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Full-Text Articles in Mathematics

The Edge-Distinguishing Game, Nathaniel Benjamin, Elisa Benthem, Cooper Burkel, Marissa E. Chesser, Mike Janssen Jul 2026

The Edge-Distinguishing Game, Nathaniel Benjamin, Elisa Benthem, Cooper Burkel, Marissa E. Chesser, Mike Janssen

Communications on Number Theory and Combinatorial Theory

In this paper, we introduce a graph coloring game called the Edge-Distinguishing Game (EDGe). The edge-distinguishing chromatic number of a graph is used to determine the moves each player can make. We determine which player has a winning strategy for particular graphs and graph families. Additionally, utilizing principles from game theory as well as previous work on a computational solution for the Game of Cycles.

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Faith-Informed Instruction In Secondary Mathematics: A Hermeneutic Phenomenological Study Of Lutheran Church–Missouri Synod Teachers, Jonathan Balsman Jul 2026

Faith-Informed Instruction In Secondary Mathematics: A Hermeneutic Phenomenological Study Of Lutheran Church–Missouri Synod Teachers, Jonathan Balsman

Doctoral Dissertations and Projects

The purpose of this hermeneutic phenomenological study was to understand the phenomenon of faith-informed instruction as experienced by secondary mathematics teachers in Lutheran Church–Missouri Synod (LCMS) schools in the United States. The theory guiding this study was Vygotsky’s theory of social constructivism, which frames educators’ instructional and theological meaning-making as socially and contextually developed through collaborative, relational learning environments. The central research question guiding this study was: What are the lived experiences of LCMS secondary mathematics teachers as they practice faith-informed instruction? This study used a hermeneutic phenomenological design to interpret teacher meaning-making and reflective practice. Participants were selected using …

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Differentiating And Accommodating Ocd And Anxiety In Mathematical Contexts, Madeline F. Gavares Jul 2026

Differentiating And Accommodating Ocd And Anxiety In Mathematical Contexts, Madeline F. Gavares

Interdivisional Studies Summer Fellows

Students in mathematics classrooms may experience emotional and cognitive challenges that affect how they engage with coursework and assessments. While math anxiety has been widely documented, less attention has been given to how obsessive-compulsive disorder (OCD), particularly checking behaviors, may influence students’ experiences in math settings. This study explores how students who report math anxiety and those who report OCD symptoms describe their engagement with math tasks and test-taking. Drawing on survey and interview data from students and teachers, this study examines how these experiences are articulated and perceived in academic math contexts, rather than evaluating ability or outcomes. By …

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Double-Scoring: Reliable Extraction Of Strong Lottery Tickets, Bryce Christopherson, Jack Baretz, Darian Colgrove, Salah Dandan Jul 2026

Double-Scoring: Reliable Extraction Of Strong Lottery Tickets, Bryce Christopherson, Jack Baretz, Darian Colgrove, Salah Dandan

Mathematics Faculty Publications

The lottery ticket hypothesis proposes that large random neural networks contain sparse subnetworks that can match the performance of dense models after compara- ble training. A stronger version asserts that sufficiently overparameterized random networks contain subnetworks that are already accurate before any weight training. Existing theory establishes that such strong lottery tickets exist, but reliable ex- traction remains difficult. We revisit edge-popup, a frozen-weight score-training method for extracting strong tickets, and identify layerwise sparsity selection as a central bottleneck. We introduce double-scoring, an augmented score-space parameterization that replaces a layerwise sparsity search with optimization over enlarged score tensors. We prove …

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A Bayesian-Optimized Ensemble Deep Learning Framework For Automated Detection And Classification Of Retinal Diseases In Ghana Using Oct Images, Gifty Duah, Eric Nyarko, Gideon Nana Amo, Theophilus Dwamena Frimpong, Anani Lotsi Jul 2026

A Bayesian-Optimized Ensemble Deep Learning Framework For Automated Detection And Classification Of Retinal Diseases In Ghana Using Oct Images, Gifty Duah, Eric Nyarko, Gideon Nana Amo, Theophilus Dwamena Frimpong, Anani Lotsi

School of Mathematical & Statistical Sciences Faculty Publications

Retinal diseases pose a significant global health challenge due to their potential to cause severe visual impairment and blindness. This study aimed to develop a robust deep learning ensemble framework for the automated detection and classification of retinal diseases from optical coherence tomography (OCT) images. This study used OCT images from WATBORG Eye Services in Ghana, including glaucoma, macular edema, posterior vitreous detachment (PVD), and healthy eyes. The data preprocessing steps included augmentation, resizing, and one-hot encoding. The dataset was divided into training (56%), validation (14%), and testing (30%) sets using stratified sampling. Six convolutional neural network (CNN) architectures, Visual …

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Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇ Jul 2026

Notes On The Geometry Of Electromagnetic Fields And Maxwell’S Equations Along A Nonnull Curves In Nonflat-3d Space Forms MQ3(C), Fatma Almaz, Cumali̇ Eki̇ci̇

Turkish Journal of Mathematics

In this paper, the directional derivatives in accordance with the orthonormal frame {T→, N→, B→} are defined in Mq3(c), the extended Serret-Frenet relations by using Frenet formulas are expressed. Furthermore, we express the bending elastic energy function for the same particle in Mq3(c) according to curve γ(s, ξ, η) and we tried to interpret it from a geometric perspective of the energy for unit vector fields. Also, Maxwell’s equations are expressed for the electric and magnetic field vectors …

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Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür Jul 2026

Biharmonic Curves In Warped Product Manifolds I ×FMN(C), Şaban Güvenç, Ci̇han Özgür

Turkish Journal of Mathematics

We explore the geometric properties of biharmonic curves in warped product manifolds of the form I ×f Mn(c), where I is an open interval and Mn(c) is a space of constant curvature. By establishing a main theorem, we analyze four distinct cases to reveal deeper curvature-related characteristics of these curves, including situations where they are slant. Finally, we construct three examples in I ×f S2(1).

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Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae Jul 2026

Generalized Submaximality And Paracompactness In Ideal Topological Spaces Via Δβ*-𝔍-Open Sets, Chawalit Boonpok, Areeyuth Sama-Ae

Turkish Journal of Mathematics

This paper explores the notions of δβ*-𝔍-submaximality and δβ*-𝔍-paracompactness within ideal topological spaces, viewing them as natural generalizations of the traditional concepts of submaximality and paracompactness. These concepts arise naturally in the context of ideal topology, where an ideal 𝔍 on a topological space provides additional structure for analyzing topological properties. It focuses on the study of submaximal spaces by employing δβ*-𝔍-open sets, which serve as fundamental building blocks for understanding the topological behavior in ideal spaces. Furthermore, the work provides multiple characterizations of δβ*-𝔍-paracompact spaces and examines how this property behaves …

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Observations On Recurrent Loss In The Neural Network Model Of A Partial Differential Equation: The Advection–Diffusion Equation, Jonah A. Reeger Jul 2026

Observations On Recurrent Loss In The Neural Network Model Of A Partial Differential Equation: The Advection–Diffusion Equation, Jonah A. Reeger

Faculty Publications

A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic exploration of the stability of the solutions generated by these ML approaches. Here, a recurrent network is introduced that matches precisely the evaluation of a multi-step method paired with a collocation method for approximating spatial derivatives in the advection–diffusion equation. This allows for two things: (1) the use of traditional tools for analyzing the stability of a numerical method for solving PDEs and (2) bringing to bear …

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Comparative Analysis Of Traditional And Deep Learning Time Series Architectures For Influenza A Infectious Disease Forecasting, Edmund Fosu Agyemang, Hansapani Rodrigo, Vincent Agbenyeavu Jul 2026

Comparative Analysis Of Traditional And Deep Learning Time Series Architectures For Influenza A Infectious Disease Forecasting, Edmund Fosu Agyemang, Hansapani Rodrigo, Vincent Agbenyeavu

School of Mathematical & Statistical Sciences Faculty Publications

Influenza A remains a major cause of respiratory mortality worldwide, motivating accurate forecasting to support timely preparedness and resource allocation. This study presents a comparative evaluation of two traditional seasonal time series baselines, ARIMA and Holt–Winters exponential smoothing (ETS), and six deep learning (DL) architectures (Simple RNN, LSTM, GRU, BiLSTM, BiGRU, and a Transformer) for forecasting monthly Influenza A case counts in the United States. Data from January 2009 to December 2023 were analyzed, using January 2009 to December 2022 for training and January 2023 to December 2023 for out-of-sample testing. Models were tuned using a validation split and assessed …

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Operator Theoretic Methods For Coupled Pde In General Geometries, Yuhao Mu Jul 2026

Operator Theoretic Methods For Coupled Pde In General Geometries, Yuhao Mu

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

This thesis develops and applies operator theoretic methods applied to coupled PDE analysis in general geometries, in which the coupling involves interchange across a boundary. The general geometries refer to domains with merely Lipschitz continuous boundaries (e.g. any non-convex polygon), as opposed to those with any further smoothness conditions on the boundary. The key results include a new pressure elimination method for coupled fluid–structure interaction (FSI) PDEs with boundary interchange, which allows an explicit semigroup representation of the PDE in terms of just the fluid and structure variables. This novel technique, valid over arbitrary bounded Lipschitz domains, leads to a …

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Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor Jul 2026

Pseudodifferential Absorbing Boundary Conditions For Waves, Lauren Taylor

Mechanical Engineering Theses

Absorbing boundary conditions (ABCs) are required to truncate the computational domain when performing Finite Element Analyses of exterior acoustic problems where physical domain is unbounded. ABC is applied on a fictitious boundary containing the scatterer and ideally allows outgoing waves to leave without non-physical reflections. Preventing artificial reflections is essential to benefit from the accuracy of the numerical method used. Otherwise, ABC acts as a reflective surface, and artificial reflections distort the solution in the entire domain which is not recoverable by any type of refinement. Pseudodifferential ABCs were used to describe the Dirichlet-to-Neumann map which maps known boundary values …

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Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett Jul 2026

Analytic Solutions To Oceanographic Kinematic Property Equations, James Turbett

Theses and Dissertations

With the recent advent of large submesoscale drifter deployments, interpreting the timeseries of kinematic properties (KP) - divergence, vorticity, shear, and normal strain rates observed therein is a pressing issue. The evolution equations for the four KP are derived from the two-dimensional momentum conservation equations. The resulting equations, a nonlinear coupled system of ordinary differential equations, capture the submesoscale motion of drifters along fixed ocean surfaces, with time and space scales on the order of days and kilometers. This thesis builds theory around KP timeseries behavior by solving for the analytic solutions in the particular cases that one KP is …

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Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett Jul 2026

Coupled-Pendulum Modeling In An Ode Class: An Assignment On Fourier-Initialized Gradient Descent In Machine Learning, Huy Truong, Andrew Bennett

CODEE Journal

As data-driven methods are increasingly used in science and engineering, students benefit from learning to integrate machine learning techniques with traditional mathematical modeling. We present a hands-on extra-credit assignment for an undergraduate ordinary differential equations (ODE) course that enables students to compare classical analytical methods with data-driven approaches on the same physical system. Using a coupled-pendulum system---two pendulums connected by a spring---with real experimental data acquired via video tracking of a real physical setup, students work through three models in a guided Jupyter notebook with all code provided. First, they fit a neural network with Fourier features as a purely …

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Differential Topology And The Poincaré-Hopf Theorem, Tara Saini Jul 2026

Differential Topology And The Poincaré-Hopf Theorem, Tara Saini

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we will develop the ideas needed to understand and prove the Poincaré–Hopf Theorem, which connects the local behavior of smooth vector fields to global topological properties. We will begin by introducing smooth manifolds and smooth maps, which are the basis of differential topology. We will then define derivatives of smooth maps through tangent spaces and use these to classify points. To build toward the theorem, we will introduce orientation, degree, and smooth vector fields. These concepts will culminate in a proof of the Poincaré–Hopf Theorem, aided by Brouwer’s Fixed Point Theorem. Finally, we will apply the result …

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A Closed Form For The Pulsar Sequence, Ryan Z. Liu Jul 2026

A Closed Form For The Pulsar Sequence, Ryan Z. Liu

Rose-Hulman Undergraduate Mathematics Journal

In this paper, we study the Pulsar Sequence, an integer sequence derived from Latin-square-based “Pulsar puzzles” introduced by the Cracking the Cryptic YouTube channel. A Pulsar puzzle consists of two interlocked spirals of circled and uncircled squares, generating the Dual and Pulsar sequences, respectively. We investigate the properties of the Pulsar puzzle and focus our work on constructing the Pulsar Sequence, allowing us to solve a Pulsar puzzle of any size. A general formula to calculate any term of the Pulsar Sequence is proposed at the end of the paper.

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A Categorical Framework For Modeling Genetic Drift, Taylor G. Mendes Jul 2026

A Categorical Framework For Modeling Genetic Drift, Taylor G. Mendes

Rose-Hulman Undergraduate Mathematics Journal

Genetic drift describes changes in allele frequencies that arise from chance sampling in finite populations. This paper develops a categorical framework for organizing the structural features of drift. Population states are modeled as objects, evolutionary transitions as morphisms, reversible transitions as groupoid morphisms, and structure-preserving comparisons between models as functors. Group actions are used to describe deterministic evolutionary operators such as mutation and selection, while orbits and fixed points identify reachable allele-frequency states and stable absorbing outcomes. Universal properties are then used to describe drift as a coherence condition connecting stochastic transitions with deterministic evolutionary maps. The resulting framework complements …

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Multiplicity Of Laplacian Eigenvalues That Can Be Represented By Sum Of Two Squares Using Number Theory, Changfeng Zhou Jul 2026

Multiplicity Of Laplacian Eigenvalues That Can Be Represented By Sum Of Two Squares Using Number Theory, Changfeng Zhou

Rose-Hulman Undergraduate Mathematics Journal

In this article, we use results of Number Theory to prove the conjecture on the eigenvalue problem of a 2D elliptic PDE proposed by P.Korman in his recent paper \cite{ref}: for any even integer $2k$, one can find an eigenvalue $N$ that can be represented as $N=a^{2}+b^{2}$, with integers $a\neq b$ with multiplicity $2k$, while for any odd integer $2k + 1$, one can find an integer $M$ that can be represented as $M=a^{2}+b^{2}$ with $a\neq b$ and multiplicity $2k+1$. In addition, the manuscript gives the formula to find those $N$'s.

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Symmetries In Apollonian Circle Packings, Clyde Kertzer Jul 2026

Symmetries In Apollonian Circle Packings, Clyde Kertzer

Rose-Hulman Undergraduate Mathematics Journal

An Apollonian circle packing is generated from a Descartes quadruple (a set of four mutually tangent circles) by repeatedly filling the spaces between mutually tangent circles with further tangent circles. By studying the circles' curvatures $a,b,c,d$, two distinct types of symmetric packings appear: one where $a+b+c=d$ and one where $c=d$. We give complete parameterizations of these symmetric packings and count how many packings of each type are contained by a given enclosing circle.

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A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer Jul 2026

A Differential Equation–Based Epidemiological Model Of Post-Operative Chronic Pain In Scoliosis Patients With Data-Driven Analysis, Paige Zhu, Padmanabhan Seshaiyer

CODEE Journal

Chronic post-surgical pain (CPSP) is a common and often overlooked complication following surgical correction of idiopathic scoliosis, impacting long-term patient wellbeing despite improvements in surgical outcomes. This project introduces a novel epidemiological framework to model the progression of CPSP using a compartmental structure. By applying a coupled system of nonlinear differential equations, we simulate pain trajectories over time and assess the effectiveness of surgical interventions. The model is implemented for a single-cohort population and extended to a two-cohort design to compare outcomes between Posterior Spinal Fusion (PSIF) and Vertebral Body Tethering (VBT) procedures. Further stratification by patient age enables us …

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Fixed-Parameter Extrapolation And Aperiodic Order, Stephen Fenner, Frederic Green, Steven Homer Jul 2026

Fixed-Parameter Extrapolation And Aperiodic Order, Stephen Fenner, Frederic Green, Steven Homer

Mathematics

Fix any λ∈C. We say that a set S⊆C is λ-convex if, whenever a and b are in S, the point (1-λ)a+λb is also in S. We investigate the properties of λ-convex sets and their (topological) closures, and we prove a number of facts about them. Let Qλ⊆C be the least λ-convex superset of {0,1}. Generalizing results of R. G. E. Pinch, we give a sufficient condition on λ for Qλ and some other related λ-convex sets to be discrete by introducing the notion of a strong PV number. These conditions give rise to a number of periodic and aperiodic …

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Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation, Gary Towsley, Olympia Nicodemi Jul 2026

Trattato Dell’Alcibra Amuchabile (Anonimo): A Guided Translation, Gary Towsley, Olympia Nicodemi

Geneseo Authors

The Trattato dell’Alcibra Amuchabile is a pre-modern algebra text from c. 1365. It is written in a Tuscan dialect of Italian and is situated in the abbacus school tradition, schools that taught the mathematics needed for a mercantile society. Like all the algebra written in Italy at the time, it was inherited from al-Khwarizmi and, like his, written with no symbols—no x’s, y’s, plus signs, etc. It was what is sometimes called “rhetorical algebra.”  There is very little source  material available in English from this important era in the history of algebra. This book helps fill that gap. …

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Toward A Didactical Phenomenology For The Completeness Axiom, Sean Larsen, Tenchita Alzaga Elizondo, Kristen Vroom, Stephen Strand Ii Jul 2026

Toward A Didactical Phenomenology For The Completeness Axiom, Sean Larsen, Tenchita Alzaga Elizondo, Kristen Vroom, Stephen Strand Ii

School of Mathematical & Statistical Sciences Faculty Publications

The study is part of an instructional design project focused on introductory real analysis. The goal of the project is to develop a theoretically grounded and empirically supported instructional approach that builds on students’ experiences in the calculus sequence to engage them in the reinvention of the rigorous foundations of the calculus. An essential aspect of this foundation is the completeness of the real numbers. Drawing on the didactical phenomenology heuristic from the theory of Realistic Mathematics Education (RME), we conducted an iterative instructional design study focused on the completeness axiom. The work proceeded in two phases. First, we conducted …

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Math 119: Math For Elementary School Teachers Instructor Guide, Seth Lehman Jul 2026

Math 119: Math For Elementary School Teachers Instructor Guide, Seth Lehman

Open Educational Resources

OER instructor guide for Math 119: Math for Elementary School Teachers at Queens College

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Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender Jul 2026

Cdt-1d Cnn Integration With Simpson-Sobolev Regularization For High-Frequency Options Trading: With Fem-Based Heston Option Pricing, Daniel M. Margolis, Johannes Tausch, Arthur K. Selender

Mathematics Theses and Dissertations

This dissertation presents a computational framework for high-frequency options trading that combines Cross-Data-Type 1-D Convolutional Neural Networks (CDT-1D CNN) with Simpson-Sobolev regularization for directional prediction, and finite element methods (FEM) for realistic option pricing during backtesting. The core innovation lies in developing a mathematically rigorous regularization approach that maintains the adaptability of modern deep learning while enabling accurate evaluation through stochastic volatility models. The primary contribution is the Simpson-Sobolev regularization scheme, which extends traditional Sobolev regularization by incorporating Simpson’s rule for numerical integration. This approach achieves higher-order accuracy in approximating the Sobolev norms that control function smoothness. Simpson’s rule attains …

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Math 119: Math For Elementary School Teachers Syllabus, Seth Lehman Jul 2026

Math 119: Math For Elementary School Teachers Syllabus, Seth Lehman

Open Educational Resources

OER course syllabus for Math 119, Math for Elementary School Teachers, at Queens College

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Matching The Stars To A Game Of Aggression, E. Chambers, Kristen Barnard Jun 2026

Matching The Stars To A Game Of Aggression, E. Chambers, Kristen Barnard

Electronic Proceedings of Undergraduate Mathematics Day

Region against region and army against army, we chart and battle among the stars! This paper studies the combinatorial game Aggression using graph-theoretic models. We focus on how winning strategies depend on the structure of the game graph, with particular attention to star graphs, matchings, and their disjoint union. The results presented here come from research conducted under the guidance of Dr. Kristen Barnard during the summer of 2025. We begin by introducing the game, describing the rule set used, and explaining how maps can be represented as graphs. From there, we examine how adjacency, placement order, and tie-breaking rules …

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Strict Steiner Symmetrization For Polygons, Joseph Chai, Sun-Yung Alice Chang Jun 2026

Strict Steiner Symmetrization For Polygons, Joseph Chai, Sun-Yung Alice Chang

Electronic Proceedings of Undergraduate Mathematics Day

In this note, we introduce a method called Strict Steiner Symmetrization (see Section 2.2) that is an altered form of Steiner Symmetrization that fixes the number of vertices. The context of this paper will be to prove the Isoperimetric Inequality in R2 via approximation by polygons. Specifically, to establish that among all n-gon domains in the plane, the regular m-gon, m ≥ n, uniquely minimizes the isoperimetric ratio and that the limit of this regular polygon (that is the circle) achieves equality in the isoperimetric inequality. This note is an extracted portion of my junior thesis (A Polygonal Proof of …

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Predator-Prey Dynamics: Exploration And Logistic Extension Of The Lotka-Volterra System, Amanda Maylath, Samuel Brensinger Jun 2026

Predator-Prey Dynamics: Exploration And Logistic Extension Of The Lotka-Volterra System, Amanda Maylath, Samuel Brensinger

Electronic Proceedings of Undergraduate Mathematics Day

The Lotka-Volterra system is a classic model of predator–prey interactions, capturing the interdependent growth and decline of two species. Using a dynamical systems approach, we identify fixed points, linearize the system via the Jacobian, and analyze phase space trajectories to determine stability and long-term behavior. This analysis provides insight into predator-prey dynamics without requiring explicit solutions. We further extend the model by incorporating a carrying capacity for the prey, reflecting more realistic population dynamics.

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Huffman Tree Uniqueness, Elijah Diller, Adam Volk Jun 2026

Huffman Tree Uniqueness, Elijah Diller, Adam Volk

Electronic Proceedings of Undergraduate Mathematics Day

The Huffman algorithm is a standard algorithm used to generate an optimized binary encoding of a string. Using this algorithm, it may be possible to come up with more than one possible optimized binary encoding for a given string, so the following question arises: what strings have a unique optimized binary encoding? By unique encoding, we mean a unique vertex-labeled binary tree resulting from the Huffman algorithm. We do not worry about edge labels as every binary tree corresponding to a string with n distinct characters has 2n−1 ways of assigning the edge labels and determining the code. This investigation …

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