Mathematics Commons^™

Aqqd: Annotated Quranic Qira’At Dataset, Linda Smail, Mohammed Lataifeh, Md Sohazur Islam Sozib, Arthur Diniz De Souza

All Works

AQQD (Annotated Quranic Qira'at Dataset) is an open audio dataset of Quranic recitations annotated across canonical Qira'at styles. The dataset is designed to support research in machine learning, speech and audio processing, computational linguistics, and Quranic studies. The current release contains 24,183 WAV audio files from 309 reciters and covers 70 selected Quranic Surahs segmented into representative verses and phonetic variation points. Of these, 23,111 recordings were collected from publicly available sources, including official reciter websites, the Midad repository, MP3Quran, and verified YouTube channels, while an additional controlled subset of 1,072 recordings was obtained from a single reciter recorded as …

Decidability Of The Orbit Problem Over Q(X), Joshua Holden, Alexa Renner

Mathematical Sciences Technical Reports (MSTR)

The orbit problem is the problem of whether, given x, y ∈ Qn and an n × n matrix A, there exists an i ∈ N such that Aix = y. In 1980, Kannan and Lipton proved that the orbit problem is decidable. We show that a generalization of the orbit problem, where the field is Q(X) for X a countable set of transcendentals, is also decidable. We define the orbit power problem for an arbitrary group G to be the problem of when, given x, y ∈ G, there exists an n ∈ Z such that xn = y. …

Advantages Of Dynamic Representation For Related Rates Problems In Calculus, Eri Osuna

Electronic Theses, Projects, and Dissertations

Related-rates problems are a standard yet persistently difficult topic in first-semester calculus. Research increasingly recommends dynamic visualization tools such as GeoGebra, but direct comparisons of static and dynamic representations in related-rates settings remain scarce. This qualitative study examines how representation type shapes the quality of students' reasoning and their perceived experience during related-rates problem solving. Six mathematics students who had completed Calculus —a group of four undergraduates and a pair of graduate students—completed a static sliding-ladder task and a dynamic airplane-and-camera task supported by an interactive GeoGebra applet, followed by an interview. Findings indicate that the two representations supported reasoning …

Geodesic Completeness And The Hopf-Rinow Theorem, Christopher Farias

Electronic Theses, Projects, and Dissertations

Differential geometry is concerned with the properties of calculus and geometry on curved n-dimensional manifolds. As a result, thinking about such a space often runs counter to the Euclidean geometer's intuition of distances, angles, and transformations. This thesis aims to build up to proving an important result in the study of Riemannian manifolds: the Hopf-Rinow theorem.

In Chapter 2, we begin by defining what a manifold is and showing that the collection of directional derivatives at a point on the manifold spans a tangent vector space. After defining a basis and a metric for this space, in Chapter 3, we …

Comparing 3-Connectedness And Roundness In Matroid Theory, Blanca Delia Larios

Electronic Theses, Projects, and Dissertations

A matroid is a discrete mathematical object that abstracts and connects the various notions of independence found throughout mathematics. Such notions of independence include linear independence, algebraic independence, as well as notions of independence that arise in graph theory. There are many broad classes of matroids. Important examples include binary matroids, graphic matroids, regular matroids, uniform matroids, and various levels of connected matroids. Some of the most important problems in matroid theory involve characterizing classes of matroids so that such characterizations can be used to prove results concerning these matroid classes. This thesis is a study of two important classes …

Student Attitudes And Perceptions Of Proof In Mathematics, Emelin G. Sibrian Marquez

Electronic Theses, Projects, and Dissertations

Traditionally, mathematical proof is viewed primarily as a tool for validation or verification. However, proof holds many other important roles such as discovery, reasoning, explanation, and justification. For many students, these other roles are not always obvious. Those encountering rigorous proof for the first time often find the process abstract, intimidating or disconnected from their previous learning. This disconnect can lead to negative attitudes as students transition from computational mathematics to advanced proof-based mathematics. Utilizing a mixed-methods approach, this study examined undergraduate and graduate mathematics students at a Hispanic-Serving Institution (HSI) in Southern California. We investigated what students perceive the …

Stabilized Continuous Galerkin Methods For Heat Transport In Fully Coupled Nonlinear Thermo-Poroelasticity In Heterogeneous Porous Media, Payel Dey

Open Access Theses & Dissertations

This thesis focuses on the numerical approximation of a coupled Thermo-Hydro-Mechanical (THM) model with advective heat transport in heterogeneous media. The governing equations consist of three coupled equations: the momentum balance, the fluid mass balance, and the energy balance. The primary unknowns are displacement, pressure, and temperature. In this system, the fluid pressure determines the Darcy flux, and this flux transports heat through the advective term in the energy equation. Since the Darcy flux is computed numerically from the flow equation, the conservation properties of the flow approximation can affect the temperature solution. This effect is especially important when thermal …

Pseudo-Riesz Bases, Deborpita Biswas

All Dissertations

In this dissertation, we will introduce the concept of pseudo-Riesz bases, extending the influential notion of near-Riesz bases first proposed by J. Holub in the 1990s. Our goal is to develop an analogous theory for pseudo-Riesz bases, obtaining results parallel to those known for near-Riesz bases, with suitable modifications.

We will develop the foundational theory of pseudo-Riesz bases. Unlike classical Riesz bases, these sequences need not be complete or independent; however, they still retain meaningful expansion properties. We will investigate the conditions under which a Bessel sequence can be transformed into a Riesz basis through finite modifications. In particular, we …

A Finite Element Model To Analyze Crack-Tip Fields In A Transversely Isotropic Strain-Limiting Elastic Solid, Saugata Ghosh, Dambaru Bhatta, S. M. Mallikarjunaiah

School of Mathematical & Statistical Sciences Faculty Publications

This paper presents a finite element model for the analysis of crack-tip fields in a transversely isotropic strain-limiting elastic body. A nonlinear constitutive relationship between stress and linearized strain characterizes the material response. This algebraically nonlinear relationship is critical as it mitigates the physically inconsistent strain singularities that arise at crack tips. These strain-limiting relationships ensure that strains remain bounded near the crack tip, representing a significant advancement in the formulation of boundary value problems (BVPs) within the context of first-order approximate constitutive models. For a transversely isotropic elastic material containing a crack, the equilibrium equation, derived from the balance …

Convergence Theory For Deep And Multi-Grade Neural Architectures, Lei Huang

Mathematics & Statistics Theses & Dissertations

This dissertation studies two complementary notions of convergence arising in modern neural network models: the convergence of recursively constructed neural network architectures and the convergence of optimization algorithms used for training neural-network-based image restoration models. The first part develops a convergence theory for deep neural networks (DNNs) viewed as recursively generated sequences of functions. Within an Lp framework motivated by statistical learning, sufficient conditions are established under which increasing-depth neural network sequences converge to well-defined limiting functions. The analysis covers both bounded-width and unbounded-width architectures, establishes explicit convergence rates, and motivates a network initialization strategy derived from the convergence conditions. …

Bayesian Variable Selection In High-Dimensional Ordinal Quantile Regression Models, Mai Dao, Md. Sakhawat Hossain, Zhuanzhuan Ma

School of Mathematical & Statistical Sciences Faculty Publications

Quantile regression (QR) provides a flexible statistical framework for modeling the entire conditional distribution of the response variable, making it useful for analysis in various fields. Despite its advantages, existing methods for QR often encounter numerical challenges in high-dimensional settings, especially for those with ordinal responses. In this paper, we use a latent-response framework to construct a Bayesian hierarchical model to conduct parameter estimation and variable selection for ordinal QR. Using the asymmetric Laplace working likelihood and the horseshoe prior for the regression coefficients, we obtain the posterior samples to be screened by the sequential two-means clustering process to identify …

Opening The Lantern: The Leiden Declaration, Mark Huber

Journal of Humanistic Mathematics

The Leiden Declaration on Artificial Intelligence and Mathematics provides insight into how mathematicians view their discipline. However, when positioning mathematics against AI, the declaration falls short in recognizing recent advances. This column introduces the reader who might be unfamiliar with these new methods through the formal language Lean and discusses how these new abilities might change the way journals operate.

Wanted: A Book Reviews Editor For The Journal Of Humanistic Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

To help us procure regular book review submissions and ensure that we can indeed include a solid book review in each upcoming issue, we would like to have an enthusiastic book worm join our small editorial team. In other words, we are looking for a book reviews editor.

We will review all applications that have been submitted by October 15, 2026. We hope to have our new book reviews editor start their term by January 2027.

Visualizing Irrationality: Digit Mosaics In Okabe–Ito, Raven Quilestino-Olario

Journal of Humanistic Mathematics

Five visual mosaics translate 10,000-digit segments of well-known mathematical constants into color. For each constant, the digits are placed in a 100×100 grid read left to right and top to bottom, including the digit before the decimal point, and each digit (0–9) is mapped to a color in the Okabe–Ito palette. A matching bar chart shows the digit counts within the same window, allowing quick comparison of how evenly digits appear. The series includes π, e, √2, φ, and the Euler–Mascheroni constant γ. Together, the mosaics and counts turn numerical randomness into visual harmony while keeping the work readable for …

The Pi-Royal Tire, Erik Talvila

Journal of Humanistic Mathematics

In this humorous story, the half-wit proprietor of a tire manufacturing company thinks knowing pi to more digits will allow the production of rounder tires. An applied mathematician is recruited to fulfill a ridiculous industrial research agenda.

Riding The Rails Of Reason: A Dialogue On Truth, Logic, And Proof, Surinder Pal Singh Kainth

Journal of Humanistic Mathematics

On a quiet train ride, I found myself in conversation with Noor, an inquisitive teenager with sharp questions about truth, logic, and mathematical proof. As we talked, I used the train itself as a metaphor to explain how mathematical proofs provide certainty, far beyond what repetitive verification alone can offer. Our discussion ranged from common misconceptions about the foundations of logic to the need for clear definitions and axioms. We also touched on fundamental ideas such as the challenges posed by the Axiom of Choice and the limitations revealed by Gödel’s incompleteness theorem.

In Praise Of Smaller Models, Pedro Poitevin

Journal of Humanistic Mathematics

No abstract provided.

Count, Robin Young

Journal of Humanistic Mathematics

It's the thought that counts? No, it's this canzone that counts! This poem explores the philosophy of counting through five stanzas from shoreline pebbles to Godel's incompleteness theorems. Counting becomes our guide through Zeno's paradoxes, irrational numbers, Cantor's infinities, and quantum measurement problems. The poem counts, recounts, and discovers that some things simply cannot be counted.

Group Theory For Poets, Holley Friedlander

Journal of Humanistic Mathematics

This poem instructs the reader on how to put a group structure on an arbitrarily chosen set. Through accentual, rhyming verse, it playfully discusses the beauty and utility of groups as a mathematical concept via examples and applications. This work is inspired by the Patricia Toht book, Pick a Pine Tree.

My Journey To Mathematics, Thao Thuan Vu Ho

Journal of Humanistic Mathematics

No abstract provided.

A Lament For Linear Algebra, Jasmine A. Elmrabti

Journal of Humanistic Mathematics

What assumptions underlie our axiomatic definitions? A meditation on the nature of linear algebra and its metaphysical implications during use, this poem is a reflection on the markedness of discrete entities upon which we rely to utilize the axioms of linear algebra.

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 Logic Of Leaves: Mathematical Poems And Graphs, Ksawery Tomczak

Journal of Humanistic Mathematics

This collection explores the intersection of mathematics and poetry through six original works that blend formal rigor with lyrical expression. Each poem draws from a distinct mathematical concept—proof, set theory, combinatorics, graph theory, and cardinality—reframing it through metaphoric and aesthetic lenses. From the lyrical contemplation of infinite sets to the emotive longing of a graph in love, the verses reveal the emotional resonance and philosophical depth embedded in mathematical thought. The collection culminates in a visual piece rendered in \LaTeX and TikZ, illustrating all integer partitions of the number five as a branching tree, accompanied by a poem that sings …

College Algebra: A Key Element To Degree Completion, Christopher Charlie Jett, Gregory Downing

Journal of Humanistic Mathematics

College Algebra is often under scrutiny because it serves as a critical gateway to graduation for students enrolled in our nation’s undergraduate degree programs. In this paper, we problematize the authority typically ascribed to this course and discuss meeting students’ discipline-specific needs in core mathematics courses such as it. To help facilitate college student success with respect to mathematics course requirements, we recommend that educational constituents and leaders expand dual-enrollment opportunities, infuse culturally relevant practices, and leverage other core mathematics courses as alternatives to College Algebra. In doing so, we add to the ongoing conversation about addressing this issue in …

An Essay On Teaching And Learning Mathematics: Through The Lens Of Artificial Intelligence, Music, And Sports, James Diederich

Journal of Humanistic Mathematics

This essay is aimed at a wide audience: anyone who has engaged in learning or teaching math. It provides a unique perspective drawn from a mathematician’s interests in working with K-12 teachers, familiarity with artificial intelligence (AI), and amateur pursuits of learning to play an instrument and of learning a difficult sport. While I delve into these topics, no special background is needed in the slightest. In particular, I draw lessons from some failures in AI that reflect on why the conventional procedural approach to teaching and learning math fails many students. I also provide insight into how we learn …

Graduate Student Reflections On Mentoring Undergraduate Researchers In Mathematics, Melissa Beerbower, Jillian Cervantes, Pamela E. Harris, Kimberly J. Harry, Matt Mcclinton, Gabriella Pinter

Journal of Humanistic Mathematics

This is an interview with four graduate students who for the first time mentored undergraduate students during a summer research program. The interviewees present their lessons learned in mentoring and advice to other graduate students looking to mentor students.

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

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 …

Developing A Learner-Centered Teaching Routine, Hyeeun Jang

Journal of Humanistic Mathematics

This paper shares my story of developing, from Fall 2022 to Spring 2025, a learner-centered teaching routine for my undergraduate mathematics courses. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a short end-of-class exit check, at times supported by quick visuals in Mathematica and, when useful, Python. Instead of relying on extended traditional lectures, the routine emphasizes collaborative problem solving and invites students to articulate and check their reasoning together. I used this routine mainly in my elementary statistics classes, but also in calculus and linear algebra. The evidence I …

Numbers, Patterns, And Memories: Early Experiences Of Mathematicians And Mathematics Education Researchers, Constantinos Xenofontos

Journal of Humanistic Mathematics

This paper offers a reflective analysis of early mathematical experiences shared by fifty-six mathematicians and mathematics education researchers, including my own, as part of Cambridge Mathematics’ “Seven Questions with . . . ” interview series. Drawing on thematic analysis, I identify five key patterns across participants’ recollections: the context of early mathematical engagement, the influence of significant others, emotional responses, shifts in mathematical thinking, and mathematics as a social or competitive experience. Many accounts emphasise informal, everyday encounters with mathematics—often preceding formal education—as central to developing interest and confidence in the subject. The findings challenge the notion of innate mathematical …