, focusing on the complex case. He will also present sharper versions of two known results. Part of the presentation will pay tribute to the remarkable contributions of several classical Bulgarian mathematicians to problems involving the distribution of zeros of a function and its derivative(s).

Length Bias Estimation Of Small Businesses Lifetime, Simeng Li

Honors Theses

Small businesses, particularly restaurants, play a crucial role in the economy by generating employment opportunities, boosting tourism, and contributing to the local economy. However, accurately estimating their lifetimes can be challenging due to the presence of length bias, which occurs when the likelihood of sampling any particular restaurant's closure is influenced by its duration in operation. To address the issue, this study conducts goodness-of-fit tests on exponential/gamma family distributions and employs the Kaplan-Meier method to more accurately estimate the average lifetime of restaurants in Carytown. By providing insights into the challenges of estimating the lifetimes of small businesses, this study …

Cranks For Partitions With Bounded Largest Part, Dennis Eichhorn, Brandt Kronholm, Acadia Larsen

School of Mathematical & Statistical Sciences Faculty Publications

For 80 years, Dyson’s rank has been known as the partition statistic that witnesses the first two of Ramanujan’s celebrated congruences for the ordinary partition function. In this paper, we show that Dyson’s rank actually witnesses families of partition congruences modulo every prime . This comes from an in-depth study of when a “multiplicity-based statistic” is a crank witnessing congruences for the function p ` n, m˘ , which enumerates partitions of n with parts of size at most m. We also show that as the modulus increases, there is an ever-growing collection of distinct multiplicity-based cranks witnessing these same …

Bridging The Chasm Between Fundamental, Momentum, And Quantitative Investing, Allen Hoskins, Jeff Reed, Robert Slater

SMU Data Science Review

A chasm exists between the active public equity investment management industry's fundamental, momentum, and quantitative styles. In this study, the researchers explore ways to bridge this gap by leveraging domain knowledge, fundamental analysis, momentum, crowdsourcing, and data science methods. This research also seeks to test the developed tools and strategies during the volatile time period of 2020 and 2021.