Applied Mathematics Commons^™

Using Provided Guided Notes In Coordinated Introductory First-Year Mathematics Courses, Jennifer L. Huber

Mathematics Dissertations

The goal of this study is to investigate how standardized guided notes shape instructional practices and student engagement in coordinated introductory first-year college mathematics courses at a large public university. The researcher explored three multi-section introductory mathematics courses with overlapping learning objectives. Each course required students to purchase a student workbook as part of the instructional materials for the class. The instructors taught primarily from the workbook containing guided notes created by a former coordinator of the course. The researcher used a mixed-methods approach. Instructors and students participated in surveys, class observations and provided class meeting notes. Instructors shared additional …

Investigating The Connection Between Als Through The Mutation R522s In The Rna Binding Protein, Dennia Estrella-Vargas, Lydia Uptain

Mathematics

Amyotrophic lateral sclerosis (ALS) is a fatal disease that causes the deterioration of motor neurons , death is usually due to respiratory paralysis. The variant R522S was chosen because it is near a hot spot of pathogenic variants. It is an arginine-to-serine swap, this swap is present in pathogenic variants near the 522 position, such as R514S, R521S, R524S. Recent evidence suggests that arginine-deficiency can influence disease progression.

Inverse Problems For The Radiative Transport Equation In Local And Non-Convex Geometries, Faith E. Hensley

Theses and Dissertations--Mathematics

Inverse problems for the radiative transport equation (RTE) arise in a wide range of imaging applications, including optical tomography and problems motivated by non-line-of-sight imaging. Classical reconstruction methods rely heavily on ballistic, or unscattered, photons and typically require full boundary access, leading to severe instability and limited applicability in geometrically constrained settings. This dissertation investigates inverse radiative transport problems with restricted boundary data and develops reconstruction techniques based on scattered photons. The central focus of this work is the analysis and isolation of the single-collision term in the collision expansion of solutions to the RTE. By exploiting its distinct analytical …

Using Ai To Analyze Survey Data, Sara Martucci

Open Educational Resources

This assignment in Methodology in Sociology/Criminology engages students in the full research process by guiding them through variable selection, data analysis, interpretation, and critical reflection on AI-assisted decision-making. Using a class-generated survey dataset (or an existing dataset), students develop a research question, identify independent and dependent variables, and formulate a hypothesis. They then compare their selections with those suggested by an AI tool, analyzing differences in reasoning and variable choice. Through SPSS, students generate frequency tables, charts, and scatterplots to examine relationships between variables, including potential intervening factors. The assignment culminates in a group presentation and reflective analysis on the …

Beyond Full Fine-Tuning: The New Playbook For Adapting Deep Neural Networks, Cristian S. Mcgee

Honors Undergraduate Theses

Fine-tuning is the process of teaching and specializing a pre-trained neural network on a downstream task. Fine-tuning is a rapidly growing topic in artificial intelligence domains; however, many fine-tuning endeavors are highly specialized without a coherent framework connecting them. This work presents a unified perspective on fine-tuning methods and performance metrics. Our perspective organizes the methods in terms of how they are applied to fine-tuning. This framework showcases methods that (i) update effective subspaces of the pre-trained model, (ii) change the adaptation optimization procedure, and (iii) alter the representations of the embedded input. Additionally, we present unconventional metrics such as …

Inequality In The Urban Forest: Modeling Tree Canopy Dynamics Through Demographics And Restoration Strategies, Eve Johansson

Honors Theses

Urban tree canopies play an important role in environmental quality, public health, and neighborhood livability, yet their distribution is highly uneven and often reflects historical patterns of inequality. In Brooklyn, long-term processes such as redlining, uneven development, and demographic change have contributed to persistent disparities in access to green space.

This thesis examines how urban tree canopy evolves across space and time in Brooklyn and how different restoration strategies affect long-run outcomes. The analysis uses demographic and canopy data from 1990-2020, considering race, income, employment, and educational attainment. Among these, education is the most consistent predictor of canopy coverage, with …

Using L1-Magic For Feature Enhancement And Reduced Redundancy In Hyperspectral Data, Ashley Alfred

Mathematics Dissertations

Hyperspectral imaging offers detailed spectral information, but achieving high spatial resolution typically requires large and expensive equipment. This study explores an alternative approach: enhancing low-quality hyperspectral bands using an L1-norm minimization technique known as L1-magic. The goal is to improve the utility of low-cost hardware by preserving discriminative features, promoting sparsity, and reducing spectral redundancy. We apply L1-magic to enhance low-quality bands and hypothesize that this method selectively amplifies key features while suppressing redundant information. Experimental results indicate that the enhanced bands approach the quality of high-resolution data, enabling robust feature extraction without reliance on high-end hyperspectral cameras.

Global Weak Solutions Of Optical Variational Wave System, Shahrazad Hamed Alnafie

Graduate Theses, Dissertations, and Problem Reports (ETD)

The coupling of a variational wave equation with Maxwell’s equations gives rise to the optical variational wave system, a hyperbolic PDE system that models the director field of the nematic liquid crystals. This system presents unique analytical challenges that have not been addressed in the existing literature. In this dissertation, we study the one-dimensional case of this system.

We establish the global existence of conservative weak solutions to the associated Cauchy problem. The hyperbolic system is derived using the energy variational method. Through a sequence of suitable coordinate transformations, we reformulate the system while preserving its hyperbolicity. Due to degeneracy …

A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey

Williams Honors College, Honors Research Projects

This honors project will build a 1D Symmetric Interior Discontinuous Galerkin (SIPDG) solver in Rust for Stum-Liouville type problems such as the Poisson equation, with Robin, Dirichlet, and Neumann boundary conditions. The work will cover the full pipeline: starting from the strong form of the PDE, deriving the DG weak form, implementing element and interface operators, and assembling or apply the discrete operator. Rust's safety and concurrency (e.g, via Rayon) will be used to explore serial and parallel performance. A test-driven development approach will be used to maintain a strong suite of tests. The project will result in a documented …

A Bayesian Late-Fusion Supportability Framework For Rare-Disease Severity Prediction In Glut1 Deficiency Syndrome, Jordan M. Rodriguez

Mathematics Dissertations

Glucose transporter type 1 deficiency syndrome (GLUT1-DS) is a rare neurometabolic disorder with heterogeneous neurological and developmental severity. Because patient-level severity is not observed as a single validated outcome, this dissertation develops a Bayesian late-fusion supportability framework for constructing and predicting an ordered latent severity phenotype from clinical, genetic, and EEG-derived evidence. The primary target was constructed in a larger clinical cohort using age-5 symptom burden and learning cognition, then assigned to an aligned multimodal prediction cohort. Target-defining variables were excluded from supervised predictors, and models were evaluated using patient-exclusive cross-validation with training-fold preprocessing and fold-wise EEG PCA.

The primary …

Type Ii Diabetes Treatment Comparison Via Compartment Modeling, Abigail M. Collins

Theses and Dissertations

Type II diabetes mellitus affects one in ten adults worldwide, yet the effects of treatment type and adherence level on developing complications and quality of life have not been well characterized at the population level, and mathematical modeling offers a structured way to examine these dynamics. This thesis adapts the Boutayeb et al. (2004) model to incorporate dynamic treatment types and levels of adherence, producing nine scenarios in which complication development rate and complication recovery rate differed, to compare peak complications and quality of life across treatment and adherence conditions. Using a system of ordinary differential equations and compartment modeling, …

Dataless Neural Networks For Boolean Satisfiability And Network Optimization, Andrew Evan Gautier

Graduate Theses, Dissertations, and Problem Reports (ETD)

Combinatorial optimization problems (COPs) require searching over a finite solution space subject to constraints, with the goal of satisfying an objective function. They arise in operations research, scheduling, resource allocation, circuit design, and many other fields. Many problems in combinatorial optimization (including satisfiability and network design) are NP-hard. Traditionally, researchers have built approximate solvers that return near- optimal solutions efficiently by developing increasingly sophisticated heuristics and meta- heuristics. Deep learning has provided new opportunities for improving combinatorial solvers by leveraging neural guidance to prune the search space. Traditional neural networks have distinct drawbacks in this context: separate training and …

Eigenvalue Spacing Distributions And The Weak Disorder Limit For Random Schrodinger Operators, Kyle E. Hammer

Theses and Dissertations--Mathematics

We study a collection of discrete Schrodinger Operators with random potentials through the lens of global and local eigenvalue spacings. We discuss the three models: the standard scaled disorder Anderson Model, the Anderson-Bernoulli Polymer Model, and the Discrete Fractional Laplacian Anderson Model. First, we discuss the scaled disorder case using the invariant measure and its application to the density of states in the weak disorder limit. We also prove the limit of the local and global eigenvalue spacings in the non random case, and demonstrate numerically how randomness affects the eigenvalue spacings. We then discuss a special family of random …

A Mathematical Frameworks For Singular, Nonlinear Phenomena: Applications To Nematocyst Firing And Inhomogeneous Nls With Coulomb Potential, Abdulrahman Alharbi

Theses and Dissertations

Nematocysts are specialized cellular organelles found in all cnidarians, including corals and jellyfish, as well as in some single-celled protists such as dinoflagellates. These organelles display remarkable diversity in morphology and function, playing roles in prey capture and defense. The firing of a nematocyst is one of the fastest accelerations in nature, yet the underlying physical mechanisms remain not fully understood. In this work, we address key questions: how sufficient force is generated to overcome the fluid boundary layer, whether fluid–structure interaction models can reproduce observed dynamics, and what mechanisms trigger discharge.

Our research investigates models based on osmotic pressure …

Applications Of Machine Learning For Evaluating Downward-Coupled Stratosphere-Troposphere Interactions And Subseasonal Forecasts Of Opportunity, Elena M. Fernandez

Electronic Theses & Dissertations (2024 - present)

Wintertime stratospheric dynamics provide key information for understanding atmospheric teleconnections and improving subseasonal-to-seasonal (S2S) predictions on timescales of two weeks to two months. Periods of enhanced predictability, often referred to as forecasts of opportunity, arise from large-scale teleconnected variability, within which the stratosphere serves as an important precursor for tropospheric states, such as near-surface temperatures. While traditional diagnostics of downward coupled stratosphere-troposphere interactions typically rely on zonal-mean representations of wind and geopotential height, this dissertation presents an alternative vortex-centric framework through metrics that capture the daily geometric and dynamical evolution of the stratospheric polar vortex. The proposed stratospheric …

The Effects Of Overwash On Barrier Island Evolution And Building A Barrier Island Measure Of Resistance, Beth Thomas

Theses and Dissertations

Barrier islands are critical for coastal communities, as they serve as a natural buffer against storm surge, waves, and the effects of rising sea levels, protecting life and property. These islands continuously evolve due to both normal and severe environmental conditions; global warming makes it increasingly difficult to predict the evolution of these islands due to increases in storm frequency and intensity. We present a cellular model of barrier island evolution consisting of biotic and abiotic processes including the effects of vegetation, wind, ocean currents, and gravity. The model is used to predict the future evolution of barrier islands off …

Mathematical Models With Clinical Applications For Improving Health Outcomes, Helen Harris

Theses and Dissertations

In clinical settings, patients are exposed to many risks and stressors that could result in adverse health outcomes. Here we present mathematical models that seek to address these risks. First, we present a Markov Chain model to investigate the effect of medication reconciliation (MR) completion on patient health outcomes in the intensive care unit. Using this model, we simulate the annual incidence of adverse drug events (ADEs) for three different ADE rates. Based on the simulated results, we conduct a cost-benefit analysis for various levels of compliance to determine the financial implications of increasing MR completion depending on the baseline …

Machine Learning-Based Intrusion Detection System For Iot Networks Using The Rt-Iot 2022 Dataset, Bukunmi Ebenezer Afolabi

Theses, Dissertations and Capstones

The rapid expansion of the Internet of Things (IoT) has transformed modern computing by enabling seamless connectivity among heterogeneous devices across diverse application domains. However, this increased interconnectivity has significantly enlarged the attack surface of IoT networks, exposing them to a wide range of sophisticated cyber threats. Conventional security mechanisms often lack the capability to detect emerging attacks in real time, thereby necessitating the development of intelligent Intrusion Detection Systems (IDS) capable of accurately identifying malicious network activities. This study developed and evaluated a machine learning-based intrusion detection framework for multiclass IoT attack detection using the RT-IoT2022 dataset. The dataset …

Quantum Mechanics As A Framework For Data Assimilation And Its Application To Atmospheric Parameterization, David Freeman

Dartmouth College Ph.D Dissertations

Quantum mechanics, as a mathematical system, can be understood as a generalization of classical probability theory. Quantum Mechanical Data Assimilation (QMDA) is a method in which classical dynamical systems are embedded into a quantum mechanical setting, with an associated data assimilation scheme leveraging the operator algebraic setting. In this dissertation, the algebraic structure underlying the operator theoretic formulation of QMDA is discussed. A procedure for closure of dynamical systems based on QMDA, known as Quantum Mechanical Closure (QMCl), is then constructed, and the procedures for constructing the quantum embeddings and implementing QMCl in practice are laid out and implemented for …

Quantum General Relativity V2, James Glimm, James Glimm

Department of Applied Mathematics & Statistics Faculty Publications

We construct a quantum general relativity theory.. The construction includes specification of a cosmological model. Based on type Ia supernova data, the model has zero dark energy and zero cosmological constant.

The analysis is at the level of theoretical physics, with some mathematical details omitted.