Mathematics Commons^™

Fourier Series For Singular Measures In Higher Dimensions, Chad Berner, John E. Herr, Palle E.T. Jorgensen, Eric S. Weber

Mathematics and Statistics Faculty Research & Creative Works

For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal L2 Fourier expansions. Our results hold for probability measures μ with finite support in Rd that satisfy a certain disintegration condition that we refer to as "slice-singular". In this general framework, we present explicit L2(μ)-Fourier expansions, with Fourier exponentials having positive Fourier frequencies in each of the d coordinates. Our Fourier representations apply to every f∈L2(μ), are based on an extended Kaczmarz algorithm, and use a new recursive μ Rokhlin disintegration representation. In detail, our Fourier series expansion for f is in terms of the …

Unconditionally Optimal Convergent Zero-Energy-Contribution Scheme For Two Phase Mhd Model, Jinjin Yang, Shipeng Mao, Xiaoming He

Mathematics and Statistics Faculty Research & Creative Works

This paper focuses on the unconditionally optimal error estimates of a fully discrete decoupled scheme for two-phase magnetohydrodynamic (MHD) model with different viscosities and electric conductivities, by using the zero-energy-contribution (ZEC) method for the temporal discretization and mixed finite elements for the spatial discretization. Based on the ZEC property of the nonlinear and coupled terms of the model, an ordinary differential equation is designed to introduce a nonlocal scalar auxiliary variable which will play a key role in the design and the energy stability of the decoupled scheme. Combining fully explicit treatment on the nonlinear and coupled terms with the …

Order-2 Delaunay Triangulations Optimize Angles, Herbert Edelsbrunner, Alexey Garber, Morteza Saghafian

School of Mathematical & Statistical Sciences Faculty Publications

The local angle property of the (order-1) Delaunay triangulations of a generic set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2 asserts that the sum of two angles opposite a common edge is less than π. This paper extends this property to higher order and uses it to generalize two classic properties from order-1 to order-2: (1) among the complete level-2 hypertriangulations of a generic point set in R2" role="presentation" style="box-sizing: border-box; margin: 0px; padding: 0px; position: relative;">R2R2, the order-2 Delaunay triangulation lexicographically maximizes the sorted angle vector; (2) among the maximal level-2 hypertriangulations …

Analytical Method For Solving Systems Of Fractional Initial Value Problems Using The Modified Atangana-Baleanu Derivative, Lana Mohammad Aref

Theses

This thesis presents an analytical method to solve systems of fractional initial value problems using the Modified Atangana-Baleanu Fractional Derivative. The proposed approach leverages an improved operational matrix method, incorporating an iterative, direct computation technique to simplify the solution process and reduce computational costs. Foundational concepts in fractional calculus and block pulse functions are introduced, followed by the derivation of operational matrices tailored for fractional systems. Theoretical analysis establishes the existence and uniqueness of solutions, along with uniform convergence and error estimates. Practical examples and applications are presented that demonstrate the efficiency, accuracy, and versatility of the method in solving …

Project Title: Maximizing The Volume Of A Cardboard Box To Save Trees– An Application Of Polynomial Functions To Address Global Issues [Mathematics], Lucie Mingla

Open Educational Resources

MAT 115 College Algebra & Trigonometry/Precalculus

Project Title: Maximizing the Volume of a Cardboard Box to Save Trees– An Application of Polynomial Functions to Address Global Issues

Reflective Narrative:

This project was inspired by my participation in the "Designing and Implementation of STEM Co-Curricular Activities" CTL seminar in Spring 2023. I am grateful to Drs. Bukurie Gjoci, Daniel Gertner, Ingrid Veras, and Midas Tsai, along with fellow participants, for their invaluable feedback that helped shape its development. The project was implemented in two College Algebra and Trigonometry courses. I participated in two seminars to further develop this project. The Community …

For Chow Variety Try This New Dessert Recipe, Jane P. Sheldon

Journal of Humanistic Mathematics

A positive addition to any dinner table or social function, this baked good can be served plane or à la mode.

Integration Bar, Erik Talvila

Journal of Humanistic Mathematics

In this humourous story, the narrator is dragged by their friend to a crazy bar for a late night of wild drinking and dancing. Except, the drinking is replaced with computing integrals.

Constanto Mysterium - A Paradise Of Shifting Constants, Vijay Fafat

Journal of Humanistic Mathematics

Mathematicians speak of constants of mathematics. Some of these constants are known to high-heavens. Some remain hidden in the obscurity of erudition. And to be frank, while every real number is a mathematical constant, we don’t know much about most of them (is not the set of transcendental numbers incommensurable without us knowing or understanding very many of them?).

So what elevates some constants above others? Is this elevation just a measure of the ignorance of mathematicians who have explored but a small patch of an infinite quilt, a case of six wise men trumpeting the – well, the trumpet …

Welcome 2025—The Year Of A Magical Number, Md Sadikur Rahman

Journal of Humanistic Mathematics

This is a poem to welcome the new year 2025 and note its relevance to mathematics.

A Ramsey Theory Essay: The Dinner Party, Ryan Coghill

Journal of Humanistic Mathematics

This is a poem inspired by Ramsey’s theorem. Its main characters are; Frank Ramsey, Issai Schur, Richard Rados, Bertel van der Waarden, Ronald Graham and Paul Erdos, some of the pioneers of the field of Ramsey theory. There has been care put into each paragraph so that it’s lines can be viewed as though they were nodes on a graph which share traits with each other of rhyme, theme and length which can be paired in 2 states, sharing and unique in such a way that one might find coloured graph edges when working in the field of Ramsey theory.

Math Is A Tiger And A Pecan, William Cocke

Journal of Humanistic Mathematics

Using perfect secrecy and the ability to identify gibberish in a given language, we encode two poems in one. This allows for a single cipherpoem to have multiple plainpoems associated with it. The result is a form of superposition where neither poem is the more correct interpretation than the other.

The poem presented is about two distinct aspects of mathematics: the tiger to be sought after and hunted; or a pecan that we have surrounded but cannot crack open.

My Academic Life -- A Poem, Sonja Petrovic

Journal of Humanistic Mathematics

No abstract provided.

Belonging, Lawrence M. Lesser

Journal of Humanistic Mathematics

No abstract provided.

What Happened When I Took Calculus For The First Time At Age 47, Britt Kaufmann

Journal of Humanistic Mathematics

These five poems are inspired by being in high school math classes and could be used in the classroom for cross-curricular enrichment.

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.