Mathematics Commons^™

The Stem Gender Gap: Can It Be Closed?, Makenna Roberts

Undergraduate Honors Capstone Projects

Despite increasing gender parity in many professional fields, women remain underrepresented in STEM industries, particularly in math-intensive areas such as engineering, computer science, and physics. This report explores the persistent gender gap in STEM through analysis of two data sources: gendered differences in the US national Scholastic Aptitude Test (SAT) performance and post-graduate employment patterns among scientists and engineers.

The first portion of the analysis examines SAT score data from 2018 to 2024, with a focus on high-performing test-takers. Using Python and R, data was extracted and visualized to compare male and female performance on the Math and Evidence-Based Reading …

Koszul Cohomology Of Canonical Products, Alexander Scott Duncan

Graduate Theses and Dissertations

In this thesis, we give a complete classification of the Koszul cohomology groups K_p,₁(C, B, ω_C ⊗ B) on a smooth curve C of genus g ≥ 2 with B p-very ample. Such a classification in the case B = ω_C has been incomplete until [5]. The classification follows easily from our main result which precisely calculates K_p,1(C, B, B ω_C ⊗ B) in terms of h⁰(C, B). This result also handles the case B = ω_C. A straightforward …

The Food Truck: A Multi-Product Newsvendor With Trans-Shipment Cost, Samuel Ajibola

Electronic Theses and Dissertations

The Newsvendor Problem is a key model in supply chain management that focuses on determining the optimal order quantity to minimize costs under uncertain demand. This thesis introduces the Food Truck Problem, an extension of the Newsvendor model that incorporates nonlinear transshipment costs for inventory transportation. In this context, a Food Truck must determine the optimal stock levels for multiple products while minimizing costs related to stock shortages, excess inventory, and transportation. Unlike traditional Newsvendor models, our approach explicitly considers a quadratic transshipment cost, which necessitates the use of Lagrangian duality and Karush-Kuhn-Tucker (KKT) conditions for analysis. Moreover, we apply …

Data Science For Engineers, Heidi Moulton

Undergraduate Honors Capstone Projects

Undergraduate research is a core pillar of Utah State University’s College of Engineering. Many students become involved with research during their Junior and Senior years and begin to generate various forms of data. Most students, however, have received little formal education on how to process data, and there are currently no readily available resources within the College of Engineering. As a Mechanical Engineering and Data Science double major, I found the data processing techniques I learned in my Data Science courses invaluable as an undergraduate researcher, and now as a Mechanical Engineer at Apogee Instruments, I frequently draw upon these …

Decision Space Decomposition For Multiobjective Programs, Emma Soriano

All Dissertations

Being inspired by the parametric decomposition theorem for multiobjective optimization problems (MOPs) of Cuenca and Miguel (2017), and by the block- coordinate descent for single objective optimization problems, we present a decom- position theorem for computing the set of minimal elements of a partially ordered set. This set is decomposed into subsets whose minimal elements are used to retrieve the overall minimal elements. We apply this approach to strictly convex MOPs de- composing their decision space into lines. The line decomposition benefits from the fact that a multiobjective line search problem is equivalent to solving a collection of single objective …

Countering Deficit Narratives Through A Blackcrit Lens By Examining Case Studies Of Black College Mathematics Students’ Classroom Experiences, Akhenaton Wilbourn

All Dissertations

This dissertation examines the lived experiences of 11 Black college mathematics students at their predominantly white institution (PWI) through the lens of Black Critical Theory (BlackCrit) to counter deficit narratives about the racial achievement gap (RAG) in mathematics education courses. Deficit narratives often attribute disparities between Black and white students’ mathematical performance to assumed deficiencies in Black students’ abilities rather than systemic inequities, historical marginalization, and ongoing anti-Blackness in educational settings (Cobb & Russell, 2015; Kress, 2021). Using multiple case studies, this study explores how anti-Blackness manifests in mathematics classrooms, how students navigate tensions between multiculturalism, neoliberal educational policies, and …

The Spectral Asymptotics Of Toeplitz Operators On Hilbert Spaces Of Analytic Functions, Trevor Camper

All Dissertations

Many physical systems, whether they are ocean waves or particles moving through space, can be described using the mathematical language of “partial differ- ential equations.” In many circumstances, it is useful to study how these equations amplify an input to the equation, in which case the amplification factor is called an “eigenvalue.” The usefulness of these amplification factors is that they can be used to describe properties of the physical system. In this dissertation, I have studied this amplification factor for a related set of equations called “Toeplitz operators.” In par- ticular, I have studied eigenvalues using statistical techniques. The …

Development Of Saddlepoint Methodologies For Sparse Sample Multiple Parameter Generalized Linear Models And Correlated Data Scenarios, Christopher Johnson

All Graduate Theses and Dissertations, Fall 2023 to Present

Parameter estimation using maximum likelihood techniques may be biased when sample sizes are small, event rates are low, or otherwise sparse counts exist in a parametric model. This in turn may lead researchers to draw invalid statistical conclusions when conventional methods are utilized. The saddlepoint approximation has potential to lessen the degree of bias in sparse data conditions through its use of moments beyond the mean and variance, which allows for more accurate approximations using a smaller number of observations. We propose two novel saddlepoint methods for use in practical analysis scenarios, as an alternative to maximum likelihood estimation. First, …

A Survey Of Master's Qualifying Exam Practices And Content In Real Analysis, Zachary M. Coverstone

All Graduate Theses and Dissertations, Fall 2023 to Present

Graduate programs in mathematics are intended to develop experts in mathematics. As part of a graduate program, many students are expected to engage in a qualifying examination that can serve myriad purposes. This dissertation investigates real analysis qualifying examinations at the master's level through a nation-wide survey of institutions in the Association of Public and Land-Grant Universities (APLU). This study reveals the practices in administration of real analysis qualifying exams, institutions reported offering traditional, pencil-and-paper exams and generally asked students to prepare individually using previously administered exams. The survey results show that approximately two in three APLU institutions offering master's …

A Dg-Algebra Structure With Divided Powers On The Generalized Taylor Resolution, Raul F, Alvarez

Theses and Dissertations

This thesis investigates the construction of a DG Γ-algebra structure on the Generalized Taylor Resolution (GTR) associated with monomial ideals. The classical Taylor resolution is known for providing a free but generally non-minimal resolution, leading to computational challenges and inefficiencies in algebraic analysis. In contrast, the GTR preserves essential algebraic structures while optimizing the resolution process, offering a more efficient and comprehensive framework for studying monomial ideals.

We introduce a novel DG Γ-structure that incorporates divided powers into the GTR, enhancing its multiplicative and homological properties. This structure preserves strict graded commutativity and is fully compatible with the differential graded …

Reuben Hersh's What Is Mathematics, Really? (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reuben Hersh’s 1997 book What is Mathematics, Really? popularized a trend in the philosophy of mathematics that was gaining some traction at the time it was written. This essay examines Hersh’s work within the broader historical context of 19th- and 20th-century developments in mathematics and philosophy of mathematics. It also focuses on Hersh’s antagonism toward the influence of religion on (philosophy of) mathematics, concluding by briefly considering two positions taken by Christian mathematicians associated with ACMS in defense of such a connection.

Equity Vs. Excellence: Dichotomy Or Duo?, Nadjia I. Logans

Honors Program: Senior Projects (Public)

In this thesis, I investigate recent changes in mathematics education and how these developments connect to the principles of equity and excellence. I place a special focus on “active learning” methods. My methodology primarily consisted of interviews with educators, along with analyzing literature from math education researchers. I first define and explain the motivations behind active learning instruction methods. Next, I explore not only how instructors define equity and excellence but how educators perceive the role of the two principles within education. Finally, I challenge the pervasive media portrayal of equity and excellence as being mutually exclusive. Instead, I find …

Culture And Context: How Frames Of Teaching And Of Learning Mathematics Form And Change For Graduate Student Instructors, Johan Benedict Arroyo Cristobal

Dissertations and Doctoral Documents, University of Nebraska-Lincoln, 2023–

Why do instructors teach the way that they do? This question is key in understanding how and why asset-based or deficit-based practices are enacted in the classroom. In consequence, this question also gives insight into how the environment where students learn is shaped. Mathematics education research, in particular, has been concerned with how instructors respond to students’ contributions in the classroom and how these ways of responding can (dis)empower students.

One way to answer this question is to understand how instructors frame their own teaching and their students’ learning. Frames are mental constructs which help individuals filter details, interpret information, …

Efficient Fully Bayesian Approach To Brain Activity Mapping With Complex-Valued Fmri Data, Zhengxin Wang, Daniel B. Rowe, Xinyi Li, D. Andrew Brown

Mathematical and Statistical Science Faculty Research and Publications

Functional magnetic resonance imaging (fMRI) enables indirect detection of brain activity changes via the blood-oxygen-level-dependent (BOLD) signal. Conventional analysis methods mainly rely on the real-valued magnitude of these signals. In contrast, research suggests that analyzing both real and imaginary components of the complex-valued fMRI (cv-fMRI) signal provides a more holistic approach that can increase power to detect neuronal activation. We propose a fully Bayesian model for brain activity mapping with cv-fMRI data. Our model accommodates temporal and spatial dynamics. Additionally, we propose a computationally efficient sampling algorithm, which enhances processing speed through image partitioning. Our approach is shown to be …

Stochastic Analysis With Operational Calculus In Reliability, Hend Hamdan Al-Jahani

Theses and Dissertations

Our dissertation models several reliability systems subject to occasional random shocks of random magnitudes W1,W2,..occurring at times tau0, tau2,..In Model 1, the underlying system becomes inoperational if it wears out due to aging specified by a monotone increasing continuous function Delta identifying system's wear at any time t>=0 . The system is deemed inoperational if delta crosses a sustainability threshold at some moment T=(delta )^-1(D). The precise time T is difficult to identify making the realistic failure time randomly delayed and thus identified at some opportune observation epoch. The system can also fail due to damages by external shocks, …

Relaxation Maximum-Based Iteration Method For Solving The Generalized Absolute Value Equation, Ximing Fang, Zhidong Wang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The generalized absolute value equation (GAVE) has wide applications in scientific computing. Establishing a high performance computing method to solve the GAVE is a hot research topic in recent years. In this paper, with the aid of the maximum function, the GAVE is decomposed of two equations, and then we present the relaxation maximum-based (RM) iteration method. To see the feasibility of the method, we discuss the necessary and sufficient conditions for the GAVE to have a unique solution. Next, the convergence analysis of the RM iteration is discussed under some convergence conditions. Moreover, some numerical examples of low and …

The Improved New Intersection Theorem Revisited, Lars Winther, Luigi Ferraro

School of Mathematical & Statistical Sciences Faculty Publications

We prove a generalized version of Evans and Griffith’s improved new intersection theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegative degrees, has I-torsion homology in positive degrees, and the homology in degree 0 has an I-torsion minimal generator, then the length of the complex is at least dimR−dimR/I. This improves the bound htI obtained by Avramov, Iyengar, and Neeman in 2018.

On Finite Groups With Essential Dimension 2 Over ℚ, Michael Huggins

Theses and Dissertations

We determine all finite subgroups of Aut(X) which have essential dimension 2 over ℚ, where X is a minimal Del Pezzo surface of degree at least 5. Additionally, finite groups with essential dimension 2 whose order is divisible only by the prime numbers 2 and 3 are classified with the exception of the groups dic ₁₂ , C₁₂, and Dih₂₄, whose essential dimensions remain unknown, but may possibly be equal to 2.

Analysis And Derivation Of The Compressible Euler System With Nonlinear Velocity Alignment: An Investigation Into Collective Behavior, Mckenzie Meredith Black

Theses and Dissertations

Collective behavior refers to the observable patterns, actions, or movements that emerge within a group of entities, such as individuals, animals, or particles, when they interact with each other. In this study, we concentrate on the pressureless compressible Euler system, expanding it to incorporate a family of nonlinear velocity alignment. This extension represents a nonlinear iteration of the Euler-alignment system within collective dynamics, revealing intriguing asymptotic emergent phenomena such as alignment and flocking. Our investigation explores different types of nonlinearity and nonlocal communication protocols, unveiling a diverse spectrum of asymptotic behaviors within the system.

In focusing on the derivation, we …

Symmetries Of Del Pezzo Surfaces, Jonathan Smith

Theses and Dissertations

For each del Pezzo surface X of degree d, the action of the automorphism group Aut(X) on the exceptional curves of X induces a map ρ : Aut(X) → W(R_d), where W(R_d) is the Weyl group of a root system R_d dependent on the degree of X. The image of ρ is well defined up to conjugacy in W(R_d), so we say that a group G acts by automorphisms on a del Pezzo surface X of degree d if a representative of the …