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Found Poem By Abraham De Moivre, Richard Delaware

Journal of Humanistic Mathematics

No abstract provided.

Book Review: Zero's Whisper By Tom Petsinis, Sarah Glaz

Journal of Humanistic Mathematics

Tom Petsinis is an internationally acclaimed Australian novelist, playwright, and poet. He also holds a Ph.D. degree in mathematics and works as a mathematical adviser at Deakin University, Melbourne. Zero’s Whisper, Petsinis’ tenth poetry collection, offers a rich blend of the literary and the mathematical. The collection, comprising of over one hundred fourteen-line poems, is divided into nine sections, each of which considers a different aspect of a world steeped in mathematics and poetry. This review aims to provide a taste of the poetry and the themes included in the book. To discover all its hidden delights, one needs to …

Compare Problems: Complexity In Content And Language, Gladys Krause

Journal of Humanistic Mathematics

When learning to teach mathematics in elementary school, pre-service teachers (PSTs) spend considerable time studying word problems. Here I present a resource I have created for my mathematics methods course in order to engage PSTs in learning about these problems and to support them in identifying these problem types.

Let’S Teach More Accurate And Inclusive History! The Case Of Islamic Contributions To Mathematics And Science, Nuh Aydin

Journal of Humanistic Mathematics

Schools commonly teach a history of mathematics and science that is Eurocentric. This selective version of the history of science, called Classical Narrative by some, is rooted in colonial times and mindset, and has reinforced certain negative opinions about other cultures. It ignores or downplays contributions to mathematics and sciences from non-western civilizations, and falsely attributes many scientific discoveries to European scholars. Medieval Islamic Civilization, which had strong connections to Renaissance Europe, serves as a clear example of how this narrative is distorted. Based on research on primary sources since the middle of the 20th century, we now know that …

From Shudu [Sudoku 數獨] To Dushu [Learning Of Mathematics 讀數]?, Man Keung Siu

Journal of Humanistic Mathematics

The puzzle game Sudoku has been popular for over two decades, and even at one time became a craze for the public. This paper will briefly describe what the game is, a little bit of its history, and how to play it, but will leave the details to the many published books about the game. Some interesting and difficult mathematical problems relevant to the game will be highlighted, again leaving the detailed discussion to specific books published on this issue. The main point the paper tries to focus on is a discussion on the cognitive and the psychological aspects of …

Examples Of Mathematics Personified, Amenda N. Chow

Journal of Humanistic Mathematics

Synesthesia is a cognitive condition in which multiply senses are stimulated at once. There are different types of synesthesia. For example, in a documented study [9], a person with synesthesia when considering the number three associates it as a male and a jerk. This association is persistent, always the same and automatic. Presented here are a variety of examples about mathematics in personified form. These examples focus on using personification as a way to better understand and appreciate mathematics.

On Gödel’S Incompleteness Theorem, David Pierce

Journal of Humanistic Mathematics

Gödel’s Incompleteness Theorem is about the logic of mathematics. It is that a certain mathematical structure is so rich that its theory cannot be completely axiomatized. This means there will always be true statements about the structure that cannot be proved as theorems from previously given axioms. To give meaning to this conclusion, we review some examples of mathematical theorems, and their proofs, in geometry, algebra, and logic; we also give an example of a structure that is so simple (while still being interesting) that its theory can indeed be completely axiomatized. First we look at a couple of popular …

Exploring Commutativity In A Hindi Language Classroom, Kumar Gandharv Mishra

Journal of Humanistic Mathematics

Commutativity is an important concept in mathematics. However, not much emphasis is given to it in the elementary or secondary school curriculum, as there is a lack of interesting noncommutative examples at this level. Since most examples of binary operations provided deal with numbers, commutativity appears trivial. In this article we offer an interesting example of noncommutativity that is familiar to Indian school children from a different context. Students in India study a chapter based on the joining of vowels in Hindi grammar. This process is analogous to producing commutative as well as noncommutative operations. When we bring in mathematical …

Revisiting A 19th Century Vector Algebra Book, Olcay Coskun, Alp Eden, Ersin Karabudak

Journal of Humanistic Mathematics

Hidden gems of mathematics can be recovered when one digs into what might seem an obscure text. In 1882, military officer Vidinli Hüseyin Tevfik Pasha published a book on vector algebra titled Linear Algebra. In this article we revisit the second edition of this book, emphasizing the special multiplication that we call the ’v-product’. This product has both geometric and algebraic characteristics. We attempt to clarify its relationship with complex and quaternion multiplication both geometrically and algebraically. The resulting algebra is called the Vidinli algebra. This algebra admits a Lie algebra structure that gives rise to Heisenberg algebra. We introduce …

Graphical Timetables As A Real-Life Example Of Different Representations Of Functions, Olav G. Imenes

Journal of Humanistic Mathematics

This paper examines 203 pre-service teachers' reactions and learning when they were introduced to a real-life situation in which it is natural to publish officially both graphs and tables of a given function: the situation of operating a railway. I found that almost all the pre-service teachers managed the easiest tasks, like calculating speeds, distances, and time for train represented by graphs. However, the more complicated tasks, which required interpretations of the graphs and tables, such as planning for a delayed train, finding which trains were locals, freight trains etc., were more difficult for them to grasp. There were few …

A Practical Rule Of Divisibility By 7 In Uqlīdisī’S Kitāb Al-Fuṣūl Fī Al-Ḥisāb Al-Hindī, Müjdat Takıcak, Mertkan Şimşek

Journal of Humanistic Mathematics

There are many known examples of divisibility rules in modern mathematics. However, some of these rules are far from being practical, such as the current divisibility rule by 7. A far more useful method can be found in the work of the tenth-century Islamic mathematician Abū al-Ḥasan al-Uqlīdisī (d. 980), who proposed a divisibility rule for 7 in his treatise Kitāb al-Fuṣūl fī al-Ḥisāb al-Hindī. Compared to modern techniques, Uqlīdisī’s rule is both simpler and more practical. This article (re)introduces this rule, and provides an exposition of the mathematical reasoning that underpins it.

Bayes In The Brain: A Review Of Everything Is Predictable: How Bayesian Statistics Explain Our World, (2024) By Tom Chivers., Michael T. Catalano

Numeracy

Tom Chivers’ Everything is Predictable: How Bayesian Statistics Explain Our World, is an interesting and wide-ranging narrative on Bayesian thinking, its history, and its applicability to both our everyday lives and the pursuit of scientific truth. Although appropriate for the non-expert, afficionados and teachers of quantitative literacy should find the plethora of examples, links to psychology as it applies to how people reason about probabilities, and even Chivers’ philosophical musings informative and thought-provoking.

The Effectiveness Of Remote Patient Monitoring In Reducing The Risk Of Rehospitalizations In Covid-19 Patients: A Meta-Analysis, Dela Riadi, Indang Trihandini, Dewi Nirmala Sari, Fikri Wijaya

Kesmas

An integrated analysis of various Remote Patient Monitoring (RPM) studies is needed to evaluate the reduction rate of the risk of rehospitalization in COVID-19 patients. This meta-analysis aimed to provide an overview of the effectiveness of RPM. A literature search through online databases (PubMed, Science Direct, Scopus, ProQuest, and Embase) was conducted from 2019 to 2022. After using the Cochrane Collaboration's risk of bias tool, five studies on COVID-19 were selected. Based on the data collected from 2,685 participants (intervention = 1,060, control = 1,625), the use of RPM was found to reduce rehospitalization by 0.56 times compared to not …

Cross-Cultural Adaptation And Validation Of Ranas-Based Instrument For Measuring Latrine Use Behavior In Indonesia, Vera Yulyani, Fatwa Sari Tetra Dewi, Iswanto Iswanto

Kesmas

Using toilets is a simple way to prevent diarrhea, yet no validated tool exists to measure this habit. This study aimed to develop and validate instruments for measuring latrine use consistency. This questionnaire was adapted from the risk, attitude, norm, ability, and self-regulation (RANAS) framework developed in India and modified for Indonesia. It was evaluated by three experts using the content validity index (CVI). The face validity index (FVI) was pilot-tested on 40 community respondents. Variables measured included behavior, habits, intentions to use toilets, knowledge, attitudes, norms, abilities, and self-regulation. Question items with relevance and clarity scores of item CVI …

Algebraic Multigrid Methods For Nonsymmetric And Indefinite Problems: Theory And Applications, Ahsan Ali

Mathematics & Statistics ETDs

Algebraic multigrid (AMG) is a well-established and highly efficient solver for symmetric positive definite (SPD) systems arising from elliptic and parabolic PDEs, while nonsymmetric systems from hyperbolic PDEs remain a significant challenge. This dissertation develops AMG methods and theory for nonsymmetric problems. First, we develop a novel approach combining mode constraints from energy-minimization AMG with local approximations of ideal restriction in $\ell$AIR, resulting in constrained $\ell$AIR (C$\ell$AIR), which demonstrates scalable convergence across advective and diffusive problems. Second, we extend optimal AMG theory by deriving spectral radius estimates for the two-grid error transfer operator using matrix-induced orthogonality, enabling convergence predictions for …

Non-Spectator Behavior Of A Neutral Phosphine Ligand Driven By A Redox-Active Boron Cluster, Jared R. Riffle, Cash L. Jowers, Sarah Luna, Mark D. Smith, Dmitry V. Peryshkov

Faculty Publications

A new concept of ligand ambiphilicity that relies on the redox behavior of the indirectly coordinated boron cluster scaffold instead of the direct involvement of a single center in a ligand is introduced. A copper(I) complex of a carboranyl-based triphosphine, [t^BuP-closo-{C₂B₁₀}-^PhP-closo-{C₂B₁₀}-t^BuP]CuPF₆, in acetonitrile solution coordinates an exogenous X− anion (X− = Cl− or N3−) at the phosphorus center of the ligand and not at the cationic metal site to form [t^BuP(X)-nido-{C₂B …

Learning From Conditional Data Distributions, Jizhou Huang

McKelvey School of Engineering Graduate Student Theses & Dissertations

Traditional machine learning paradigms often rely on a single global model trained on an entire dataset, aiming for broad generalization across all instances. However, in many real-world applications, the underlying data distribution is heterogeneous, and meaningful predictions often require models that focus on specific subpopulations rather than treating the data as a whole. This motivates the study of learning from conditional distributions, a framework where predictive models are designed to capture the structure and properties of restricted subsets of the data, leading to improved accuracy, fairness, and interpretability. This dissertation explores three key subproblems that exemplify different aspects of learning …

Multiclass Cyberbullying Detection Using Advanced Neural Network Architectures: A Comparative Study Amidst The Covid-19 Pandemic, Mahyar Alinejad

Data Science and Data Mining

Amidst the COVID-19 pandemic, the digital communication landscape has seen an unprecedented rise in cyberbullying incidents. Addressing this critical issue, our study develops and evaluates a novel multiclass cyberbullying detection framework employing several advanced neural network architectures—namely Neural Networks (NN), Convolutional Neural Networks (CNN), Long Short-Term Memory networks (LSTM), and Gated Recurrent Units (GRU). Utilizing a balanced dataset created through Dynamic Query Expansion, this research benchmarks the performance of these models in accurately classifying cyberbullying according to specific victim attributes such as age, ethnicity, gender, and religion. Our results demonstrate that LSTM and GRU models, in particular, exhibit superior performance …

Multiclass Cyberbullying Detection Using Advanced Neural Network Architectures: A Comparative Study Amidst The Covid-19 Pandemic, Mahyar Alinejad

Data Science and Data Mining

Amidst the COVID-19 pandemic, the digital communication landscape has seen an unprecedented rise in cyberbullying incidents. Addressing this critical issue, our study develops and evaluates a novel multiclass cyberbullying detection framework employing several advanced neural network architectures—namely Neural Networks (NN), Convolutional Neural Networks (CNN), Long Short-Term Memory networks (LSTM), and Gated Recurrent Units (GRU). Utilizing a balanced dataset created through Dynamic Query Expansion, this research benchmarks the performance of these models in accurately classifying cyberbullying according to specific victim attributes such as age, ethnicity, gender, and religion. Our results demonstrate that LSTM and GRU models, in particular, exhibit superior performance …

Comparative Study Of Machine Learning Models For Predicting The Market Value Of Professional Football Players, Álvaro Salvador López

Master's Theses or Doctor of Nursing Practice

The market value of professional football players is a critical factor in decision-making for clubs, agents, and analysts. Accurate player valuation impacts transfers, contract negotiations, and financial planning. In recent years, data-driven approaches have emerged to support traditional scouting with predictive analytics. This thesis presents a comparative study of machine learning models to estimate the market value of football players based on historical performance and personal attributes.

This thesis presents a comparative study of two independently developed machine learning systems designed to predict the market value of football players for the 2020–2021 season. Both systems were trained using real data …

A Data-Driven Approach To Time Series Forecasting And Clustering Of U.S. Regional Drug Overdose Mortality, Koshali Hamy Muthunama Gonnage

Mathematics & Statistics ETDs

The increasing rate of drug overdose deaths in the United States poses a critical public health challenge, particularly due to the surge in synthetic opioids and other high-risk substances. This study presents a data-driven framework that integrates time series forecasting and clustering techniques. Monthly mortality data for five key drug types: cocaine, fentanyl, heroin, methamphetamine, and oxycodone were analyzed using four time series forecasting models: ARIMA, ETS, TBATS, and NNAR. These models were evaluated using standard accuracy metrics RMSE, MAPE, and MAE to assess predictive performance. Signal decomposition approach based on Singular Value Decomposition and subspace modeling was employed to …

Improved Rational Approximations Of Pi, Nelson Carella

Publications and Research

The irrationality exponent of a real number α is defined by maximal value μ(α) ≥ 1 such that the inequality |p/q − α| < 1/qμ(α) is true for finitely many rational approxi- mations by relatively prime pairs p/q. The earliest result introduced the upper bound μ(π) ≤ 42 for the irrationality exponent of π. Subsequently, it was improved by many authors. The more recent result introduced the improved upper bound μ(π) ≤ 7.6063. This note introduces an improved irrationality exponent μ(π) ≤ 3. The optimal value is expected to be μ(π) = 2.

Optimizing Distributed Boundary Exchanges For Benchmarks, Solvers And Sparse Matrix Operations, Gerald Collom

Computer Science ETDs

Boundary exchanges dominate the cost of both stenciled codes and those that rely on sparse matrix operations. The performance of large boundary exchanges is limited by synchronization overheads and injection bandwidth limitations. Irregular boundary exchanges incur additional overheads due to the large number of required messages. This thesis investigates multiple methods for improving the performance and scalability of both Cartesian and irregular boundary exchanges. Since boundary exchanges are typically performed iteratively, persistent communication presents an opportunity for optimization by sharing and amortizing setup costs. Partitioned communication is also explored to increase asynchrony, reducing bottlenecks from synchronization overheads and data congestion. …

Exploring Adversarial Threats To Neuralhash: A Perceptual Hashing Algorithm, Gurleen Kaur

Student Theses

Perceptual hashing algorithms are algorithms that generate content-based image hashes by extracting perceptual features from the images. Unlike cryptographic hashes, which exhibit significant changes with even slight input alterations, perceptual hashes do not change when modifications like compression, color correction and brightness are applied to the images. These hashes are designed to remain similar for inputs that are visually or perceptually alike, which has led to their widespread application in detecting duplicate images, finding similar images for reverse image search and to detecting inappropriate content of Child sexual abuse (CSAM) images by comparing image hashes with dataset of known perceptual …

Network Intelligence For Next-Generation Wireless Networks: Advancing Distribution And Coordination, Yonatan Melese Worku

Electrical and Computer Engineering ETDs

Next-generation wireless networks, encompassing 6G and beyond, face rigorous demands for ultra-low latency, ubiquitous connectivity, exceptionally high data rates, and robust security, necessitating innovative approaches to resource optimization and network protection. This dissertation proposes a pioneering framework that synergizes advanced methodologies—deep reinforcement learning, deep learning, blockchain, and multi-agent systems—to address these challenges. Distributed architectures, underpinned by AI-driven multi-agent systems, form the backbone of this framework, enabling seamless integration and intelligent orchestration across diverse domains. The research advances IoT-based systems leveraging machine learning for resource efficiency in healthcare applications, develops reinforcement learning-driven frameworks to optimize energy and coverage for Unmanned Aerial …

Phase Nanoscopy With Correlated Frequency Combs, Xiaobing Zhu

Optical Science and Engineering ETDs

In this dissertation a sensing method applying to any physical quantity that modifies optical phase is developed. Two pulses are produced inside a synchronously pumped Optical Parametric Oscillator, generating two identical, undistinguishable frequency combs. The physical quantity to be measured applies a small phase shift/round trip to one of the pulses, resulting in a frequency shift of the corresponding comb. The latter frequency is measured as a beat by interfering the two combs on a detector. A world record resolution, close to the quantum limit, of 0.033 nanoradian (corresponding to 0.006 fm in displacement) is achieved. A detailed analysis of …

Advancing Diamond Quantum Sensors: Isotropic Flux Concentrators And Phase Noise Mitigation, Maziar Saleh Ziabari

Optical Science and Engineering ETDs

Two methods for improving the sensitivity of nitrogen vacancy quantum sensors in diamond are explored. First, by passively concentrating the magnetic flux, three orthogonally oriented ferrite truncated cone pairs amplify the field isotropically by 19 times, allowing measurement of Earth's field without a bias field and increasing sensitivity. Through thorough analysis, modeling and tuning a novel 3-dimensional flux concentrator system, we achieve a fractional standard deviation of less than 1% anisotropy and quantify minimal deadzones and ambient temperature-limited variations below 40 nT/hour. Second, we characterize, model and calculate phase noise in NV experiments, which in NV sensors is effectively indistinguishable …

A Systematic Approach To The Characterization Of Liquid-Vapor Coexistence In Platinum, Meghan K. Lentz

Physics & Astronomy ETDs

Platinum is a material standard used in high pressure and shock compression experiments at Sandia National Laboratories. During experiments, materials are subjected to a very large range of thermodynamic conditions, during which materials regularly enter the liquid-vapor coexistence region. Despite its status as a standard, the region around the liquid-vapor critical point is poorly understood for platinum, with reported critical temperatures spanning approximately 7000 K. In this dissertation we conduct density functional theory based molecular dynamics (DFTMD) simulations for platinum for a range of temperatures and densities near liquid-vapor coexistence. The phase diagram for platinum is refined near the critical …

Modeling Mars Chaos Terrains As Fracture Mosaics, Aidan C. Buie

Earth and Planetary Sciences ETDs

Chaos terrain exists on several planetary bodies but most notably on Mars. With 30 different named terrains and hundreds of chaotic or ”chaos-like” terrains, they are one of the most prominent and visible features on the planet. Chaos terrains have many visible similarities to each other: they all are comprised of polygonal blocks separated by fractures or channels. These blocks vary from angular to rounded and from flat plateaus to small hills, and the fractures vary from flat floored to ”v” shaped. Often, a single chaos will contain all of these morphologies. Most of the 30 named chaoses on Mars …

A Mutational Analysis Of Thatisin: How Single Point Mutations Impact The Biosynthetic Process Of A Group 16 Graspetide, John F. Boynton Jr

Chemistry and Chemical Biology ETDs

Abstract:

Graspetides are a family of Ribosomally synthesized and Post-translationally modified Peptide (RiPP) natural products named for their ATP Grasp Macrocyclases. We identified several Graspetide Biosynthetic Gene Clusters containing common double glycine cleavage motifs and attempted characterization of the mature Graspetides. One of the resulting peptides, Thatisin, has a topology with two interlocking macrolactones installed by a single ATP Grasp Ligase named ThtC. Here we use single and double point mutations to observe the impact or variation on the installation of these macrocycles. Alanine scan mutagenesis is used to assess leader peptide residues in the precursor peptide ThtA to determine …