Mathematics Commons^™

Rockin’ Rover On The Rainbow Road, Michael Kolta, Lawrence Burgee, Ying Yuan

Transformations

This paper presents a progressive series of age-appropriate lesson plans for grades K-12 that all use the same interdisciplinary activity to educate students about Science, Technology, Engineering, Art, and Mathematics (STEAM) simultaneously. Technology from Texas Instruments (TI) was employed including a TI Nspire graphing calculator that can run Python programs, a TI Innovator Hub, and a TI Rover. The TI Rover is a small, robotic car that has sensors and is controlled by the calculator via the Hub hardware interface. A Python program was developed that uses the color sensor in the Rover to detect the color on colored paper …

From Reluctance To Resilience: The Link Between Attitude And Growth Mindset In Calculus Students, Olivia Valente, Kathryn E. Pedings-Behling, Amy N. Langville

Journal of Educational Research and Practice

Many postsecondary students enter general education mathematics courses with negative attitudes, shaping their willingness to engage with the content. This study explores the relationship between students’ attitudes towards mathematics and their growth mindset, revealing effective strategies to enhance learning experiences, particularly for students who are reluctant learners. The research investigates two questions: (1) How do students’ Attitude Toward Mathematics Inventory (ATMI) scores and Growth Mindset Scale (GMS) scores relate? and (2) Do gender or course modality affect this relationship? This study addresses a gap in literature by examining how enjoyment, motivation, self-confidence, and perceived value connect with growth mindset. The …

Machine Learning For Predictive Energy And Emissions Modeling Of Vehicles And Power Grids In The United States, S M Tanvir Faysal Alam Chowdhoury

Dissertations

The environmental benefits of electric vehicle (EV) adoption depend on more than replacing internal combustion engine vehicles with electric powertrains. EV adoption reshapes electricity demand, interacts with regional generation mixes, and influences travel behavior and congestion, creating a coupled transportation-energy system in which vehicle and power-plant emissions must be evaluated together. This dissertation develops machine-learning frameworks for predicting energy consumption and emissions from vehicles and power grids under rising EV adoption. The first component forecasts grid emissions from EV charging. Using simulation data from NREL's Cambium database, a Prophet-based time-series framework predicts carbon dioxide, nitrous oxide, and methane emission rates …

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 …

Positive Curvature And Discrete Abelian Symmetry, Lee Kennard, Elahe Khalili Samani, Catherine Searle

Mathematics

By replacing the torus with an elementary abelian two-group, we generalize Grove and Searle’s maximal symmetry result and Wilking’s half-maximal symmetry result for positively curved manifolds with an isometric torus action. © The Author(s) 2026.

A Stabilized Weighted Interior Penalty Method For Thermal Convection Model In Heterogeneous Porous Media, Yuanyuan Hou, Qianqian Ding, Xiaoming He, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

In this article, we propose and analyze a stabilized weighted interior penalty method for solving the thermal convection problems in heterogeneous porous media. We first transform the thermal convection model into the pressure primal form with homogeneous Neumann boundary condition and develop a symmetric weighted interior penalty method to handle the discontinuous Darcy number and automatically adjust the penalty coefficient corresponding to the varying permeability. Then we recover the velocity by a stabilized method and incorporate it into the energy equation to obtain the temperature. The stability and convergence rates of the numerical solutions are rigorously proved and verified by …

Spatial Prediction Under Uncertainty: Methodological And Computational Advances In Bayesian Maximum Entropy, Kinspride K. Duah

All Graduate Theses and Dissertations, Fall 2023 to Present

Environmental decisions such as infrastructure design, water management, and snow load estimation depend on spatial data that are often incomplete or uncertain. In many cases, measurements are not exact values but ranges, reflecting limitations in data collection methods. Traditional mapping techniques typically simplify these uncertain measurements, which can lead to less accurate predictions. This dissertation introduces improved statistical tools for making spatial predictions when data are uncertain or partially known. By utilizing a framework called Bayesian Maximum Entropy (BME), this research demonstrates how exact measurements and range-based data can be combined in a mathematically consistent way. The work demonstrates that …

Learning Latent Structure In High-Dimensional Data Via Geometry And Graphs, Haozhe Chen

All Graduate Theses and Dissertations, Fall 2023 to Present

Modern datasets often contain many measured variables for each observation, such as gene-expression levels, brain activity signals, or features in tabular data. These data are also often noisy, meaning that useful patterns are mixed with measurement error or irrelevant variation. Although such datasets can appear complex, they are frequently represented by simpler hidden structures, such as trajectories, clusters, or relationships between observations. This dissertation develops methods for uncovering these hidden structures by learning geometric and graph-based representations directly from data. The first part introduces Functional Information Geometry, which represents local patterns in high-dimensional data using functional features and constructs a …

Unifying And Expanding Global And Local Variable Importance Methods For Explainable Machine Learning, Kelvyn K. Bladen

All Graduate Theses and Dissertations, Fall 2023 to Present

Machine learning methods are powerful analytical tools used across all scientific disciplines and many other fields of investigation for prediction and inference from diverse data sources. Despite their broad applicability, machine learning methods are often highly complex and difficult to interpret. Developing a greater understanding of which variables most influence a response is essential for increasing the interpretability of these models and supporting informed decision-making. This research focuses on improving how we evaluate the importance of these variables.

One common approach is to shuffle the values of a variable and see how much the model accuracy gets worse. Another approach …

Applications Of Machine Learning To Gas Plume Analysis In Longwave Infrared Hyperspectral Images, Scout C. Jarman

All Graduate Theses and Dissertations, Fall 2023 to Present

Each pixel from a hyperspectral camera measures the intensity of light over a continuous range of wavelengths, which is in contrast to traditional color cameras, which just measure the intensity of red, green, and blue wavelengths of light. Longwave infrared hyperspectral images can be used to detect gases from a distance by measuring how different materials emit and absorb heat. This makes them useful for applications such as monitoring industrial emissions or locating hazardous gas leaks. In practice, however, gas signatures in these hyperspectral images are often weak and easily obscured by variations in the background scene, making reliable identification …

Mapler: An R Package For Estimating The Impact Of Climate Change On Maple Syrup Production, Matthew T. White

All Graduate Theses and Dissertations, Fall 2023 to Present

Successful maple sap tapping depends on the freeze/thaw cycle (i.e., temperatures fluctuating above/below freezing) during the winter and spring. Climate change threatens to alter the timing and duration of the tapping season. This necessitates research into how maple sap tapping will be impacted by climate change in order to help maple syrup producers prepare for the future. We define a sap day as a day where the freeze/thaw cycle occurred. Using information climate scientists use to predict future temperatures, we calculate how many sap days could occur each year. We develop software to analyze these sap day calculations to determine …

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 …

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.