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Integrating Hydrology And Human Water Footprints: A Case Study Of The Great Salt Lake Basin, Rachel Lynne Seeley Aug 2026

Integrating Hydrology And Human Water Footprints: A Case Study Of The Great Salt Lake Basin, Rachel Lynne Seeley

All Graduate Theses and Dissertations, Fall 2023 to Present

Global demand for water is outrunning supply, and how we account for water is part of the problem. Many water management frameworks are based solely on how much physical water moves through rivers, aquifers, and other water bodies, missing the water that is embedded in food and other products a region produces and exports. This study developed a new, generalizable water accounting framework that incorporates this “hidden water,” known as virtual water, into water management and applied the framework in the Great Salt Lake Basin.

The Great Salt Lake is shrinking, and an often-overlooked driver of the lake’s decline is …


Hidden Symmetries And Higher Dimensional Rotating Black Holes, Luis Fernando Temoche Hurtado Aug 2026

Hidden Symmetries And Higher Dimensional Rotating Black Holes, Luis Fernando Temoche Hurtado

All Graduate Theses and Dissertations, Fall 2023 to Present

A standard approach to probing the dynamics of a physical system is to expose it to an external perturbation—such as an incident wave—and analyze its response after the interaction. Mathematically, this procedure is formulated in terms of differential equations governing the evolution of the perturbation.

In the context of black hole physics, an analogous strategy can be employed by studying the response of the event horizon to external perturbations. The differential equations describing these interactions are often invariant under nontrivial transformations, revealing hidden symmetries that help explain distinctive features of higher-dimensional black holes.

By exploiting these hidden symmetries in the …


Investigation Of Yy Production Methods For Invasive Channel Catfish Ictalurus Punctatus Population Management, Andrew M. Wisniewski Aug 2026

Investigation Of Yy Production Methods For Invasive Channel Catfish Ictalurus Punctatus Population Management, Andrew M. Wisniewski

All Graduate Theses and Dissertations, Fall 2023 to Present

Aquatic invasive species are one of the leading causes of native fish declines in the Southwestern United States. Channel Catfish Ictalurus punctatus were introduced into the Colorado River Basin, including the San Juan River, New Mexico, Colorado, and Utah for fishery enhancement during the 20th century. This introduction has contributed to the decline of native species and despite intensive mechanical removal efforts, the Channel Catfish population has persisted in the San Juan River. The Trojan Sex Chromosome approach is a promising eradication strategy that proposes the production and release of Trojan sex chromosome carriers (YY) to skew a targeted population’s …


A Data-Driven Nutrient Density Scoring Framework For Beef Using Principal Component Analysis, Teja Vuppala Aug 2026

A Data-Driven Nutrient Density Scoring Framework For Beef Using Principal Component Analysis, Teja Vuppala

All Graduate Theses and Dissertations, Fall 2023 to Present

Beef is one of the most nutrient-rich foods in the human diet, providing high-quality protein, iron, omega-3 fatty acids, B vitamins, and a wide range of other compounds important to health. However, current nutrition scoring systems used on food labels were designed to compare different foods to one another — for example, beef versus broccoli — and do not work well for judging the nutritional quality of different beef samples relative to each other. A grass-fed steak and a conventionally-finished steak can carry nearly identical Nutrition Facts panels while differing substantially in their content of omega-3 fatty acids, vitamins, and …


The Relativity Of Education: Student Perspectives On Artificial Intelligence In Community College, Ashley Greta Magana Aug 2026

The Relativity Of Education: Student Perspectives On Artificial Intelligence In Community College, Ashley Greta Magana

Electronic Theses, Projects, and Dissertations

This hermeneutic phenomenological study examined how diverse community college students experience and make meaning of the integration of generative artificial intelligence (AI) into their educational contexts. Although AI is quickly transforming higher education through automated grading, personalized learning systems, and new models of assessment, the discourse surrounding its implementation remains dominated by administrators, faculty, and institutional stakeholders, while the perspectives of students, specifically community college students who are often historically underrepresented and economically marginalized, are systematically excluded. Most existing research is quantitative and centered on universities, leaving a critical gap in qualitative understanding of the most diverse population in higher …


When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto Aug 2026

When The Best-Fit Model Is Not Best: The Glass Slipper Fallacy And Latent Growth Mixture Modelling, Jonathan L. Chia, Markus Wettstein, Andree Hartanto

Research Collection School of Social Sciences

Despite the use of latent growth mixture modelling (LGMM) to study longitudinal changes, existing practices may inadvertently impede this very investigation. Although subgroup trajectories may theoretically differ in their structure (e.g., some subgroups being linear, some curvilinear), the current convention advocates overreliance on the baseline model to derive subsequent profile trajectories, which may obscure these structural differences. In this article, we provide a brief description of extant LGMM practices, after which we explicate the pitfalls of the current approach. Finally, we provide a principled approach for LGMM research moving forward. Specifically, we recommend specifying a set of theoretically plausible models …


Technique-Level Normalization For Cybersecurity Intelligence: An Empirical Evaluation Of Att&Ck Attribution From Hids Alerts Using Fine-Tuned Transformers And Metadata Re-Ranking, Emad Sherif Aug 2026

Technique-Level Normalization For Cybersecurity Intelligence: An Empirical Evaluation Of Att&Ck Attribution From Hids Alerts Using Fine-Tuned Transformers And Metadata Re-Ranking, Emad Sherif

International Journal of Cybersecurity Intelligence & Cybercrime

Cybercrime investigations increasingly depend on the ability to interpret large volumes of automated security events. For organizations without dedicated security operations centres, a situation common among small and medium enterprises, the manual translation of raw alerts into structured threat intelligence represents a critical bottleneck that slows investigative triage and limits cross-case comparability. This paper evaluates an automated enrichment pipeline designed to address this bottleneck by mapping security events to standardised adversary behaviour labels drawn from the MITRE ATT&CK framework, supporting both operational response and cybercrime investigation workflows. We compare three pipeline configurations, a general-purpose encoder model, a cybersecurity domain-adapted variant, …


Modeling Mean And Variability Of Anxiety In Ecological Momentary Assessment Data Using Mixed-Effects Location–Scale Models, Trenzy Odero Aug 2026

Modeling Mean And Variability Of Anxiety In Ecological Momentary Assessment Data Using Mixed-Effects Location–Scale Models, Trenzy Odero

Electronic Theses and Dissertations

Ecological Momentary Assessment is a method of collecting repeated measures of people in real time within natural environments. This results in hierarchical data that has a significant amount of variation at the person level. The traditional linear mixedeffects models assume that the residual variance is constant, which might not be true when the residual variance varies among individuals as well as in time. This thesis uses mixed-effects location-scale (MELS) models to model the mean and variance of an EMA outcome together. By introducing the possibility of variability in residual variance within and across individuals and with covariates, the MELS framework …


Human-Centered Electric Vehicle Adoption Framework For Smart Mobility: Modeling Perceived Range And Charging Anxiety As A Psychological Barrier, Fatemeh Nazari, Abolfazl (Kouros) Mohammadian, Thomas Stephens Aug 2026

Human-Centered Electric Vehicle Adoption Framework For Smart Mobility: Modeling Perceived Range And Charging Anxiety As A Psychological Barrier, Fatemeh Nazari, Abolfazl (Kouros) Mohammadian, Thomas Stephens

Civil Engineering Faculty Publications

Electric vehicles (EVs) offer a transformative pathway toward reducing the environmental, economic, and health-related externalities of internal combustion engine vehicles in urban settings. Despite substantial advances in battery technology, charging infrastructure expansion, and supportive policy incentives, EV penetration remains limited which poses challenges for smart and sustainable mobility planning. A critical yet insufficiently modeled barrier to adoption lies in the psychological perceptions surrounding electric driving range and charging reliability, which is commonly framed as “range anxiety,” but more broadly reflecting perceived range and charging anxiety. To address this gap, this study introduces a latent psychological construct capturing individuals’ perceived range …


Federated Learning For Early Medical Diagnosis: Enhanced Diabetic Retinopathy Detection In Smart Healthcare, Mohammad Nasajpour Esfahani Aug 2026

Federated Learning For Early Medical Diagnosis: Enhanced Diabetic Retinopathy Detection In Smart Healthcare, Mohammad Nasajpour Esfahani

Master's Theses

This thesis investigates the role of federated learning as a privacy-preserving solution for modern healthcare challenges. In traditional machine learning, sensitive medical data must be centralized for model training, raising concerns about privacy, security, and regulatory compliance. Federated learning offers an alternative by allowing hospitals, clinics, and personal health devices to collaboratively train shared models without exchanging raw patient data. The study first explores how federated learning is being used across various healthcare domains, including cancer detection, medical imaging, and disease prediction— highlighting its potential to support secure collaboration across institutions. It addresses key benefits such as data privacy, scalability, …


Drought And Diet Breadth: Does Insect Specialization Influence Herbivory When Plants Are Under Stress?, Jakob Palmer Aug 2026

Drought And Diet Breadth: Does Insect Specialization Influence Herbivory When Plants Are Under Stress?, Jakob Palmer

All Graduate Theses and Dissertations, Fall 2023 to Present

Climate change will alter precipitation worldwide, causing more frequent and severe drought events worldwide. Drought affects many ecological processes, including plant-herbivore interactions, which are critical to biodiversity and ecosystem health. A variety of plant characteristics can influence herbivory – such as how hairy, nutritious, or toxic a leaf is – and drought has been shown to alter many of these traits. Unique characteristics of herbivore species are also important: herbivores can either feed on a variety of plants (generalists) or a group of closely related plants (specialists). Specialists can cope with traits of the plants they eat, while generalists are …


Greenhouse Gas Flux Response In Biochar- And Compost-Amended Lawn Soils Under Simulated Water Saturation Conditions, Angel Salinas, Chu-Lin Cheng, Engil Pereira, Rafael M. Almeida, James Jihoon Kang Aug 2026

Greenhouse Gas Flux Response In Biochar- And Compost-Amended Lawn Soils Under Simulated Water Saturation Conditions, Angel Salinas, Chu-Lin Cheng, Engil Pereira, Rafael M. Almeida, James Jihoon Kang

School of Earth, Environmental, & Marine Sciences Faculty Publications

Understanding greenhouse gas emission dynamics in lawn soils is important for improving climate change mitigation strategies in urban and suburban landscapes. In this greenhouse mesocosm study, carbon dioxide (CO2), methane (CH4), and nitrous oxide (N2O) fluxes were measured from 12 turfgrass soil columns arranged in an unreplicated, completely randomized 4 × 3 factorial design. Four amendment treatments (biochar, compost, bio-com [1:1 volume ratio of biochar and compost], and unamended control) were combined with three water-table conditions (full saturation, half saturation, and unsaturated), with a single column representing each treatment combination. Columns were irrigated at 1 cm day−1 for 24 days, …


Indigenous Community Research Opportunities, Sharon Hausam, Aaron M. Canter Aug 2026

Indigenous Community Research Opportunities, Sharon Hausam, Aaron M. Canter

Faculty Publications

This is a working paper produced as part of National Science Foundation project #2115169, “Transforming Rural-Urban Systems: Trajectories for Sustainability in the Intermountain West,” known as the “Intermountain West Transformation Network” (TN), led by the University of New Mexico with institutional partners at three additional universities in New Mexico, two in Arizona, and one each in Utah, Colorado, and Washington. The TN’s Indigenous and Tribal engagement was supported through a contract with Dr. Sharon Hausam, additional work by Aaron M. Canter, coordination with Dr. Lani Tsinnajinnie, and an Advisory Committee on Indigenous Information Needs primarily comprised of Indigenous representatives in …


Mathematics As Creative Structure: A Review Of Marcus Du Sautoy’S Blueprints, Sangeetha Balakrishnan, Latha R Jul 2026

Mathematics As Creative Structure: A Review Of Marcus Du Sautoy’S Blueprints, Sangeetha Balakrishnan, Latha R

Journal of Humanistic Mathematics

Marcus du Sautoy’s Blueprints: How Mathematics Shapes Creativity (2025) makes a provocative claim that creativity emerges not in opposition to constraint, but through it. Working through nine mathematical “blueprints” — symmetry, randomness, the Fibonacci sequence, among others — du Sautoy traces recurring structural patterns across artistic practice, natural phenomena, and mathematical thought. The argument is ambitious and persuasive. In this review we consider what the book adds to longstanding conversations about the relationship between scientific and humanistic ways of knowing, and reflect on what it means to reframe mathematics as an imaginative and exploratory enterprise rather than a purely technical …


The Urysohn Lemma: Munkres Variation, Irida Altman Jul 2026

The Urysohn Lemma: Munkres Variation, Irida Altman

Journal of Humanistic Mathematics

There is a tradition of Mathematics contributing to the understanding of Music. This article sets out to contribute in the other direction. It uses musical sensibilities to feel its way through a piece of mathematics called the Urysohn Lemma, suggesting the presence of rhythmic, melodic, and harmonic elements within standard proving practices of contemporary Western mathematics. This article employs a literary-philosophical technique of viewing a text in one discipline (mathematics) through the conceptual lens of another (music). As such, this article reports on no experiments—reading the article is the experiment. Each reader performs it for themselves.


Prime Numbers Are Written On Your Hand: You Simply Have Not Been Counting Correctly, Nona Servais Kamdem Simo, Awa Traore Jul 2026

Prime Numbers Are Written On Your Hand: You Simply Have Not Been Counting Correctly, Nona Servais Kamdem Simo, Awa Traore

Journal of Humanistic Mathematics

Prime numbers have resisted systematic description for over two millennia. We propose that part of the difficulty may lie in an insufficiently attentive examination of one’s own hands. In particular, we assign the natural numbers to the joints of the human hand according to a cyclic traversal protocol, and make a handful of observations which can naturally be translated into number-theoretic properties of prime numbers. We show that these properties lead us to natural activation thresholds of a unified three-phase sieve algorithm — the resulting framework provides, for the first time, a zone-based partition of the admissible space with explicit …


Front Matter Jul 2026

Front Matter

Journal of Humanistic Mathematics

No abstract provided.


Effectiveness Of Irrigated Pastures, Nikolai Gavrilovich Andreev Jul 2026

Effectiveness Of Irrigated Pastures, Nikolai Gavrilovich Andreev

IGC Proceedings (1977-2023)

Irrigated pastures are of greatest relevance to stabilizing the general fodder situation, for reasons of the high yield and low cost of pasture forage. If irrigation and fertilization are pro­vided, best yields may be expected from forage plant mixtures which consist of five species: three grasses and two legumes. Fertilizer appli­cation must be quantified, depending on the soil nutrient status and in conformity with agrochemical test results and soil maps. The use of slurry obtained from livestock farms is useful not only for higher pasture forage yields but also for better protection of ground water and surface water. Irrigated pastures …


Governance, Culture, And Law: The Expanding Scope Of Environmental Science And Sustainable Development Research, Ahyaudin Sodri, Herdis Herdiansyah Jul 2026

Governance, Culture, And Law: The Expanding Scope Of Environmental Science And Sustainable Development Research, Ahyaudin Sodri, Herdis Herdiansyah

Journal of Environmental Science and Sustainable Development

Environmental science emerged as a discipline based on physical measurements, such as soil pollutant levels (Ailijiang et al., 2022), ecological restoration (Yue et al., 2026), city surface temperature (Shafizadeh-Moghadam et al., 2025), and microbial density in air samples (Hayleeyesus & Manaye, 2014). However, its objects of study increasingly extend beyond the confines of the laboratory. Questions that were once sufficiently answered with measurement data now require answers through draft laws, Constitutional Court decisions, financial reports of mining companies, and even traditional ritual discourses governing community access to forests. In other words, environmental …


Emergent De Sitter Expansion And Closed Topology From The Cosmic Fabric Model As An Open Thermodynamic System: Resolving The Negative Bulk Modulus Paradox, T G. Tenev, C B. Ward, T F. Tenev, M F. Horstemeyer Jul 2026

Emergent De Sitter Expansion And Closed Topology From The Cosmic Fabric Model As An Open Thermodynamic System: Resolving The Negative Bulk Modulus Paradox, T G. Tenev, C B. Ward, T F. Tenev, M F. Horstemeyer

Faculty Publications and Presentations

The Cosmic Fabric Model establishes a continuum-mechanics isomorphism to General Relativity by representing physical space as an elastic three-dimensional hyperplate embedded in a four-dimensional spatial bulk. Reproducing vacuum kinematics requires a vanishing P-wave modulus, which in turn implies a negative bulk modulus—an apparent thermodynamic instability in a closed system. This paradox is resolved by recasting the framework as an open system: the instability is not pathological but instead drives cosmic expansion. In this interpretation, the observable universe is a lower-energy solid formed through continuous solidification from a higher-dimensional precursor fluid. Using multiplicative kinematics from finite-growth mechanics, the model shows that …


Gradients Of Abandonment, William Tatman Jul 2026

Gradients Of Abandonment, William Tatman

Geography ETDs

As urban-rural disparities drive depopulation in rural areas worldwide, local strategies emerge as pathways for resilience. Research on Ojika, a Japanese island that has lost 75% of its population since the 1960s, reveals an Abandonment Gradient: a nuanced pattern of disuse adapted to modern polycrises. Extending the concept of "lying fallow" to homes and infrastructure, this thesis focuses on abandonment practices that reflect complex realities of labor, capital, and climate uncertainty. Rather than viewing depopulating communities as passive victims of out-migration, this paper argues they are critical sites for generating crisis response. Communally crafted attitudes toward unused space and more-than-human …


Timelines Over Tokens: Summarization, Prompting, And Explainable Fine-Tuning For User-Level Suicide Risk Detection, Aditya Tekale Jul 2026

Timelines Over Tokens: Summarization, Prompting, And Explainable Fine-Tuning For User-Level Suicide Risk Detection, Aditya Tekale

Master's Theses

This research presents a two-stage pipeline for user-level suicide risk detection from Reddit: first, inference-only prompting with summarization; second, fine-tuned encoder classification with explainability and expert validation. The data are user-level: each of the 500 C-SSRS Reddit items is one user’s chronologically concatenated posts and comments (a user timeline), annotated by psychiatrists. Stage one: six prompting strategies zero-shot, few-shot, chain-of-thought, tree-of-thought, least-to-most, and self-consistency are evaluated across six LLMs on multi-class and binary formulations; simple zero-shot achieves the highest balanced accuracy (0.53 multi-class). Error analysis shows longer inputs associate with misclassification (p = 0.002); domain-specific summarization (timelines >2,000 tokens) reduces …


Exploring The Nature And Role Of Local Cation Ordering In Disordered Rock Salt Cathodes For Li- And Na-Ion Batteries, You Wang Jul 2026

Exploring The Nature And Role Of Local Cation Ordering In Disordered Rock Salt Cathodes For Li- And Na-Ion Batteries, You Wang

Chemistry and Chemical Biology ETDs

Cation-disordered rock-salt (DRX) cathodes provide a highly tunable platform for next-generation Li- and Na-ion batteries, but their electrochemical behavior is strongly influenced by local structural features hidden in average crystal structures. This dissertation systematically investigates local cation ordering in Li- and Na-based DRX cathodes to understand its effects on Li+/Na+ transport, redox activity, structural evolution, and electrochemical performance. In Li-based systems, Raman spectroscopy and electrochemical analysis reveal that local layered cation ordering in Mn- and Fe-based DRX cathodes is closely correlated with electrochemical behavior. Over-stoichiometric Li-based DRX oxyfluorides further demonstrate that excess Li can regulate local cation ordering, improve Li+ …


Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman Jul 2026

Mapping And Modeling Threat-Evoked Brain States After Early Life Adversity, Taylor W. Uselman

Biomedical Sciences ETDs

Early life adversity (ELA) increases lifelong neuropsychiatric vulnerability. Yet how ELA reorganizes brain-wide activity and circuit coordination across later experience remains unclear. This dissertation tests the hypothesis that ELA alters adult brain-wide activity and responses to threat through disrupted coordination among neural systems that regulate emotional experience, including prefrontal-limbic and monoaminergic systems. Longitudinal manganese-enhanced MRI of adult mice exposed to standard or fragmented early care, combined with computational processing and statistical modeling, quantified brain states before, during, and long after innate predator threat. These studies established that acute threat evokes large-scale, distributed brain activity that evolves over time. ELA potentiates …


New Distance Distributions Of Asymptotic Giant Branch Stars And Their Role In Tracing Galactic Structure, Rajorshi Bhattacharya Jul 2026

New Distance Distributions Of Asymptotic Giant Branch Stars And Their Role In Tracing Galactic Structure, Rajorshi Bhattacharya

Physics & Astronomy ETDs

Asymptotic giant branch (AGB) stars are among the final evolutionary stages of low- and intermediate-mass stars and among the most luminous cool stellar populations in the Milky Way (MW). Their strong infrared emission allows them to be observed through regions of high interstellar extinction, making them useful tracers of the inner MW. However, their use is limited by unreliable distances because many are dust-obscured and variable, while geometric parallaxes are often unavailable or uncertain. This thesis develops statistical distance-estimation methods for large samples of oxygen-rich AGB stars. The resulting distances broadly agree with literature estimates, supporting their statistical reliability for …


Extending The Discovery Space Of Tess: Probing Underexplored Exoplanet Populations, Mallory L. Harris Jul 2026

Extending The Discovery Space Of Tess: Probing Underexplored Exoplanet Populations, Mallory L. Harris

Physics & Astronomy ETDs

This dissertation investigates how cold exoplanets can be identified despite the strong observational bias of exoplanet surveys toward short-period systems. Planets at wider orbital separations remain comparatively poorly constrained, limiting tests of planetary-system formation and the prevalence of outer architectures beyond compact systems. To address this gap, I use two complementary approaches. First, I develop a transit-search pipeline for TESS Full-Frame Images that identifies both isolated and repeated transit-like signals around nearby M dwarfs and characterizes the dominant false-positive classes that limit sensitivity in this regime. I then present TOI-904 c, the coldest planet discovered by TESS around an M …


Algorithmic Sculpting Of Complex Fused Silica Surfaces For Nondestructive, Mode-Matched Cavity Quantum Electrodynamics: Adaptive Co2 Milling And Simulation-Guided Ultrafast Inscription, From Fiber Fabry-Perot Cavities To Monolithic Architectures, Meagan E. Parker Jul 2026

Algorithmic Sculpting Of Complex Fused Silica Surfaces For Nondestructive, Mode-Matched Cavity Quantum Electrodynamics: Adaptive Co2 Milling And Simulation-Guided Ultrafast Inscription, From Fiber Fabry-Perot Cavities To Monolithic Architectures, Meagan E. Parker

Optical Science and Engineering ETDs

Quantum sensors achieve exceptional measurement sensitivity through coherent, well-isolated quantum systems, but practical deployment is hindered by destructive readouts that require repeated state preparation and create long system dead times. Optical cavities enable continuous, nondestructive measurements with minimal back-action, yet integrating high-finesse cavities into scalable quantum devices remains limited by existing fabrication methods. To overcome these constraints, an adaptive CO₂ laser-milling platform was developed. Guided by glass thermodynamics and melt dynamics, this closed-loop system uses in-situ phase-shifting interferometry to sculpt complex fused-silica surfaces with sub-nanometer root-mean-square roughness. The platform was validated by fabricating extended-length fiber Fabry–Pérot cavities and monolithic micro-cavity …


Exploring The Role Of A Mushy, Crustal Compliant Region In Volcano Deformation, Grant A. Block Jul 2026

Exploring The Role Of A Mushy, Crustal Compliant Region In Volcano Deformation, Grant A. Block

Physics & Astronomy ETDs

Volcanoes are both creative and destructive forces that have shaped and continue to shape our world from early geologic time to the present day. Continued study of volcanic processes not only better prepares us for monitoring volcanic hazards but also allows us to better understand processes fundamental to Earth as we know it, such as the generation of the atmosphere and accretion of the continents. This dissertation focuses on an integral part of volcanic processes: the trans-crustal magmatic transport system. Specifically, we investigate regions of these transport systems where magma pools in melt-rich lenses within broader regions of low melt-fraction, …


Monoids With K-Strictly Local Geodesic Languages, William M. Hong Jul 2026

Monoids With K-Strictly Local Geodesic Languages, William M. Hong

Master's Theses

A paper by Gilman, Hermiller, Holt and Rees (2011) prove that a group G finitely generated by X is virtually free if and only if the language of geodesics words in G over X is k-strictly local if and only if the word problem is context-free. If M is a monoid finitely generated by X, we define Γu(M,X) to be the underlying, undirected graph of Γ(M,X). We prove that if the language of geodesics in Γu(M,X) based at the identity is k-strictly local, then the monoid and semi-group word problems are context-free.


Fermat's Last Theorem Over Quadratic Number Fields, Richie Tay Jul 2026

Fermat's Last Theorem Over Quadratic Number Fields, Richie Tay

Master's Theses

Fermat’s Last Theorem states that the equation xn + yn = zn has no nontrivial integer solutions for n ≥ 3. While the rational case is completely solved, the situation over quadratic number fields is not as straightforward. For some exponents nontrivial solutions exist, while for others they do not. This thesis studies Fermat-type equations over quadratic number fields, combining classical methods with more modern techniques from the theory of elliptic curves. The thesis first reviews the rational cases n = 2, n = 3, n = 4, then develops the necessary background on quadratic number fields, including rings of …