Mathematics Commons^™

A Computational And Experimental Study Of Energy Extraction From Vertical Axis Wind Turbines In Realistic Environments, Kevin Vargas

Theses, Dissertations and Culminating Projects

This thesis presents preliminary analyses on the performance of small scale vertical axis wind turbines (VAWTs) conducted through both experimental and computational methods. Laboratory experiments were carried out in the Complex Fluids Laboratory at Montclair State University to evaluate turbine behavior under controlled conditions. The key focus of this work was to investigate the impact of inlet blockage on turbine performance, simulating real-world environmental constraints such as flow obstruction and urban interference and measuring power generated via laboratory tools. Computational fluid dynamic (CFD) simulations were performed to further analyze flow characteristics and validate experimental observations and trends. Turbine geometries were …

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.

The Tones And Frequencies Of A Glockenspiel, Edward Czudak

Theses, Dissertations and Culminating Projects

In this thesis, I will analyze the tones and frequencies of a glockenspiel based on the results of Warburton’s 1954 article, “The Vibration Of Rectangular Plates,” [12]. I will be measuring and modeling the frequencies of a glockenspiel and connect them with the analytical and expected numerical solutions. The solutions will be based on the plate equation along with the boundary conditions of a rectangle free on all edges. I will look at the high modes of vibration for the bars and their corresponding overtones in the acoustic spectrum.

Bounded Multiplication And Composition Operators On Sequence Besov Spaces, Robert Anderson

Mathematical Sciences Undergraduate Honors Theses

The sequence Besov space $b_p$, $p>1$, is the space of analytic functions $f(z)=\sum_{n=0}^{\infty} a_n\, z^n$ on the open unit disk

$\mathbb D$ with $$\sum_{n=0}^{\infty} n^{p-1}\, |a_n|^p< \infty\, .$$

We will give a brief introduction to the space $b_p$, as well as explore how certain operators behave on the space. For example, let $\varphi$ be an analytic self-map of $\mathbb D$. We study the multiplication operator $M_\varphi$ on $b_p$ and look at examples including when $\varphi$ is a polynomial. We also study the composition operator $C_\varphi$ on $b_p$, and in more depth on $b_2$ the Dirichlet space. The culmination will be an …

Numerical And Harmonic Analysis Of Simplex Number Parity, Hunter Dm Hannula

All NMU Master's Theses

The primary object of this thesis is the study of periodicity in the parity of simplex numbers by number-theoretic and harmonic methods. The regular d-simplex numbers are introduced geometrically, arithmetically, and combinatorially. We demonstrate that all sequences indexing even d-simplex numbers are defined by finitely many congruences in a single modulus, and are thus quasiperiodic. We therefore show that these "even index-sequences" are  particular elements in an affine space of functions, providing a natural decomposition result. We then introduce the discrete Fourier transform to construct the periodic parts of each index sequence, enabling the development of explicit forms for the …

Mississippi Early Childhood Math Resource Guide: Supporting Mathematical Development From Birth Through Age Eight, Melissa Luckett, Systems Change Lab, Mississippi State University, Social Science Research Center, Mississippi State University

Books

The Mississippi Early Childhood Math Resource Guide is a comprehensive, research-informed digital publication designed to support the development of foundational mathematical skills in children from birth through age eight. Developed by the Systems Change Lab at Mississippi State University's Social Science Research Center, the guide translates evidence-based early mathematics concepts into practical, accessible strategies for educators, families, and caregivers. 

Organized by developmental stages, the guide integrates learning domains, age-appropriate math skills, and everyday instructional practices to promote the use of "math talk" and embedded learning opportunities across settings. It incorporates activities, instructional strategies, and resources aligned to support both formal …

An Exploration Of The Autorotating Pendulum Model, Vlad Nita

Theses, Dissertations and Culminating Projects

Autorotation is the spontaneous rotation of an object, usually caused by an external fluid flow. The study of autorotation has many physical applications, such as in the design of wind/water turbines. In this thesis, we explore a nonlinear pendulum ordinary differential equation (ODE) which is used to model rotating plates in a fluid and has the capacity to reveal autorotation. In the context of an ODE, autorotation emerges as a bifurcation past oscillations, when the initial velocity of the system crosses a particular threshold. In his classic study from 1983, Lugt [14] utilizes this equation to capture experimental autorotation. Copeland’s …

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 …

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 …

Gradient Based Optimization Methods For Robust Learning And Biomedical Signal Modeling, Jarrod Mau

All Graduate Theses and Dissertations, Fall 2023 to Present

This dissertation explores how modern artificial intelligence techniques can be used to better understand complex biological data. Specifically, it develops new machine learning based methods and applies them to two important biomedical problems: analyzing brain signals and studying protein behavior.

The first part of the work introduces a new machine learning approach designed to improve how computers classify structured data. Traditional neural networks are powerful but can sometimes generalize poorly. This research proposes a method that combines the flexibility of neural networks with the reliability of ensemble techniques, leading to more robust and accurate predictions across different types of datasets. …

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 …

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 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 …

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 …

Rainbow Dominating Sets Of Graphs, Samuel L. Powell

All Graduate Theses and Dissertations, Fall 2023 to Present

The content of this thesis may be compared to a stack of plates with a common design that are broken, one at a time. If the plates are broken into large enough pieces you would be able to choose one fragment from each broken plate to discover the entire design that the plates share. For example, if you were still missing the center of the design after taking a piece from some plates, you could look for the piece of the next broken plate with the region in question.

We study the question of how many broken plates might guarantee …