Physical Sciences and Mathematics Commons^™

Anschaulich: Visualization, Imagination, Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Donyi Polo Apatani, Sejal Saraiya

The STEAM Journal

The Apatani are a non-nomadic, nature worshipping tribe who consider the Sun and the Moon their God, the Sun considered female and called Mother Sun. They have a sibling relationship with nature and perceive prosperity as a harmonious condition between man and nature.

Dense Geometry Of Music And Visual Arts: Vanishing Points, Continuous Tonnetz, And Theremin Performance, Maria Mannone, Irene Iaccarino, Rosanna Iembo

The STEAM Journal

The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of …

Parametric Natura Morta, Maria C. Mannone

The STEAM Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.

Unfolding Humanity: Cross-Disciplinary Sculpture Design, Gordon D. Hoople, Nate Parde, Quinn Pratt, Sydney Platt, Michael Sween, Ava Bellizzi, Viktoriya Alekseyeva, Alex Splide, Nicholas Cardoza, Christiana Salvosa, Eduardo Ortega, Elizabeth Sampson

The STEAM Journal

Unfolding Humanity is a 12 foot tall, 30 foot wide, 2 ton interactive metal sculpture that calls attention to the tension between technology and humanity. This sculpture was conceived, designed, and built by a large group (80+) of faculty, students, and community volunteers at the University of San Diego (USD). The piece is a dodecahedron whose pentagonal walls unfold under human power, an engineered design that alludes to Albrecht Dürer's 500-year-old unsolved math problem on unfolding polyhedra. When closed, the mirrored interior of the sculpture makes visitors feel as though they are at the center of the universe. The idea …

The Mathematics Of Gossip, Jessica Deters, Izabel P. Aguiar, Jacquie Feuerborn

CODEE Journal

How does a lie spread through a community? The purpose of this paper is two-fold: to provide an educational tool for teaching Ordinary Differential Equations (ODEs) and sensitivity analysis through a culturally relevant topic (fake news), and to examine the social justice implications of misinformation. Under the assumption that people are susceptible to, can be infected with, and recover from a lie, we model the spread of false information with the classic Susceptible-Infected-Recovered (SIR) model. We develop a system of ODEs with lie-dependent parameter values to examine the pervasiveness of a lie through a community.

The model presents the opportunity …

The Ocean And Climate Change: Stommel's Conceptual Model, James Walsh

CODEE Journal

The ocean plays a major role in our climate system and in climate change. In this article we present a conceptual model of the Atlantic Meridional Overturning Circulation (AMOC), an important component of the ocean's global energy transport circulation that has, in recent times, been weakening anomalously. Introduced by Henry Stommel, the model results in a two-dimensional system of first order ODEs, which we explore via Mathematica. The model exhibits two stable regimes, one having an orientation aligned with today's AMOC, and the other corresponding to a reversal of the AMOC. This material is appropriate for a junior-level mathematical …

Consensus Building By Committed Agents, William W. Hackborn, Tetiana Reznychenko, Yihang Zhang

CODEE Journal

One of the most striking features of our time is the polarization, nationally and globally, in politics and religion. How can a society achieve anything, let alone justice, when there are fundamental disagreements about what problems a society needs to address, about priorities among those problems, and no consensus on what constitutes justice itself? This paper explores a model for building social consensus in an ideologically divided community. Our model has three states: two of these represent ideological extremes while the third state designates a moderate position that blends aspects of the two extremes. Each individual in the community is …

Modeling The Spread And Prevention Of Malaria In Central America, Michael Huber

CODEE Journal

In 2016, the World Health Organization (WHO) estimated that there were 216 million cases of Malaria reported in 91 countries around the world. The Central American country of Honduras has a high risk of malaria exposure, especially to United States soldiers deployed in the region. This article will discuss various aspects of the disease, its spread and its treatment and the development of models of some of these aspects with differential equations. Exercises are developed which involve, respectively, exponential growth, logistics growth, systems of first-order equations and Laplace transforms. Notes for instructors are included.

A Model Of The Transmission Of Cholera In A Population With Contaminated Water, Therese Shelton, Emma Kathryn Groves, Sherry Adrian

CODEE Journal

Cholera is an infectious disease that is a major concern in countries with inadequate access to clean water and proper sanitation. According to the World Health Organization (WHO), "cholera is a disease of inequity--an ancient illness that today sickens and kills only the poorest and most vulnerable people\dots The map of cholera is essentially the same as a map of poverty." We implement a published model (Fung, "Cholera Transmission Dynamic Models for Public Health Practitioners," Emerging Themes in Epidemiology, 2014) of a SIR model that includes a bacterial reservoir. Bacterial concentration in the water is modeled by the Monod …

Sir Models: Differential Equations That Support The Common Good, Lorelei Koss

CODEE Journal

This article surveys how SIR models have been extended beyond investigations of biologically infectious diseases to other topics that contribute to social inequality and environmental concerns. We present models that have been used to study sustainable agriculture, drug and alcohol use, the spread of violent ideologies on the internet, criminal activity, and health issues such as bulimia and obesity.

Climate Change In A Differential Equations Course: Using Bifurcation Diagrams To Explore Small Changes With Big Effects, Justin Dunmyre, Nicholas Fortune, Tianna Bogart, Chris Rasmussen, Karen Keene

CODEE Journal

The environmental phenomenon of climate change is of critical importance to today's science and global communities. Differential equations give a powerful lens onto this phenomenon, and so we should commit to discussing the mathematics of this environmental issue in differential equations courses. Doing so highlights the power of linking differential equations to environmental and social justice causes, and also brings important science to the forefront in the mathematics classroom. In this paper, we provide an extended problem, appropriate for a first course in differential equations, that uses bifurcation analysis to study climate change. Specifically, through studying hysteresis, this problem highlights …

An Epidemiological Math Model Approach To A Political System With Three Parties, Selenne Bañuelos, Ty Danet, Cynthia Flores, Angel Ramos

CODEE Journal

The United States has proven to be and remains a dual political party system. Each party is associated to its own ideologies, yet work by Baldassarri and Goldberg in Neither Ideologues Nor Agnostics show that many Americans have positions on economic and social issues that don't fall into one of the two mainstream party platforms. Our interest lies in studying how recruitment from one party into another impacts an election. In particular, there was a growing third party presence in the 2000 and 2016 elections. Motivated by previous work, an epidemiological approach is taken to treat the spread of ideologies …

Kremer's Model Relating Population Growth To Changes In Income And Technology, Dan Flath

CODEE Journal

For thousands of years the population of Earth increased slowly, while per capita income remained essentially constant, at subsistence level. At the beginning of the industrial revolution around 1800, population began to increase very rapidly and income started to climb. Then in the second half of the twentieth century as a demographic transition began, the birth and death rates, as well as the world population growth rate, began to decline. The reasons for these transitions are hotly debated with no expert consensus yet emerging. It's the problem of economic growth. In this document we investigate a mathematical model of economic …

A Note On Equity Within Differential Equations Education By Visualization, Younes Karimifardinpour

CODEE Journal

The growing importance of education equity is partly based on the premise that an individual's level of education directly correlates to future quality of life. Educational equity for differential equations (DEs) is related to achievement, fairness, and opportunity. Therefore, a pedagogy that practices DE educational equity gives a strong foundation of social justice. However, linguistic barriers pose a challenge to equity education in DEs. For example, I found myself teaching DEs either in classrooms with a low proficiency in the language of instruction or in multilingual classrooms. I grappled with a way to create an equity educational environment that supported …

Linking Differential Equations To Social Justice And Environmental Concerns

CODEE Journal

Special issue of the CODEE Journal in honor of its founder, Professor Robert Borrelli.

Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.

What The Wasp Said, Hugh C. Culik

Journal of Humanistic Mathematics

On a bright spring day, the ancient building housing the English and Logic Departments begins to slowly collapse on itself, trapping McMann (an inept English professor) and Lucy Curt (a logician) in the office they share. As the Fibonacci repetitions of the building’s brickwork slowly peel away, McMann seizes the moment to tell Lucy stories about skunks, stories whose recurrent pattern finally leads to the unrecognized connection between a “message” burned into his ear by a wasp and the orderly universe for which he cannot find a language. At last, he looks up only to see Lucy descending a ladder, …

An 1883 Faery Tale, Scott W. Williams

Journal of Humanistic Mathematics

A poem about the construction of Georg Cantor's famous set.

Irrational Infinity, Ricky Chen

Journal of Humanistic Mathematics

A short whimsical poem on the cardinality of irrational numbers.

Cosmology, Craig W. Steele

Journal of Humanistic Mathematics

No abstract provided.

A Mathematician's Travel Memories, Michael Holcomb

Journal of Humanistic Mathematics

No abstract provided.

Geometry Of Night, Jenny Patton

Journal of Humanistic Mathematics

No abstract provided.

Ecstatic Syllabi: Four Poems, Mary Peelen

Journal of Humanistic Mathematics

Four poems with mathematical themes. Poems are entitled: Algebra I, Algebra II, Plane Geometry, Number Theory.

A Selection Of Poems From Ode To Numbers, Sarah Glaz

Journal of Humanistic Mathematics

My first poetry collection, Ode to Numbers, was published by Antrim House in September 2017 (http://www.antrimhousebooks.com/glaz.html). The book contains poems written over a quarter of a century and inspired by mathematics and my life as a mathematician. The poems in this folder are a small selection from the book—a series of seven poems focusing on events from the history of mathematics.

Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye

Journal of Humanistic Mathematics

This review explores the issues surrounding mathematics poetry and its role in challenging stereotypes about mathematics and mathematicians. In Ode to Numbers Sarah Glaz takes us from her childhood in Romania to her work as a professor at the University of Connecticut in the USA, with the constant thread of her love of mathematics. It is an intense emotional journey through time and place, arriving at mature reflection. The reader will encounter a wide range of poetic forms; some traditional, others inspired by mathematics. Glaz writes with originality, courage, insight, and generosity and this collection secures her reputation as an …

Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn

Journal of Humanistic Mathematics

Many colleges and universities offer a course in the history of mathematics. While the potential benefits for students taking such a course might be apparent, it is often less clear how teaching a history of mathematics course can be a transformational experience for faculty. We present a dialogue between the authors regarding their experiences teaching history of mathematics courses, including their motivation for doing so, the impact these experiences have had on their classroom practices and assessment methods, and the opportunities history of mathematics courses offer for incorporating social justice, equity, and inclusion into the study of mathematics. Our goal …

Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren

Journal of Humanistic Mathematics

The logos or rational language of the fifth-century BCE teacher, Gorgias, as contained in the fragment On the Nonexistent, challenges a reader to understand the relationship between the existent and the nonexistent; yet the text also offers an accessible idea of logos. Inspired by William M. Priestley's approach to the study of logos through ratios, and by Ivor Grattan-Guinness's recommendation to broaden the study of historical texts in the history of mathematics and mathematics education, and pursue their significance in a heritage sense, this article suggests that this ancient non-mathematics text by Gorgias may inspire and refresh elementary mathematics educators' …

On Mathematical Conjectures And Counterexamples, Ali Barahmand

Journal of Humanistic Mathematics

This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of number-theoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of long-term attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor.