Physical Sciences and Mathematics Commons^™

The Making Of Mathematics: An Interview With Carlo Cellucci, Marshall Gordon

Journal of Humanistic Mathematics

Carlo Cellucci is professor emeritus of the Sapienza University of Rome, and has written books on logic, mathematics, and philosophy. In the following interview conducted via back-and-forth email correspondence, he discusses his 2022 book, The Making of Mathematics: Heuristic Philosophy of Mathematics [3], which presents a new paradigm for thinking about, doing, and teaching mathematics.

The Operator Algebras Mentor Network: Impact Of Community-Based Mentoring, Anna Duwenig, Kari Eifler, Priyanga Ganesan, Lara Ismert, Viviana Meschitti, Sarah Plosker, Karen Strung

Journal of Humanistic Mathematics

The Operator Algebras Mentor Network (OAMN) is an international mentoring initiative that offers support in small groups to women and minority genders in the particularly male-dominated field of operator algebras (OA) in mathematics. Expected advantages of membership include raising awareness of the lack of gender diversity in this field, providing advice to mentees by mentors (e.g., pertaining to career or work/life balance), broadening one’s network in OA, etc. In this project, we set out to determine if membership within the OAMN is beneficial to its members. To this end we sent a questionnaire to OAMN members and a control group …

Geometry, Art, And Technology: Islamic Geometric Patterns In The Classroom, Rebin Muhammad, Mona Hajghassem, Mais Alraee

Journal of Humanistic Mathematics

In this paper, we share our experiences developing and implementing three Desmos activities. These activities aim to introduce geometric concepts such as transformation, symmetry, and geometric construction by using examples from Islamic Geometric Patterns (IGP). Our target audience for these activities is future elementary school teachers. In addition to leveraging technology, we enrich the learning process by incorporating hands-on exploration with physical IGP examples.

Revisiting The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

Journal of Humanistic Mathematics

In previous work, we have explored some of the symmetries hidden in the multiplication tables of natural numbers and integers. In this article, we dive deeper into the hidden symmetries within the distribution of positive and negative integers. We also share various ideas to explore these symmetries in a classroom setting, encouraging active engagement and deeper understanding among students.

Mathematics In The Vichten Roman Mosaic, Marko Peric, Antonella Perucca

Journal of Humanistic Mathematics

We explore the geometry of the renowned Vichten Roman Mosaic. The central section of the mosaic features a tessellation composed of octagons, half-squares, and symmetrical pentagons. We present a Sangaku-style exercise to investigate these polygons. Additionally, we examine the whirl patterns of the mosaic and the optical illusion they create. Our activities offer a mathematical exploration that requires only basic school-level mathematics, highlighting the close connection between mathematics and art.

White Horses In The Sky: Or The Magical Place Where Topology Meets Poetry, Sanziana Caraman, Lorelei Caraman

Journal of Humanistic Mathematics

What do Shakespearean words, doughnuts, cups of tea, and horses in the sky all have in common with a famous theorem? To discover the answer, we take you on a journey in a strange, enchanted land: the land where mathematics meets poetry. Here we explore how a fundamental literary trope, metaphor, and a fundamental result in topology, Brouver's Fixed Point Theorem, touch and illuminate one another. Delving into the symmetry of this transdisciplinary embrace, we find that it reveals, not only the beauty of poetry and mathematics, but that of life itself: the beauty hidden in ordinary things like a …

From The Symbol Of Inanna To Islamic Tessellations: Aesthetics Of Constructibility, Zhexiu Tu

Journal of Humanistic Mathematics

We introduce a special symbol with a long history dating back to the Sumerian period. This symbol, which was first associated with the goddess Inanna, can be constructed with compass and straightedge, a property defined as constructibility in modern geometry. Nineteenth-century mathematicians proved systematically what types of polygons and polygrams are constructible. This algebraic result shared a striking consistency with the tessellations present in medieval Islamic architecture. The geometric patterns behind the tessellations as well as the symbol of Inanna itself, if properly remodeled, can be adopted as effective tools in the teaching of algebra and Galois theory.

Ethnomathematics Projects For Projective Geometry In Distance Learning, Wen-Haw Chen, Ja'faruddin Arsyad Ide

Journal of Humanistic Mathematics

This article reports on an ethnomathematics project we developed and implemented in an online learning environment to connect with students’ cultural backgrounds and to highlight the links between their environment, culture, and mathematics. The project is based on Simple House Theory, a framework that involves the application of projective geometry in the design of traditional houses and building numbers. Our results show that this approach fostered active participation and engagement despite the standard constraints and challenges of distance learning.

What Does An Integer Sequence Sound Like?, Firdous Ahmad Mala

Journal of Humanistic Mathematics

It may be difficult to assign a sequence to every piece of music, but a piece of music can surely be assigned to every integer sequence. The Online Encyclopaedia of Integer Sequences (OEIS), a comprehensive and collaborative database of over 350,000 integer sequences, offers a unique ’listen’ feature that converts numerical sequences into melodies. This sensory approach to sequences provides a novel way to experience the beauty and complexity of mathematical patterns. We describe the process of how integer sequences are mapped to musical notes, using modular arithmetic, and discuss the various parameters that influence the resulting sound. Highlighting specific …

On The Development Of Equations In Ancient China, Wanwan Huang

Journal of Humanistic Mathematics

This article explores the evolution of equations in ancient China, detailing the development process through the presentation of various classical mathematics problems spanning four stages. We present these problems and their solutions, both using ancient Chinese terminology and modern language. With this work, we hope to offer an insightful examination of the achievements and limitations of ancient Chinese mathematicians in their work on equations, particularly in relation to culture, practical needs, and human creativity.

The Swaying Equations: An Exhibition Of Mathematical And Algorithmic Art, Awansika Nimuthumana, Anuradha Mahasinghe

Journal of Humanistic Mathematics

An exhibition of mathematical and algorithmic art took place on 30th September and 01st October 2023 at the Lionel Wendt art gallery in Colombo, Sri Lanka. To our knowledge, this is the first-ever mathematical art exhibition in Sri Lanka. This report contains a brief overview of the artworks and some highlights of the exhibition.

Engaging Mathematicians One Step At A Time: Math Trails, Mary L. Dalton, Jennifer Yantz

Journal of Humanistic Mathematics

Mathematics is present in everything we see and do. Sometimes we look past it, looking for some mathematical mystery when the beauty of mathematics is evident in the most obvious ways. One way to engage students to notice connections to mathematics in these everyday objects and events is to direct them in a guided math trail. A math trail is an activity where participants follow a map or guide to various locations while they are encouraged to take notice of connections to mathematical patterns and concepts in the objects around them. An important benefit is that going on a math …

Chatgpt As A Boundary Object Between In-School And Out-Of-School Mathematical Practices: The Case Of Numeracy Practices, Murad E. Jurdak

Journal of Humanistic Mathematics

This article explores the theoretical basis and practical potential of ChatGPT in bridging the gap between school-based and out-of-school mathematical practices. Drawing on Cultural Historical Activity Theory and the concept of boundary objects, we highlight how ChatGPT can serve as a boundary object to connect these two domains. Our analysis of ChatGPT-generated lesson plans designed to align with out-of-school practices reveals that the model had the greatest impact on the social and institutional relations component of the numeracy practices framework [6], while their impact was weakest in the values and beliefs component.

An Unlikely Duo: Injecting Art Projects In The Lower-Division Mathematics Classroom, Douglas T. Pfeffer, Christina Durón

Journal of Humanistic Mathematics

Too often society has sterilized mathematics to the point that many view it as drab and deplete of aesthetic intrigue---in higher education, this is particularly true of students in the lower-division classroom. In this paper, we propose the use of art projects as a novel way to alter this perspective. Art projects function as a hands-on, active way to invite students to both identify connections between math and various non-mathematical disciplines as well as view math as overall more intriguing, inviting, and interesting. This paper details our implementation and discusses anonymously solicited survey data that highlights our successes.

Teaching Mathematics For Labour Emancipation: An Autoethnography Of A Math Teacher In Mykonos, Dimitris T. Maris, Konstantinos P. Christou

Journal of Humanistic Mathematics

A wealthy society does not necessarily ensure a good education for its students, just as it does not guarantee wealth for its workers. In this paper we visit a junior high school mathematics classroom on the Greek island of Mykonos, where a significant number of students are employed. In this context, we explore how a mathematics teacher, inspired by social justice mathematics, can empower students in their work environments. We adopt an autoethnographic approach in our narrative, presenting the process of designing and implementing specific mathematical activities aimed at revealing the issue of labour exploitation in the touristic Greek islands. …

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.

Collision Avoidance And Vegetation As Drivers Of Collective Motion In Australian Plague Locusts, Nathan S. Hasegawa

HMC Senior Theses

The Australian plague locust (Chortoicetes terminifera) is an agricultural and ecological pest that causes tens of millions of dollars in crop damage each year. In this thesis, we develop mathematical models of hopper bands, dense formations of juvenile locusts that move across a vegetated field and destroy plants in their path. We develop agent-based and PDE models of hopper bands moving through vegetation to examine how recently discovered behavior where locusts slow down to avoid collisions with other locusts may influence the shape, speed, and destructiveness of hopper bands. We find that collision avoidance may cause locusts to …

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.

The Impact Of Llms Usage On Learning Outcomes For Software Development Students: A Focus On Prompt Engineering, Mohammed Owaidh Aljohani

CGU Theses & Dissertations

This study investigates the impact of large language model (LLM) usage, specifically ChatGPT, on student learning outcomes in programming education. The research adopts a mixed-methods approach, combining quantitative survey data from students and qualitative interviews with instructors. The study addresses three research questions: (1) the effect of LLM usage on undergraduate students' learning outcomes, (2) the influence of prompt engineering skills on this relationship, and (3) instructors' perceptions on these relationships. Quantitative data were collected from 159 students across two Saudi universities using a structured online survey with sections covering demographic information, LLM usage, self-reported programming understanding, and prompt engineering …

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 …

A Proof Of Np-Completeness For The K-Means Clustering Algorithm, Brooke C. Feinberg

Scripps Senior Theses

The k-means clustering algorithm is one of the most widely used clustering techniques in data analysis and machine learning, yet its exact computational complexity remains subject to ongoing theoretical investiga- tion. This work establishes the NP-completeness of k-means by proving (1) it is NP-hard and (2) it lies in NP. To demonstrate NP-hardness, we construct a series of polynomial-time reductions from well-known NP-complete problems. Specifically, we reduce 3sat to Vertex Cover, and then reduce Vertex Cover to k-means, thereby establishing the computational hardness of the k-means clustering problem. We then prove k-means is in NP, and thus conclude it is …

Verification Of Real-Time Smoke Simulations: A Case Study On Early Summer North American Wildfire Events, Daniel Bonilla

Pitzer Senior Theses

As wildfire intensity and frequency escalate in times of unprecedented climate change and severe droughts, it is important to enhance forecasting models that accurately and efficiently predict wildfire smoke movement. NOAA’s experimental Rapid-Refresh Forecasting System with Smoke and Dust (RRFS-SD) aims to improve upon the High-Resolution Rapid Refresh- Smoke (HRRR-Smoke), by extending the domain to include all of North America and incorporating new developments in physics and wildfire parameterizations. Our work explores the process of adding satellite Aerosol Optical Depth (AOD) data, through AERONET, as an additional method of verification of the RRFS-SD experimental model. Using a case study on …

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 …