Mathematics Commons^™

Math Is _______: A Study On Prospective Teachers' Perceptions Of Math And Teaching Math, Kayla Mead, Katherine Baker

Journal of Humanistic Mathematics

In this project, we examined one cohort of twenty-eight college students and their perceptions of mathematics at the beginning and end of a semester-long mathematics content course for K-8 prospective teachers (PTs). More specifically, our study explored PTs’ perceptions of what mathematics is and what mathematics teaching is, and how and why those perceptions might change over the semester-long mathematics course. PTs’ perceptions were captured through open-ended surveys and follow-up interviews. Our intention was to better understand the reasonings for changes in perceptions during the course to support teacher educators in their work of preparing prospective teachers.

Stem Major Perspectives For Humanizing Undergraduate Mathematics Classes, Kelly Macarthur, Derek Williams, Bryce Hughes

Journal of Humanistic Mathematics

Using the eight dimensions of the rehumanizing framework [32] by Gutiérrez, built on a sociopolitical foundation, we report on research findings about what Latin* [41], Native American, LGBTQ+ and/or women science, technology, engineering, and mathematics (STEM) majors at two primarily white institutions (PWI) perceive as humanizing in their mathematics courses. In analysis of interviews with twenty students, we found that the core aspects of a humanized learning experience center relationality and a caring classroom environment. We then explore tensions that arose regarding the implementation of one teaching strategy reflecting the Cultures & Theirstories rehumanizing dimension, suggesting that implementation of such …

Rehumanizing Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Galoistheory And The Arithmetic-Geometric Series, Daniel Vargas

HMC Senior Theses

Motivated by classical works of Gauss and Euler on the AGM, Ono and his

collaborators Griffin et al. (2023); McSpirit and Ono (2023) have investigated

the union of AGM sequences over finite fields 𝔽𝑞, where 𝑞 ≡3 mod 4. A

recent preprint Kayath et al. (2024) extends some of their results to all finite

fields with odd characteristic. We refine these works when 𝑞≡5 mod 8. In

particular, we explicitly determine the components of these graphs and their

total population. We also use Galois-theoretic results to make progress in

the search for cycles over finite fields with odd characteristic.

Localized Kernel Methods For Signal Processing, Sippanon Kitimoon

CGU Theses & Dissertations

This dissertation presents two signal processing methods using specially designed localized kernels for parameter recovery under noisy condition. The first method addresses the estimation of frequencies and amplitudes in multidimensional exponential models. It utilizes localized trigonometric polynomial kernels to detect the multivariate frequencies, followed by a more detailed parameter estimation. We compare our method with MUSIC and ESPRIT, which are classical subspace-based algorithms widely used for estimating the parameters of exponential signals. In the univariate case, the method outperforms MUSIC and ESPRIT under low signal-to-noise ratios. For the multivariate case, we develop a coordinate-wise projection and registration approach that achieves …

Existence And Uniqueness Of The Solution Of A Traffic Flow Partial Differential Equation On Multi-Lane Freeways, Sina Zareian

CGU Theses & Dissertations

In this dissertation, we shall prove the existence of a solution of the stochastic partial differential equation describing the density of cars on a multi-lane freeway using the operator splitting method. Furthermore, we shall prove the uniqueness of the solution of the stochastic differential equation which forms when we apply the operator splitting method to the traffic flow stochastic partial differential equation.

Diophantine Avoidance, Number Fields, And Quadratic Forms, Sehun Jeong

CGU Theses & Dissertations

Diophantine avoidance has been studied by several authors in recent years. This term refers to effective results on existence of points of bounded size (where size is measured by norm or height, depending on the context) in a given algebraic set avoiding some specified subsets. The application of avoidance conditions allows to understand how ``well distributed" are points of bounded size in a given set. If it is possible to find them outside of some prescribed collection of subsets of the set in question, then it suggests that they are evenly distributed, in some appropriate sense. Our first result investigates …

Classical And Quantum Computational Methods For Predicting Fluid Transport In Fracture Networks, John Kath

CGU Theses & Dissertations

This dissertation addresses the challenge of modeling complex geophysical systems by developing efficient surrogate models and scalable quantum algorithms. Our approaches provide uncertainty quantification, assessing confidence in estimates while accounting for subsurface heterogeneity. These innovations are designed to replace costly solvers with parsimonious emulators. In combination with multi-fidelity and quantum techniques, they make physics-informed modeling computationally feasible. One of our studies involves the use of Gaussian process regression to generate Bayesian predictions for gas transport in 3D discrete fracture networks. This provides accurate estimates while offering substantial savings over computationally intensive high-fidelity simulations. Additionally, we study multi-fidelity modeling through the …

Random Graph Models For Dual Graphs, Anne Friedman

Scripps Senior Theses

This paper aims to better characterize dual graphs derived from state districting maps by developing random graph models that replicate their structural properties. Dual graphs provide a simplified way to represent districting maps, making it computationally feasible to analyze their structure. These representations enable researchers, legislators, and courts to assess district compactness, detect signs of gerrymandering, and generate alternative districting plans. A deeper understanding of the structural patterns of these dual graphs can help researchers choose or design more effective algorithms for redistricting analysis. The random graph models developed in this study serve as testbeds for evaluating algorithmic approaches to …

Optimizing Decision-Making In A Cerebral Palsy Model Using Reinforcement Learning, Richard Ampah

Pitzer Senior Theses

This study presents an original interdisciplinary investigation into how reinforcement learning (RL) can model motor and cognitive defects and potentially improve motor and cognitive functions in individuals with cerebral palsy (CP), a non-progressive neurological disorder that impairs movement and adaptability. Integrating computational neuroscience and machine learning, the research applies policy gradient methods and Markov Decision Processes (MDPs) to simulate adaptive learning in agents with and without CP-related constraints.

The central aim is to compare the cumulative rewards of optimal policies, derived from value iteration, and human-like learning policies using the REINFORCE algorithm, both with and without the Bellman baseline. The …

Empirical Analysis Of Political Districting Splitability Via Uniform Spanning Trees In Polynomial Time, Brooke C. Feinberg

Scripps Senior Theses

This work expands a recently proven conjecture that a polynomial fraction of all uniform spanning trees (USTs) are splittable into k balanced partitions on grid graphs to real-world political districting plans. We investigate whether similar structural properties hold for the planar dual graphs of U.S. counties (cnty) and tracts (t), using Wilson’s algorithm to generate uniform random spanning trees and Breadth- First Search (BFS) to check for splitability into balanced partitions. Our empirical findings suggest that real-world districting plans can be split into 2-balanced, connected partitions in a fraction of polynomial time. This result highlights the potential for scalable redistricting …

Geometric Dimensionality Reduction, Daniel Livschitz

CGU Theses & Dissertations

The emergence of AI models developed through computationally intensive training has resulted in a surge of research into dimensionality reduction techniques that spans across numerous mathematical disciplines. In this thesis we establish Geometric Dimensionality Reduction, a non-linear data compression technique that utilizes low dimensional manifolds embedded in dimensional spaces to form composite contraction-and-projection maps. Geometric Dimensionality Reduction is predominantly demonstrated through a novel algorithm entitled LGE (Livschitz-Gu-Eyunni) that utilizes Multicomplex rotation groups and polyspherical coordinates to define a single tuneable logarithmic map from ℝ 2푛 to ℝ 푛+1 with deterministic time complexity, geometric tunability, and semi-reversibility. Significant breakthroughs in the …

Integrating Sentiment Analysis In Predictive Models: A Comparative Study On Game Popularity On Steam, Khaleefa Alhemeiri

CMC Senior Theses

Over the past decades, the gaming industry has managed to evolve into a multi-billion-dollar enterprise. Gaming platforms such as Steam foster unprecedented amounts of engagement among players worldwide daily. In this thesis, we investigate the effect of incorporating sentiment-driven metrics, specifically YouTube view counts and positive reviews, into predictive models for game popularity. In addition, by comparing our linear regression sentiment-based approach to the Bayesian hierarchical folded normal model used by De Luisa et al. (2021), we can understand the many differences, strengths, and limitations of each methodology. In our thesis, we focus on three games. Each is of varying …

Analyzing Political Sentiment On Micro-Blogging Data: A Lexicon And Machine Learning Approach To The 2024 U.S. Presidential Election, Ava Grey

CMC Senior Theses

This paper explores the trends in sentiment towards U.S. presidential candidates Kamala Harris and Donald Trump through micro-blogging social media text during the five months leading up to the election. Two datasets of varying sizes and origins were used to contextualize and validate analysis findings. The analyses include both a lexicon-based approach and a machine learning predictive method. Common sentiment analysis techniques like term frequency, term frequency inverse, various lexicons, and n-grams were utilized during the lexicon approach. During the modeling, a random forest was utilized in addition to the methods used during the lexicon approach. Results showed that overall …

Mathematical Modeling Of Cancer Tumor Evolution, Belgacem Al-Azem

CGU Theses & Dissertations

Several mathematical models of cancer tumor evolution are presented. The aim of this endeavor is to write a thesis that fosters numerical and analytical understanding of certain mathematical models in the area of oncology as well as to offer potential predictive tools of therapeutic and clinical applicability. In this work, we give a panoramic view of the cancer phenotype, for to understand cancer, we need to "see" its biophysics. Indeed, the discovery of oncogenes led to the thinking that cancer tumor is perhaps a genetic disease. But the role of angiogenesis and other microenvironment-related discoveries (such as the role of …

Untangling The Classification Of Surfaces: An Accessibility-Centered Perspective On Topology, Charlotte N. Richards

Pitzer Senior Theses

Mathematics has clear benefits in education, from preparing students for future careers to teaching them how to problem-solve. While mathematics achievement has been falling in recent decades, students claim that the problem is not the mathematics itself, but the ‘boring’ classroom material that feels removed from real life. More advanced mathematics topics, such as topology, could offer a solution, as their applications lie in countless fields. However, topology has been restricted to upper-level mathematics, disregarding the potential benefits of making this material broadly reachable for a junior high-school audience. In this paper, we analyze five different proofs of the theorem …

Measuring The Similarity Between Trees Of Different Order, Camilo Morales

HMC Senior Theses

Graphs encode relationships between data. However, due to their versatility, it is often difficult to generalize the notion of similarity between two graphs using a distance function. Since graphs can represent various data sets, specific distance metrics need to be tailored for questions we are interested in answering or the data set we are working with. This project is motivated by ongoing investigations into the evolution of female gender representation in mathematics. By building off previous work that has taken data from the Mathematics Genealogy Project and modeled this evolution of representation via a tree, we would like to develop …

Enhancement Of Mechanical, Structural, And Electrical Properties In Advanced Composites And Vat Photopolymerized 3d Printing Nanocomposites, Poom Narongdej

CGU Theses & Dissertations

Advanced composites have gained significant attention across various industries, including aerospace, automotive, clean energy, and healthcare, owing to their exceptional mechanical properties and versatility. Fiber-reinforced polymer (FRP) composites, particularly those reinforced with carbon fibers, are extensively used as structural materials in spacecraft, aircraft, high-performance vehicles, and wind turbines due to their high strength-to-weight ratios, stiffness, durability, and tailorable mechanical characteristics. In healthcare, the advent of additive manufacturing (3D printing) has expanded the utility of advanced composites, enabling precise customization of components to meet patient-specific needs while offering design flexibility and ease of fabrication. Despite these advantages, several challenges hinder the …

Mathematics And Determinism: Chaos, Quantum Mechanics, And The Limits Of Predictive Structure, Jackson T. Salumbides

CMC Senior Theses

This thesis examines the relationship between mathematics and determinism by analyzing how chaos theory, quantum mechanics, and formal mathematical limits challenge traditional conceptions of predictability and causal structure. Chaos theory shows that deterministic systems can exhibit practical unpredictability due to sensitivity to initial conditions. Quantum mechanics introduces probabilistic outcomes that complicate deterministic interpretation, though alternative frameworks such as Bohmian mechanics and superdeterminism attempt to restore determinism at conceptual cost. Additionally, results from mathematical logic, including Gödel’s incompleteness theorems and Turing’s undecidability, demonstrate intrinsic limitations on what can be deduced or computed, even in fully deterministic systems. By synthesizing these areas, …

Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer

CODEE Journal

This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …

First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat

Journal of Humanistic Mathematics

From August 22nd to November 21st, the first Diffusion Course on “The structure of language as a connection between artificial intelligence, information and ethics” will take place on a Thursday of each month, in Ribeirao Preto, Brazil. You are cordially invited to sign up for in-person classes and join other researchers and students on this course.

7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond

Journal of Humanistic Mathematics

The 7th International Creative Mathematical Sciences Communication (CMSC) conference is scheduled for October 2024 in Trier, Germany. Initiated in Darwin, Australia in 2013, CMSC aims to explore novel methods of imparting computational thinking to diverse audiences including non-specialists, modern citizens, and children. Participants from around the world and from various and interdisciplinary disciplines such as science, education, dance, drama, and visual arts convene to exchange ideas, present experimental approaches, and collaborate on engaging children in the exploration of ongoing, unresolved research challenges.

Oh Statistics!, Heather L. Cook

Journal of Humanistic Mathematics

This poem was written about statistics and the usefulness thereof.

Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat

Journal of Humanistic Mathematics

How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)

Pi: A Perpetual Journey, Ravindra K. Bisht

Journal of Humanistic Mathematics

A brief history of the constant pi is presented with a poetic flavor.

Love Is No Mean Thing: A Larkin Logarithm, Michael P.H. Stanley Md

Journal of Humanistic Mathematics

This poem was recited at a marriage recently in Vermont. I met the groom in my freshman year. He was the first college friend I ever made, and he used to burst into the room like Cosmo Kramer and settle down in an easy-chair to think about math (my side of the dorm was quieter than his). I thought that was remarkable and delightful, and so, when the task came to write a matrimonial poem for him, I selected a mathematical conceit. The poem concludes with a mathematical paraphrasing of Philip Larkin's last line from Arundel Tomb.

Eighth Grade Algebra, Joseph Chaney

Journal of Humanistic Mathematics

This is a poem about the affirming power of algebra in the life of a teenager.

Prime Motivation Of Eratosthenes, Pamela L. King

Journal of Humanistic Mathematics

The sieve of Eratosthenes is used as a metaphor for the concept of people falling through the social safety net, and people who were once excluded, making efforts to increase inclusiveness.

Poems From The Series "At The Dimensional Border", Philip Fried

Journal of Humanistic Mathematics

Poems about the border between the second and third dimensions, on geometry and the human condition.