Physical Sciences and Mathematics Commons^™

An Exploratory Study: Determining Significant Predictors Of Academic Success On The Ohio State End Of Course Assessment In Algebra 1 For Students With Learning Disabilities And Students Identified As Gifted, Nicholas Sesonsky, Jonathan Mccullough

Master of Science in Mathematics

Since the COVID-19 pandemic, hybrid and online instruction have become more prominent formats in the educational system. This study aimed to focus specifically on students with learning disabilities and students who are identified as gifted. Based on these two subpopulations and prior literature, instructional method, class size, attendance rate, and prior academic performance were selected as potential impactful measures of students' academic success. Academic success for this study was based on the Algebra 1 Ohio State End of Course Assessment while prior academic performance was based on the Seventh-Grade Ohio State End of Course Assessment, and Ohio’s School Report Card …

"The Effect Of Students’ Place Of Residence, Length Of Time In A District, Race, And Ses On Academic And Behavioral Success", Andrew King

Master of Science in Mathematics

This study intended to determine if place of residence, length of time in a district, race, and socioeconomic status were statistically significant predictors of academic success and disciplinary issues. The study took place in the Mississinawa Valley School District, a small district in western Ohio consisting of a mix of students from both rural and urban/suburban areas. Existing literature on districts comprising rural and urban portions was missing, allowing this study to fill a gap in research. A sample of 2,002 students from the school from 2008 to 2023 was analyzed to answer two primary research questions. Three separate multiple …

Are Prior Academic Achievement, Attendance, Athletic Participation, And Demographics Significant Predictors On Iowa State Assessment Performance?, David Jabs

Master of Science in Mathematics

This research study examined if prior academic achievement, attendance, athletic participation and demographics were significant factors of IOWA State Assessment scores. The findings indicated that there were three significant factors. The three factors that were significant were prior IOWA State Assessment Scores, the number of tardies and the current GPA. This research study took place at a small private school in Cleveland Heights, OH. The analysis was completed by three different approaches. The first was a multiple regression analysis which determined the three factors already mentioned. A correlation study and an independent sample t-test were also performed. This research is …

Does Grade Level Acceleration In Math Increase Act Testing Performance When Controlling For Other Factors In One School System?, Stephen Hubek

Master of Science in Mathematics

School districts across the country are currently in the debate on how to properly accelerate students in math. In the Pleasant Local School District students in this study were accelerated through the method of grade level acceleration starting in their 6th grade year in math. This acceleration involves skipping grade levels in math based on a student’s abilities in math and classroom performance. Accelerated students in Pleasant Local Schools complete Algebra 2 via the high school curriculum and then move to CCP courses to complete through Calculus if they choose. The purpose of this study is to answer the question: …

The Effects Of Tree Cover And Urban Greenspace On Covid-19 Severity In Seattle, Wa, Kristin Harpster

Master of Science in Mathematics

This thesis explores the relationship between urban greenspace and forestry and COVID-19 severity in Seattle, Washington. Urban greenspace and forestry has been shown to play an important role in reducing air pollution, which can exacerbate COVID-19 severity. Community demographics have been shown to affect the greenspace-health relationship, therefore demographic information was included in the study. Four logistic models were created to examine the relationship between urban greenspace and forestry and COVID-19 severity. Two models examined the relationship between greenspace and COVID-19 hospitalizations and mortality respectively. A further two models included community demographics as predictor variables. The findings indicated that tree …

Effectiveness Of Corequisite Remediation: A Study On Introductory Statistics And College Algebra, Sydney Crawford, Sarah Grimm

Master of Science in Mathematics

The purpose of this study is to evaluate the effectiveness of remediation in Introduction to Statistics and College Algebra at Shawnee State University (SSU). Focusing on students with an ACT score ranging from 15-17, this study examines the effectiveness of corequisite courses to see if these courses improve student success rates compared to prerequisite courses. The background of this study is rooted by the ongoing effort of colleges and universities to enhance student success by implementing different instructional strategies, such as corequisite remediation. Logistic regression techniques were used to analyze successful completion of gateway courses as an outcome of different …

Factors Affecting Standardized Test Scores: Internal And External Factors In Ohio School Districts, Denise Layne

Master of Science in Mathematics

The focus of this study was the internal and external school district factors that influence standardized test scores within the state of Ohio. This study also looked at differences in school characteristics between income classes as well as the current Black-White achievement gap in Ohio. The topics and analyses in this study were based off James Coleman’s 1966 report titled Equality of Educational Opportunity. Data was collected from public online databases, and all Ohio school districts with sufficient data were used. Findings regarding factors that influence test scores suggest that external school district factors play a larger role in test …

Predicting Academic Achievement From Extracurricular Engagement And Sense Of Belonging, Nathan Corum

Master of Science in Mathematics

This research study examined the relationships between extracurricular activity engagement, a student’s sense of belonging to school and academic achievement. Research was conducted at a suburban high school in Ohio, with data being collected from student surveys and district provided informational data. The goal was to see if there were positive connections between these items to better help the district in determining further programs to improve student achievement. Findings indicated that sense of belonging was a significant predictor of academic achievement for the sample. However, extracurricular engagement was not found to be a significant predictor of academic achievement. Further, there …

Cognitive Processes, Self-Efficacy, And Environment: A Comprehensive Study Of Mathematics Achievement In A Private International School In China, Alexandra Bumbles, Abreu Carvalho

Master of Science in Mathematics

The purpose of this study was to investigate the complex interplay between cognitive processes, self-efficacy, and environmental factors on academic achievement in mathematics within a private international school in China. Utilizing the Social Cognitive Theory as a theoretical framework, this research aimed to elucidate the extent to which these factors serve as significant predictors of mathematics achievement. The study involved a sample of 410 students from Years 6 to 12, with data collected through While the study provides substantial insights, several limitations were noted, including the restricted generalizability due to the specific sample, potential biases from self-reported data, and the …

The Influence Of Early Introduction To Algebra On Mathematics Achievement In A Rural School District In Ohio, Brittany Burns

Master of Science in Mathematics

Algebra I is a foundation for mathematical learning. The timing of enrollment is arguably a massive factor in mathematical success. The timing in which a student enrolls in Algebra I could shape their future in education and their career. This thesis examines the effects of 8^th grade Algebra I enrollment versus 9th-grade Algebra enrollment regarding standardized test scores. The research finds that students perform higher on standardized test scores when they enroll in Algebra I in the 8th grade in comparison to students who enroll in Algebra I in the 9th grade. This finding is beneficial for the ultimate …

Gridiron Insights: Predicting Gameday Outcomes Through Regression Analysis In College Football, Ethan Reyes, Justin Beal

Master of Science in Mathematics

This research investigates the predictive power of the changes in spread, over/under betting lines, and home field advantage in determining whether the favored team in a college football betting market will cover the spread. The study examines three key factors: the change in the betting spread, the change in the over/under line, and the home-field advantage of the favored team. Using a comprehensive dataset of betting data from Draft Kings and Bovada, the study uses logistical regression techniques to analyze the relationship between these variables and the favored team’s performance against the spread. Our findings indicate that fluctuations in the …

The Influence Of Teacher Experience On Project Lead The Way Test Scores, Emily Schmitz

Master of Science in Mathematics

roject Lead the Way (PLTW) is an organization that develops engineering curriculum for all grade levels. Research has been conducted on the curriculum and other STEM curriculum to determine student achievement levels and the factors that affect student achievement. These factors include teacher retention, teacher years of experience, student demographics, etc. Investigating how a teacher impacts their students learning can help schools understand the value of a seasoned teacher. With PLTW training having high costs it can make teacher retention a bigger concern. The Highland Prep Academies utilize PLTW curriculum and have about ten trained teachers across the three schools. …

Empirically Comparing The Performance Of Lda And Qda When Classifying Customer Sales Data With Different Properties Of Normality And Equality Of Covariance Matrices, Ayuk Egbe Bate-Eya

Master of Science in Mathematics

Discriminant analysis is a statistical technique used to classify data into different classes. Many studies have compared different methods used to classify data as regards their performance. This study compares Linear Discriminant Analysis and Quadratic Discriminant Analysis under varying conditions of normality and the equality of covariance matrices. More precisely, this study seeks to determine which of the two techniques is better when classifying datasets with different properties of normality and equality of covariance matrices and aims to determine whether normality and equality of covariance matrices influence the prediction performance of each method. This study processes online stores’ customer sales …

Analyzing Significant Predictors Of Graduation Rates At A Four- Year University, Charles Barrier Jr.

Master of Science in Mathematics

The subject of graduation rates is important for both students and educational institutions alike. Students want to attend a university where they are most likely to graduate, and institutions want to provide a learning environment that is best suited for retention and graduation. This study analyzes the data of 2139 students from Shawnee State University in Portsmouth, Ohio to determine if there exist any significant predictors of graduation likelihood amongst demographic, situational, and academic predictors. A logistic regression approach is utilized to identify significant variables, and in short, high school GPA rises to the top as a predictor. This implies …

The Influence Of Wealth On Academic Performance In Secondary Schools, Dean Banziger

Master of Science in Mathematics

The purpose of this study was to determine if wealth and financial investment in public education within communities plays a significant role in the academic performance of students in West Virginia secondary schools. West Virginia is an interesting example of academic success relative to the wealth of the state. The state of West Virginia has the third highest poverty rate (17.9%) and the second lowest Gross Domestic Product per capita of all fifty states and the District of Columbia (World Population Review, 2022). West Virginia ranks dead last in average SAT scores (College Board, 2022). This study seeks to determine …

Modeling The Development & Expression Of Political Opinion: A Zallerian Approach, Avery C. Ellis

Honors Projects

Research focused on John Zaller's famous RAS model of political opinion formation and change from "The Nature and Origins of Mass Opinion" (1992). Analyzed the mathematical and psychological underpinnings of the model, the first paper to do so in over fifteen years and the first to do so through an analysis of motivated reasoning and Bayesian reasoning. Synthesized existing critiques of Zaller's model and other literature to suggest ways to build on Zaller, utilizing fundamental reunderstandings of opinions and messages from political and mathematical perspectives. Found verification for Zaller's model, confirming its value, but also found support for the proposed …

An Approach To Multidimensional Discrete Generating Series, Svetlana S. Akhtamova, Tom Cuchta, Alexander P. Lyapin

Mathematics Faculty Research

We extend existing functional relationships for the discrete generating series associated with a single-variable linear polynomial coefficient difference equation to the multivariable case.

Machine Learning Approaches For Cyberbullying Detection, Roland Fiagbe

Data Science and Data Mining

Cyberbullying refers to the act of bullying using electronic means and the internet. In recent years, this act has been identifed to be a major problem among young people and even adults. It can negatively impact one’s emotions and lead to adverse outcomes like depression, anxiety, harassment, and suicide, among others. This has led to the need to employ machine learning techniques to automatically detect cyberbullying and prevent them on various social media platforms. In this study, we want to analyze the combination of some Natural Language Processing (NLP) algorithms (such as Bag-of-Words and TFIDF) with some popular machine learning …

Dynamics And Inverse Problems For Nonlinear Schrödinger Equations, Christopher Hogan

Doctoral Dissertations

"The cubic nonlinear Schrödinger equation (NLS) is a model of interest in the study of physical problems including nonlinear optics and Bose-Einstein condensates. Of particular interest is the study of cubic NLS with inhomogeneities such as localizations of the nonlinearity or terms introducing potential barriers. We first address some preliminaries and techniques useful in the study of the cubic NLS and its variations. We then consider the cubic NLS with a localized nonlinearity in dimensions d ≥ 2. We show that solutions with data given by small-amplitude wave packets accrue a nonlinear phase that determines the X-ray transform of the …

Farey Recursion And Hyperbolic Dehn Filling, Jose Ebenezer Martinez

Graduate Student Theses, Dissertations, & Professional Papers

In this work, we present a solution to William Thurston's edge gluing equations for Dehn fillings of hyperbolic 3-manifolds. This is done for triangulations that involve the layered solid torus. Our approach uses Farey recursive functions, and we present a Farey recursive function that provides a solution to the gluing equations for any hyperbolic Dehn filling admitting a triangulation by the layered solid torus. We provide examples that demonstrate our solution for multiple 3-manifolds, and study the roots of the corresponding Farey recursive polynomials. As an additional application of our solution, we provide a formula for the complex length of …

Solutions To The Kaluza-Klein Field Equations, Abel Eshete

All Graduate Theses, Dissertations, and Other Capstone Projects

This Alternate Paper Plan explores Kaluza-Klein theory, a multidimensional framework designed to unify Einstein’s gravitational field theory and Maxwell’s electromagnetic field theory. The objectives of this research can be summarized in two key areas: The first objective is to present a comprehensive introduction to the compactified Kaluza-Klein theory. The second aim involves the application of differential geometry, specifically E ́lie Cartan’s tetrad formalism, to derive exact solutions in two distinct scenarios: a. A Levi-Civita spacetime, b. A general spherical system. Furthermore, Lagrangian and Hamiltonian formalism are utilized to define stability conditions and describe gravitational lensing and Precession of Perihelion within …

Refining The Inverse Lipschitz Constant For Injective Relu Networks, Cole Rausch

Electronic Theses and Dissertations

In this thesis, we study the Inverse Lipschitz Constant (ILC) of injective ReLU layers. We study the tightness of the ILC lower bound established in Puthawala et al. Our approach has three components. First, we find that the conditions for injectivity on lines yield a weaker condition than the general condition given in Puthawala et al. Second, we perform numerical experiments to judge the tightness of the existing ILC lower bound and find that bound is overly conservative. Third, we identify the source of the potential slack in the proof of the existing ILC bound, and perform further numerical experiments …

Facilitating Mathematics And Computer Science Connections: A Cross-Curricular Approach, Kimberly E. Beck, Jessica F. Shumway, Umar Shehzad, Jody Clarke-Midura, Mimi Recker

Publications

In the United States, school curricula are often created and taught with distinct boundaries between disciplines. This division between curricular areas may serve as a hindrance to students' long-term learning and their ability to generalize. In contrast, cross-curricular pedagogy provides a way for students to think beyond the classroom walls and make important connections across disciplines. The purpose of this paper is a theoretical reflection on our use of Expansive Framing in our design of lessons across learning environments within the school. We provide a narrative account of our early work in using this theoretical framework to co-plan and enact …

Properties Of Skew-Polynomial Rings And Skew-Cyclic Codes, Kathryn Hechtel

Theses and Dissertations--Mathematics

A skew-polynomial ring is a polynomial ring over a field, with one indeterminate x, where one must apply an automorphism to commute coefficients with x. It was first introduced by Ore in 1933 and since the 1980s has been used to study skew-cyclic codes. In this thesis, we present some properties of skew-polynomial rings and some new constructions of skew-cyclic codes. The dimension of a skew-cyclic code depends on the degree of its generating skew polynomial. However, due to the skew-multiplication rule, the degree of a skew polynomial can be smaller than its number of roots and hence tricky to …

Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter

Graduate Research Showcase

“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …

A Little More On Ideals Associated With Sublocales, Oghenetega Ighedo, Grace Wakesho Kivunga, Dorca Nyamusi Stephen

Mathematics, Physics, and Computer Science Faculty Articles and Research

As usual, let RL denote the ring of real-valued continuous functions on a completely regular frame L. Let βL and λL denote the Stone- Čech compactification of L and the Lindelöf coreflection of L, respectively. There is a natural way of associating with each sublocale of βL two ideals of RL, motivated by a similar situation in C(X). In [12], the authors go one step further and associate with each sublocale of λL an ideal of RL in a manner similar to one of the ways one does it for sublocales of βL. The intent in this paper …

Folding And Embedding Cubical Complexes, Skye Rothstein

Senior Projects Spring 2024

Senior Project submitted to The Division of Science, Mathematics and Computing of Bard College.

In this project we study the folding properties of several special classes of cubical complexes. First, we look at polyominoids, which are arrangements of congruent squares in 3-space, glued edge-to-edge at 90° and 180° angles. We construct and analyze the mechanical configuration space for n-cell polyominoids, which is a graph with vertex set given by all n-cell polyominoids, where two vertices are connected by an edge if you can transform one into the other by one hinge movement. For n = 4, we provide a complete …

Computing The Canonical Ring Of Certain Stacks, Jesse Franklin

Graduate College Dissertations and Theses

We compute the canonical ring of some stacks. We first give a detailed account of what this problem means including several proofs of a famous historical example. The main body of work of this thesis expands on our article \cite{Franklin-geometry-Drinfeld-modular-forms} in describing the geometry of Drinfeld modular forms as sections of a specified line bundle on a certain stacky modular curve. As a consequence of that geometry, we provide a program: one can compute the (log) canonical ring of a stacky curve to determine generators and relations for an algebra of Drinfeld modular forms, answering a problem posed by Gekeler …

Ring Learning With Errors, Sarah Days-Merrill

Graduate College Dissertations and Theses

Over the last twenty years, lattice-based cryptosystems have gained interest due to their levelof security against attacks from quantum computers. The main cryptosystems are based on the hardness of Ring Learning with Errors (RLWE). The Learning with Errors (LWE) problems were first introduced in 2005 by Regev [Reg09] and in 2010, [LPR10] developed the Ring Learning with Errors (RLWE) problems as candidates for safe encryption against quantum computers. Let K be a number field with ring of integers OK. For a prime q, the RLWE problems rely on samples of the form (a, b) ∈ OK/qOK × OK/qOK where a …

A Corona Theorem For Multipliers On The Dirichlet Space, Alea Wittig

Electronic Theses & Dissertations (2024 - present)

An analogue to Wolff's ideal problem for the multiplier algebra of the Dirichlet space, the main theorem provides sufficient conditions to classify membership of an arbitrary function in an infinitely generated ideal of the multiplier algebra.