Mathematics Commons^™

Content And Consequences: Impact Of Representation In Stem Higher Education Instructional Content On Marginalized Students, Nichole Ventura

Doctorate in Education

This qualitative study examined representation of historically marginalized students in STEM instructional content at the higher education level and its impact on their learning experiences. Despite growing diversity initiatives in STEM enrollment, curricular materials often fail to reflect the identities of underrepresented students. Using critical theory and interpretivist approaches, this research investigated how representation—or its absence—shapes students' sense of belonging, academic identity formation, and persistence. Through semi-structured interviews with undergraduate students from historically marginalized backgrounds, and purposeful sampling, this study captured the lived experiences of students engaging with STEM instructional materials. Interview protocols explored how students perceive their representation in …

Combinatorics Of Trees Via Derivatives Of Polynomial Functors In Homotopy Type Theory, Warren David Hatton

Boise State University Theses and Dissertations

Polynomial functors are, essentially, polynomials whose variables take values in sets, groupoids, or some other suitable category, rather than in numbers. In this thesis, we will explore three related aspects of polynomial functors over $\infty$-groupoids in the framework of homotopy type theory: first, polynomial functors provide a foundation for inductively defined data types as wellfounded trees; second, polynomial functors have a notion of derivative which, viewed in light of the connection to data types, yields a computational interpretation of differentiation; and third, suitably finite polynomial functors over (higher) groupoids yield categorified generating functions, and thus subsume the theory of combinatorial …

A Comparative Study Of Novel Methods For Variances, Taoreed Muritala

Boise State University Theses and Dissertations

Understanding variability is fundamental to knowledge advancement across various disciplines, including manufacturing, clinical research, biology and genetics. Population variances play a crucial role in processes such as quality control, treatment evaluation and the interpretation of biological mechanisms. However, statistical procedures for comparing variances across multiple populations remain less developed than those for comparing means. Classical omnibus tests, such as Bartlett's and Levene's, can detect overall variance heterogeneity but fail to identify which populations differ, thereby limiting their usefulness in multi-population analyses and increasing the risk of inflated family-wise error rates through repeated testing.

This thesis develops and evaluates three multiple …

Abelian Sandpile Models On Edge Periodic Graphs, Payton Lyons

Boise State University Theses and Dissertations

The abelian sandpile model is a Markov chain that is able to decompose any recurrent configuration into a basic alive divisor, some amount of sand placed on the sink vertex, and a series of vertex firings. In this paper we begin to explore some of the dynamics of this system when the edges of the graph are allowed to alternate between two different edge sets. This system will be framed in a similar fashion as the classical model, and then some basic numerical simulations were used to observe the threshold behavior of the system. We lay some of the initial …

Scaling Wind Farm Layout Optimisation To Meet Uk Energy Demands, Grace Richardson

The Plymouth Student Scientist

This research aims to explore the Wind Farm Layout Optimisation Problem (WFLOP) through both single- and multi-objective optimisation, to show that it can be used to create farm layouts that provide enough power for all homes in the UK. We highlight the intricacies of the problem, including the application of different algorithms and models, and the challenges of scaling the models to achieve optimal results. We employ both a Hill Climbing Algorithm (HCA) and an evolutionary algorithm (NSGA-II) to obtain wind farm layouts, and compare these to the well-known results proposed by Mosetti et al. Moreover, we present a novel …

Connections On Manifolds: A Modern Approach To Classical Differential Geometry, Jed Allen Wilshire

Theses and Dissertations

The purpose of this thesis is to connect modern differential geometry concepts to the classical differential geometry study of surfaces, specifically spheres. This thesis will cover the topics of Riemannian manifolds, tangent spaces, vectors, vector fields, the connection of Levi-Civita, the Christoffel symbols, and Riemannian curvature. Each concept will be demonstrated on the well known unit sphere manifold.

A Computational Approach To Ramanujan-Type Congruences For Products Of Level 13, Aiden Michael Lalonde

Theses and Dissertations

In this thesis, we find products that are modular forms of level 13 whose Fourier coefficients satisfy certain congruences. These products are constructed in terms of integer powers of Klein forms and the Dedekind eta function. The products that are modular forms for Γ1 (13) have vectors of exponents that are elements of a bounded polytope. A parameterization for this polytope allows us to find a complete set of products that are modular forms for Γ1 (13). The corresponding graded ring of modular forms containing these products is constructed from a finite set of generators. These generators satisfy a finite …

Insecticide-Treated Net Use And Elimination Of Malaria In Sub-Saharan African Countries: Assessing The Global Technical Strategy Using An Evolutionary Game Approach, Laxmi, Tamer Oraby, Michael G. Tyshenko, Ina Danquah, Samit Bhattacharyya

School of Mathematical & Statistical Sciences Faculty Publications

Background: Malaria continues to be a major public health challenge in Sub-Saharan Africa (SSA), where the majority of the countries have not met the World Health Assembly's endorsed Global Technical Strategy (GTS) milestones in 2020 for malaria reduction. Insecticide-treated net (ITN) usage is a well-established and effective intervention, often outperforming other measures such as indoor residual spraying (IRS). However, multiple survey studies have reported improper use of ITNs across various SSA countries. This misuse likely poses an important barrier to the intervention's success, although it remains a largely untested hypothesis.

Methods: We developed a behaviour-incidence model and statistical analysis of …

Quantization For The Mixtures Of Overlap Probability Distributions, Asha Barua, Angelina Chavera, Ivan Djordjevic, Valerie Manzano, Sergio Soto Quintero, Mrinal Kanti Roychowdhury, Hilda Tejeda

School of Mathematical & Statistical Sciences Faculty Publications

Optimal quantization for mixed distributions has emerged as a compelling area of study. In this work, we have focused on a mixed distribution formed from two uniform distributions with partially overlapping supports. For this class of distributions, we have examined the structure of optimal sets of n-means and the corresponding nth quantization errors for all positive integers n. Initially, we explicitly determined the optimal sets and quantization errors for 1 < = n < = 6. Subsequently, we established several key lemmas and propositions and proposed an algorithm that facilitates the computation of optimal n-means and quantization errors for all n >= 5. Numerical results are also presented to illustrate the application of the algorithm in deriving these quantities. The findings of this study offer valuable insight and serve as a …

Robustness Of Network Inference Algorithms Under Network Class Misspecification, Roberto Ceja

Electronic Theses, Projects, and Dissertations

Inferring phylogenies in the presence of hybridization remains a difficult problem. As a result, many current methods for reconstructing phylogenetic networks are restricted to a simple class of networks known as level-1. This restriction arises from theoretical considerations rather than empirical evidence, with real data possibly arising from complex networks. In this work, we evaluate the robustness of two level-1 network inference methods, SNaQ and NANUQ+, through a simulation study, when the input data originates from a more complex network. Specifically, we investigate whether these methods can accurately recover important features of the true species network, such as the circular …

Predictors Of Math Identity In U.S. High School Students, Edwin Flores

Electronic Theses, Projects, and Dissertations

This study explored factors related to high school students’ sense of math identity. Data from the High School Longitudinal Study of 2009 was used which is a nationally representative dataset from the National Center of Education Statistics (NCES). The sample is representative of U.S. high schoolers who began ninth grade in 2009. Multiple regression analysis was performed and factors relating to students’ prior mathematics coursework and attitudes about mathematics were found to predict students’ mathematics identity.

Keywords. Mathematics, identity, high school students

On Sobolev Spaces And The Existence Of Weak Solutions To Boundary Value Problems, Skye X. Paul

Master's Theses

Many boundary value problems that arise in mathematical models have close connections to second order elliptic partial differential equations. This thesis introduces the idea of weak derivatives and Sobolev Spaces to generalize possible solutions. Using functional analysis centered around the Lax-Milgram theorem, we show the existence of these generalized solutions to boundary value problems including Laplace's Equation, 2nd order linear ODEs, and ultimately a general second order elliptic PDE. The work cumulates with recovering a number of central theorems of functional analysis in the context of Sobolev Spaces, creating a new perspective on the solvability of these boundary value problems.

Coherent Span-Valued 2d Tqfts, Sophia Marx, Rajan Amit Mehta

Mathematics Sciences: Faculty Publications

We consider commutative Frobenius pseudomonoids in the bicategory of spans, and we show that they are in correspondence with 2-Segal cosymmetric sets. Such a structure can be interpreted as a coherent 2-dimensional topological quantum field theory taking values in the bicategory of spans. We also describe a construction that produces a 2-Segal cosymmetric set from any partial monoid equipped with a distinguished element.

Preparing Confident Elementary Mathematics Teachers: Addressing Anxiety, Building Fluency, And Strengthening Practice., Amber Diamond Pendleton

Electronic Theses and Dissertations

This dissertation, presented in three articles, examines how elementary preservice teachers (PSTs) experience and develop as mathematics learners and future educators when methods coursework deliberately integrates mathematical reasoning with affective supports. Collectively, the studies investigate how research-informed instructional design may help address mathematics anxiety (MA), mathematics teaching anxiety (MTA), procedural fluency, and instructional practice. The first article, written for practitioners and elementary mathematics teachers, illustrates how well-established instructional routines, such as number talks and student work analysis, can be facilitated to support procedural fluency in multiplication. Using classroom vignettes, this article highlights instructional moves that make structure visible, promote strategy …

An Income Subsystem As A Discrete Stochastic Leslie System: A Simulation-Based Approach, Fahd Nii Okantah Cobblah

Electronic Theses and Dissertations

This thesis formulates the household-income engine of an integrated population sim- ulator as a Discrete Stochastic Leslie System (DSLS). The nonnegative state vector nt ∈ Rk + aggregates income, savings, debt, employment, and transfers. (Here, the subscript + denotes the positive cone, i.e., vectors with nonnegative components). Annual evolution is linear in state, stochastic in coefficients: nt+1 = Ttnt + εt, with Tt : Rk + → Rk + cone-preserving. Exogenous macro drivers (inflation, employment, tax, salary inflation, mortgage) are forecast via ARIMA; forecasts multiply entries of Tt, preserving linearity in expectation while introducing realistic temporal correlation. The discrete-event implemented …

A Leslie System For A Demographic Simulation: From An Actuarial Point Of View, David Kings

Electronic Theses and Dissertations

This thesis develops a discrete stochastic linear systems interpretation of age–stage demographic evolution grounded in Leslie operators and realized in a discrete-event simulation implemented with salabim. The central claim is that one annual cycle of the simulation constitutes a cone-preserving, stochastic affine transformation on a high- dimensional population state vector indexed by age, sex, marital status, household type, employment, and education, and that the composition of yearly operators yields a random matrix product whose top Lyapunov exponent is the stochastic counterpart of the Perron–Frobenius growth rate (Caswell, 2001; Tuljapurkar, 1997)[1, 2]. The actuarial bridge is constructed by mapping simulated survival …

By The Numbers: Numeracy, Religion, And The Quantitative Transformation Of Early Modern England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: By the Numbers: Numeracy, Religion, and the Quantitative Transformation of Early Modern England by Jessica Marie Otis. New York, NY: Oxford University Press, 2024. 264 pp. ISBN: 9780197608777.

Self-Assessment In Calculus I, Bertha Naa Dei Neequaye

All Graduate Theses and Dissertations, Fall 2023 to Present

The purpose of this research investigate how undergraduate students in Calculus I at Utah State University learn and reflect on their level of understanding of Calculus I. In the study, self-assessment practices refer to students reflecting on what they have learned, rating their level of understanding and providing examples that illustrate their level of understanding. The structured and unstructured self-assessment rubrics were the two types of self-assessment rubrics used in the study. The structured self-assessment rubric provides a clear list of objectives of Calculus I topics for students to rate themselves on, while the unstructured self-assessment rubric is an open …

Machine Learning Applications: Cell Tracking And Nonparametric Estimation Of Non-Smooth Divergences, Mina Mahbub Hossain

All Graduate Theses and Dissertations, Fall 2023 to Present

This thesis brings together two important research directions: how to compare different sets of data more accurately, and how to better understand how brain cancer cells move and change shape.

In the first part, we look at a problem in statistics: measuring how different two data sources are from each other. Traditional methods often make strong assumptions, which may not always hold in real situations. Our approach avoids those assumptions by using an ensemble method, a way of combining many weak estimators into one stronger result. This makes the method more flexible and reliable, especially when dealing with complex or …

Variants Of Conway Checkers And K-Nacci Jumping, Glenn Bruda, Joseph Cooper, Kareem Jaber, Raul Marquez, Steven J. Miller

School of Mathematical & Statistical Sciences Faculty Publications

Conway Checkers is a game played with a checker placed in each square of the lower half of an infinite checkerboard. Pieces move by jumping over an adjacent checker, removing the checker jumped over. Conway showed that it is not possible to reach row 5 in finitely many moves by weighting each cell in the board by powers of the golden ratio such that no move increases the total weight.

Other authors have considered the game played on many different boards, including generalizing the standard game to higher dimensions. We work on a board of arbitrary dimension, where we allow …