Mathematics Commons^™

Conceptualizing A Responsive Design Pedagogy To Support Teachers' Responsiveness To Students' Mathematical Ideas Through Making, Denish Ogweno Akuom

Theses, Dissertations and Culminating Projects

This study develops Responsive Design Pedagogy (RDP), a conceptual and analytic model of teacher responsiveness in design-based environments, to account for how responsiveness emerges through interactions among students, tools, and tasks. Although responsiveness has been widely studied in mathematics education, limited attention has been given to responsiveness within mathematical design activity and to how teachers attend to the multiple modes through which students express their mathematical ideas. Addressing these gaps, this qualitative study examined one teacher’s enactment of responsiveness in a Learning-by-Design classroom where students designed and used 3D-printed mathematical tools. Data sources included classroom video, student design artifacts, teacher …

Data Driven Monitoring And Control Of Laser Powder Bed Fusion Process, Jose De Jesus Galarza

Theses and Dissertations

The Laser Powder Bed Fusion Process (LPBF) has been one of the main processes of additive manufacturing, enabling the manufacturing of complex geometries, customization, and lightweight parts. Modern LPBF processes have integrated monitoring systems that capture the light emissions per layer for quality assurance. However, standard defect detection algorithms have not yet achieved the high precision required due to the inherently variable nature of the signal, insufficient data for model training, and the confounding effects of the print.

The processes still have some challenges, such as characterizing the roughness from the build parameters alone, improving the pore detection using the …

A New Approach To Generate Combinatorial Patterns In Logical Analysis Of Data And Its Application To Predict College Retention, Salihah Ahmed E. Jaafari

Theses and Dissertations

Student retention and degree completion remain central challenges for higher-education institutions, with significant implications for student success, institutional effectiveness, and public accountability. While advances in predictive analytics have enabled earlier identification of students at risk of withdrawal, many commonly used machine learning approaches suffer from limited interpretability, constraining their practical usefulness for advising, intervention, and policy decision making. This dissertation addresses the problem of predicting student persistence by developing and evaluating optimization based, interpretable classification models within the Logical Analysis of Data (LAD) framework. Building on existing LAD formulations, this research introduces two novel pattern generation models, the Best Term …

I Am Still Learning, Too!: Pre-Service Teachers' Experiences Of Mathematics Anxiety In An Inquiry-Based Mathematics Education Course At Utrgv, Jeremiah James Adriano Dela Rosa

Theses and Dissertations

Mathematics anxiety is a prevalent issue in mathematics education that negatively impacts students’ learning, performance, and engagement in mathematics. Prior research suggests that mathematics anxiety is often shaped by students’ experiences and emotional responses within the classroom environment.

The purpose of this study is to explore how Pre-Service Teachers experience mathematics anxiety in an Inquiry-Based Mathematics Education (IBME) classroom. This study employed a qualitative research design supported by descriptive survey data collected through the Abbreviated Mathematics Anxiety Scale (AMAS), selected components of the Fennema-Sherman Mathematics Anxiety Scale (FSMAS), and semi-structured interviews. The survey instruments were used to provide descriptive background …

Prism: Priming Relationships In Syntax And Mathematics, Michelle J. Zhu

Honors Scholar Theses

The implementation of sheltered education programs has become increasingly prevalent in schools as new research in second language acquisition emerges. Yet despite this growing attention to ESL instructional practice, far less is known about the cognitive processes that underlie how bilingual students engage with academic content. This study investigates cross-domain structural priming between mathematical and linguistic processing in monolingual and bilingual individuals, focusing on how bilingual experience influences syntactic attachment preferences. Prior research suggests that mathematical and linguistic structures share underlying cognitive representations, and that exposure to structures in one domain can influence processing in another. Additionally, bilingualism has been …

Sumset Lower Bounds In Abelian Groups, Van T. Huynh

Honors Theses

This thesis investigates sumset lower bounds across discrete and continuous settings. We begin with general inequalities in torsion-free abelian groups and then specialize to the integers modulo prime p, where we present the Cauchy–Davenport Theorem, which establishes the bound ∣A+B∣≥min(p,∣A∣+∣B∣−1). The equality case is further examined via Vosper's Theorem, which characterizes subsets attaining this bound as arithmetic progressions under suitable conditions. The continuous analogue in Euclidean spaces is then considered, where cardinality is replaced by Lebesgue measure. In this setting, the Brunn–Minkowski Inequality provides a sharp lower bound for the Lebesgue measure of A+B and serves as a geometric counterpart …

Course Insight Portfolio: Math 1020 Business Calculus I, Ibrahim Khalilullah, M.G.M. Al Faruque, Jessica Ratovondranto, Leslie Spahr

Publications

This portfolio presents an overview of the student educational context, key course concepts, and some approaches to clarify student misconceptions associated with MATH 1020 (Business Calculus I). The portfolio includes a concept map illustrating the major topics of the course and an overview of common student misconceptions, and lesson plans designed to address those misconceptions through research informed instructional practices.

The concept map highlights the interconnected nature of topics such as functions, limits, continuity, differentiability, derivatives, optimization, graph interpretation, and applications of calculus. Particular attention is given to areas where students commonly experience difficulty, including distinguishing domain, codomain, and range; …

The Fundamental Group: A Geometric Perspective, Kayla M. Bittenbinder

All NMU Master's Theses

This thesis explores the deep mathematical connection between the flexible, continuous world of topology and the rigid, distance-preserving world of metric geometry. We begin by constructing the fundamental group of a topological space, using the concept of loops and loop homotopy to identify a global topological invariant such as a hole or puncture. We then transition to the geometric realm of metric spaces and isometries, demonstrating how the isometry group of a space algebraically encodes its rigid symmetries. To bridge these two distinct mathematical frameworks, we utilize the construction of the universal covering space. We pull back the metric from …

Combinatorial Statistics Witnessing An Infinite Family Of Congruences For A Sum Of Partition Functions, Jena M. Gregory

Theses and Dissertations

In 2007, Kronholm established The Interval Theorem, infinite families of congruences in arithmetic progression, modulo any prime ��, for ��(��, ��), the function enumerating the partitions of �� into parts whose sizes come from the set {1, 2, … , ��}. In 2022, Eichhorn, Kronholm, and Larsen proved there are combinatorial statistics described in terms of the multiplicities of the part sizes that witness Kronholm’s Interval Theorem. Here, “witness" means given a congruence of the form ��(��, ��) ≡ 0 (mod ��), we can use these statistics to classify the set of partitions of �� into �� equally sized subsets …

Bounding The Average Kissing Number, Including New Bounds For Three-Dimensional Binary Sphere Packings, Mark William Bockhaus

Theses and Dissertations

The average kissing number is defined as the supremum over all sphere packings of the value: two times the number of tangencies divided by the number balls in the packing. In this paper, we present a survey of the literature about bounding the average kissing number, beginning with the first non-trivial results, through the most up-to-date bounds. We then turn our focus to binary sphere packings: those which contain spheres of two different radii. We improve upon known bounds for the average kissing number for binary sphere packings in three-dimensions and find exact bounds for many packings.

Bayesian Change-Point Detection In Stock And Cryptocurrency Markets Using Shrinkage Priors, Yosalin Sanchez

Theses and Dissertations

Financial markets often undergo abrupt structural changes driven by political, economic, and geopolitical events, leading to substantial volatility. Detecting such change-points is crucial for identifying structural breaks, improving risk management, and enhancing forecasting performance in financial time series. This study proposes a Bayesian change-point detection framework that incorporates both the t-shrinkage prior and the Horseshoe shrinkage prior. These priors enforce strong regularization on successive differences in mean parameters, enabling the identification of piecewise constant structures in time series data. Posterior inference is conducted using Markov Chain Monte Carlo (MCMC) methods, specifically a Gibbs sampling algorithm, which iteratively samples from the …

On The Structure Of The Homotopy Lie Algebra Of Local Rings, Dawson M. Strong

Theses and Dissertations

This thesis investigates the construction and homological properties of the homotopy Lie algebra π(R) of a commutative local ring (R,m,k). Drawing upon the theoretical framework of differential graded (DG) algebras, we first establish the theory of minimal free resolutions and other standard topics in homological algebra. The core of this work details the iterative construction of the acyclic closure R⟨Y⟩ of k over R, which is achieved by the systematic adjunction of exterior and divided power variables to eliminate cycles in homology. We demonstrate that this acyclic closure serves as a minimal free resolution and provides the means to define …

When A Sum Of Cubes Equals The Square Of The Sum, Jessica M. Aguilar

Electronic Theses, Projects, and Dissertations

This thesis investigates extensions and structural generalizations of the classical identity \[ \sum_{k=1}^{n} k^3 = \left( \sum_{k=1}^{n} k \right)^2, \] traditionally attributed to Nicomachus of Gerasa. Despite its simple look, this cube - square identity reveals connections between combinatorics, multiplicative number theory, and Diophantine equations.

We begin by presenting an expanded combinatorial proof of the identity based on Stein’s rectangle - counting argument, clarifying the geometric structure underlying the formula. We then establish a multiplicative analogue using Euler’s divisor-counting function \( \tau(n) \), proving that \[ \sum_{d \mid n} \tau(d)^3 = \left( \sum_{d \mid n} \tau(d) \right)^2, \] thereby extending …

Examining Student Practices In A Technology-Mediated Math Classroom, Bradley T. Dodd

Electronic Theses, Projects, and Dissertations

It is important for math educators to make sense of student thinking in the classroom. Without opportunities to practice this skill math educators struggle to improve, particularly when students are engaging in mathematics using technology. As such, there is a need for video artifacts of students engaging with mathematics using technology for use in professional development activities (Lovett 2020). In accordance with Lovett et al.'s (2020) design principles for examining student practices in a technology-mediated environment, I carried out a study to determine whether these artifacts of student work could be created working with college undergraduates as participants. Students engaged …

Constraint-Aware Metaheuristic Optimization For Experimental Design, Benjamin N. Fuller

All Graduate Theses and Dissertations, Fall 2023 to Present

Designing experiments becomes much more challenging when many variables and strict constraints are involved, as is common in modern science and engineering. This thesis introduces a new computational and mathematical framework that efficiently searches for optimal experiments in complex, high-dimensional spaces where traditional methods fail. By combining geometric techniques with flexible optimization algorithms like particle swarm optimization, our methods handle difficult constraints while scaling to real-world problems. Built in the high-performance Julia programming language and released as open-source software, this work bridges advanced theory with practical tools, offering researchers a powerful and accessible way to design better experiments under realistic …

On The Algebraicity Of The Tic-Tac-Toe Matroid And Homogeneous Mixed Bowtie Systems, Benjamin R. Allen

Electronic Theses and Dissertations

This thesis is presented in two parts. First, we explore whether the class of algebraic matroids is closed under duality, a decades-old open question. We consider the Tic-Tac-Toe matroid as a potential candidate to answer the open question. The Tic-Tac-Toe matroid is known to satisfy many of the necessary conditions for a matroid to be algebraic and has a non-algebraic dual.  Second, we focus on decompositions of the complete mixed graph into mixed bowties. A complete mixed graph has between every pair of vertices an undirected edge and antiparallel arcs. A mixed bowtie is a graph consisting of two 3-cycles …

Analysis Of Collective Behavior In Living And Nonliving Systems, Kaitlyn Cohan

Theses, Dissertations and Culminating Projects

This thesis aims at understanding the phenomenon of of self-organization in complex dissipative systems, living and nonliving. Dissipative systems are characterized by their search for energy, interactions with their surroundings and the production of entropy, all of which result in the creation of stable structures or patterns, which persist as long as the initial environmental conditions are maintained. The two specific models that we chose to study here are (a) Futbol (or Soccer) and (b) a chemical system involving free-floating menthol crystals floating on a fluid surface to represent nonliving systems. Using experiments and mathematical models, we will try to …

Volume 17, Christian O’Neill, Kyara Greene, Savva Sidorov, Laura Bisaillon, Luke Clemmer, Hannah Gordon, Kitt Benson, Taylor Blount, Rachel Danzitz, Nicholas Duellman, Chase Gionis, Hima Fernando, Seth Franzyshen, Onyx Gonzalez, Bryan Lin, Samantha Start, Ysabel Wells, Maggie Duncan

Incite: The Journal of Undergraduate Scholarship

Introduction Dr. Amorette Barber, Director, Office of Student Research

From the Editor Dr. Hannah Dudley-Shotwell

Cover Artist’s Statement Maggie Duncan

On Mentoring Dr. Yulia Uryadova

Ukrainian Resistance in the Face of Russification: Nestor Makhno and Anarchism

by Christian O’Neill

Life Vest by Kyara Greene

Isolation and 16S rRNA Identification of Bacteria from Fire Department Connection Pipe by Savva Sidorov

The Effectiveness of Planned Exercise in Reducing ADHD Symptoms in Children by Laura Bisaillon & Luke Clemmer

Linguistic Analysis on Confidence and Communication Strategies with Disparities Between Sign Fluency and Hearing Impairment by Hannah Gordon

Freedmen in Indian Territory by Kitt …

Analyzing The Evolution Of Science: Topological Cycles And Community Detection In Knowledge Networks, Frances C. Mcconnell

Mathematics, Statistics, and Computer Science Honors Projects

How scientific knowledge grows and organizes itself is a central question in the study of science. This thesis uses tools from topology and network science to detect and characterize knowledge gaps—places in a field’s literature where related concepts do not co-occur. We develop a metric to quantify the degree of interdisciplinarity of each gap, using the community structure of the underlying network as a proxy for subfields. Across a wide range of fields, gaps reliably span multiple subfields and evolve in recognizable temporal patterns, highlighting new insights into how scientific fields are structured and their stage of development.

From The Hopf Fibration To Instantons: Geometry In Gauge Theory, Emily D. Wessman

Undergraduate Honors Capstone Projects

This paper explores the relationship between topology, differential geometry, and gauge theory through the study of Yang-Mills theory and its solutions, known as instantons. Beginning with the Hopf fibration, we show how principal fiber bundles encode topological information and appear in physical contexts such as electromagnetism. In particular, we consider how the fibration of S³ over CP¹ ≅ S² represents the Dirac magnetic monopole, and how the Chern number associated with the bundle is exactly the winding number for the monopole.

We then develop the framework of gauge theory, focusing on connections on principal SU(2) bundles …