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Limit Theorems For L-Functions In Analytic Number Theory, Asher Roberts

Dissertations, Theses, and Capstone Projects

We use the method of Radziwill and Soundararajan to prove Selberg’s central limit theorem for the real part of the logarithm of the Riemann zeta function on the critical line in the multivariate case. This gives an alternate proof of a result of Bourgade. An upshot of the method is to determine a rate of convergence in the sense of the Dudley distance. This is the same rate Selberg claims using the Kolmogorov distance. We also achieve the same rate of convergence in the case of Dirichlet L-functions. Assuming the Riemann hypothesis, we improve the rate of convergence by using …

Analytic Properties Of Quantum States On Manifolds, Manimugdha Saikia

Electronic Thesis and Dissertation Repository

The principal objective of this study is to investigate how the Kahler geometry of a classical phase space influences the quantum information aspects of the quantum Hilbert space obtained from geometric quantization and vice versa. We associated states with subsets of a product of two integral Kahler manifolds using a quantum line bundle in a particular manner. We proved that the states associated this way are separable when the subset is a finite union of products. We presented an asymptotic result for the average entropy over all the pure states on the Hilbert space H⁰(M₁,L_{1 …}

Building Blocks For W-Algebras Of Classical Types, Vladimir Kovalchuk

Electronic Theses and Dissertations

The universal 2-parameter vertex algebra W_∞ of type W(2, 3, 4; . . . ) serves as a classifying object for vertex algebras of type W(2, 3, . . . ,N) for some N in the sense that under mild hypothesis, all such vertex algebras arise as quotients of W_∞. There is an ℕ X ℕ family of such 1-parameter vertex algebras known as Y-algebras. They were introduced by Gaiotto and Rapčák are expected to be building blocks for all W-algebras in type A, i.e, every W-(super) algebra in …

Combinatorial Problems On The Integers: Colorings, Games, And Permutations, Collier Gaiser

Electronic Theses and Dissertations

This dissertation consists of several combinatorial problems on the integers. These problems fit inside the areas of extremal combinatorics and enumerative combinatorics.

We first study monochromatic solutions to equations when integers are colored with finitely many colors in Chapter 2. By looking at subsets of {1, 2, . . . , n} whose least common multiple is small, we improved a result of Brown and Rödl on the smallest integer n such that every 2-coloring of {1, 2, . . . , n} has a monochromatic solution to equations with unit fractions. Using a recent result of Boza, …

Representation Theory And Its Applications In Physics, Max Varverakis

Master's Theses

Representation theory, which encodes the elements of a group as linear operators on a vector space, has far-reaching implications in physics. Fundamental results in quantum physics emerge directly from the representations describing physical symmetries. We first examine the connections between specific representations and the principles of quantum mechanics. Then, we shift our focus to the braid group, which describes the algebraic structure of braids. We apply representations of the braid group to physical systems in order to investigate quasiparticles known as anyons. Finally, we obtain governing equations of anyonic systems to highlight the differences between braiding statistics and conventional Bose-Einstein/Fermi-Dirac …

Pt-Symmetry And Eigenmodes, Tamara Gratcheva

University Honors Theses

Spectra of systems with balanced gain and loss, described by Hamiltonians with parity and time-reversal (PT) symmetry is a rich area of research. This work studies by means of numerical techniques, how eigenvalues and eigenfunctions of a Schrodinger operator change as a gain-loss parameter changes. Two cases on a disk with zero boundary conditions are considered. In the first case, within the enclosing disk, we place a parity (P) symmetric configuration of three smaller disks containing gain and loss media, which does not have PT-symmetry. In the second case, we study a PT-symmetric configuration …

On Cheeger Constants Of Knots, Robert Lattimer

Electronic Theses, Projects, and Dissertations

In this thesis, we will look at finding bounds for the Cheeger constant of links. We will do this by analyzing an infinite family of links call two-bridge fully augmented links. In order to find a bound on the Cheeger constant, we will look for the Cheeger constant of the link’s crushtacean. We will use that Cheeger constant to give us insight on a good cut for the link itself, and use that cut to obtain a bound. This method gives us a constructive way to find an upper bound on the Cheeger constant of a two-bridge fully augmented link. …

Multi-Objective Radiological Analysis In Real Environments, David Raji

Doctoral Dissertations

Designing systems to solve problems arising in real-world radiological scenarios is a highly challenging task due to the contextual complexities that arise. Among these are emergency response, environmental exploration, and radiological threat detection. An approach to handling problems for these applications with explicitly multi-objective formulations is advanced. This is brought into focus with investigation of a number of case studies in both natural and urban environments. These include node placement in and path planning through radioactivity-contaminated areas, radiation detection sensor network measurement update sensitivity, control schemes for multi-robot radioactive exploration in unknown environments, and adversarial analysis for an urban nuclear …

Tasks For Learning Trigonometry, Sydnee Andreasen

All Graduate Reports and Creative Projects, Fall 2023 to Present

Many studies have been done using task-based learning within different mathematics courses. Within the field of trigonometry, task-based learning is lacking. The following research aimed to create engaging, mathematically rich tasks that meet the standards for the current trigonometry course at Utah State University and align with the State of Utah Core Standards for 7th through 12th grades. Four lessons were selected and developed based on the alignment of standards, the relevance to the remainder of the trigonometry course, and the relevance to courses beyond trigonometry. The four lessons that were chosen and developed were related to trigonometric ratios, graphing …

Strategy-Proof Social Choice Functions On Condorcet Domains., Flannery Marie Musk Wells

Electronic Theses and Dissertations

A social choice function is said to be strategy-proof if no voter has any motivation to lie about their true preference. Strategy-proofness is a desirable property of social choice functions so we consider here functions that always satisfy this property. We add to this property the additional desirable conditions of anonymity and neutrality and present domains on which we can get a characterization of majority rule as the only social choice function that satisfies these three properties. Furthermore, we consider what functions look like when we drop the condition of anonymity.

Representation Learning For Generative Models With Applications To Healthcare, Astronautics, And Aviation, Van Minh Nguyen

Theses and Dissertations

This dissertation explores applications of representation learning and generative models to challenges in healthcare, astronautics, and aviation.

The first part investigates the use of Generative Adversarial Networks (GANs) to synthesize realistic electronic health record (EHR) data. An initial attempt at training a GAN on the MIMIC-IV dataset encountered stability and convergence issues, motivating a deeper study of 1-Lipschitz regularization techniques for Auxiliary Classifier GANs (AC-GANs). An extensive ablation study on the CIFAR-10 dataset found that Spectral Normalization is key for AC-GAN stability and performance, while Weight Clipping fails to converge without Spectral Normalization. Analysis of the training dynamics provided further …

Applications Of Survival Estimation Under Stochastic Order To Cancer: The Three Sample Problem, Sage Vantine

Honors Program Theses and Research Projects

Stochastic ordering of probability distributions holds various practical applications. However, in real-world scenarios, the empirical survival functions extracted from actual data often fail to meet the requirements of stochastic ordering. Consequently, we must devise methods to estimate these distribution curves in order to satisfy the constraint. In practical applications, such as the investigation of the time of death or the progression of diseases like cancer, we frequently observe that patients with one condition are expected to exhibit a higher likelihood of survival at all time points compared to those with a different condition. Nevertheless, when we attempt to fit a …

Examining The Relationship Between Students’ Home Environment And Math Test Scores, Autumn Michlig

Master of Science in Mathematics

This research study examined the relationship between a student’s home environment and their STAR math score by investigating 9 home environment variables. It also examines the best model to predict STAR score from the 9 home environment variables while controlling for the covariate, prior STAR score. The results being that including the covariate in the 9 predictor model was a statistically significant improvement over not including the covariate. However, the best model to predict STAR score was a model that only included the covariate and one variable, number of people living in house(s). Furthermore, when investigating the 9 variables, it …

An Expository Analysis Of The Theorem: Every Integer Greater Than Two Is The Sum Of A Prime And A Square-Free Number, Kurt Mckenzie

Master of Science in Mathematics

The thesis focuses on a relatively recent theorem (2017) contributed by Adrian Dudek to the field of Number Theory. It states that every integer greater than two can be represented as a sum of a prime and a square-free number. This result immediately attracts attention since it bears similarities with the famous and not yet proved Goldbach’s Conjecture, namely that every even number larger than two can be represented as a sum of two primes. The expository analysis aims to understand the theorem in the general setting of the Additive Number Theory, the method of proof and previous results on …

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 …