Physical Sciences and Mathematics Commons^™

One Theorem, Two Ways: A Case Study In Geometric Techniques, John B. Little

Journal of Humanistic Mathematics

If the three sides of a triangle ABΓ in the Euclidean plane are cut by points H on AB, Θ on BΓ, and K on ΓA cutting those sides in same ratios:

AH : HB = BΘ : ΘΓ = ΓK : KA,

then Pappus of Alexandria proved that the triangles ABΓ and HΘK have the same centroid (center of mass). We present two proofs of this result: an English translation of Pappus's original synthetic proof and a modern algebraic proof making use of Cartesian coordinates and vector concepts. Comparing the two methods, we can see that while the algebraic …

Ekstasen: Love Poetry By Felix Hausdorff, Kimberly Gladman

Journal of Humanistic Mathematics

Four poems by the mathematician Felix Hausdorff are presented in English translation, together with their German originals and commentary about Hausdorff’s multidisciplinary achievements.

Teaching Mathematics With Poetry: Some Activities, Alexis E. Langellier

Journal of Humanistic Mathematics

During the summer of 2021, I experimented with a new way of getting children excited about mathematics: math poetry. Math can be a trigger word for some children and many adults. I wanted to find a way to make learning math fun—without the students knowing they’re doing math. In this paper I describe some activities I used with students ranging from grades K-12 to the college level and share several poem examples, from students in grades two to eight.

Could Raphael’S School Of Athens Contain Hidden Geometry?, Frode S. Larsen, Harald E. Moe

Journal of Humanistic Mathematics

In this article we argue that Raphael has hidden a geometric shape called a vesica piscis in his fresco The School of Athens (1510-1511). The vesica piscis, and several findings which can be interpreted as suggesting the presence of a vesica piscis in the fresco, are presented. Several of these suggestions relate to the vesica piscis drawn in the construction of an equilateral triangle in the first proposition of Euclid’s Elements. Based on findings in the fresco, we suggest that the vesica piscis should be interpreted in light of a philosophical and theological controversy which took place in Italy …

The Long Search For Collatz Counterexamples, Oliver K. Clay

Journal of Humanistic Mathematics

Despite decades of effort, the Collatz conjecture remains neither proved, nor refuted by a counterexample, nor formally shown to be undecidable. This note introduces the Collatz problem and probes its logical depth with a test question: can the search space for counterexamples be iteratively reduced, and when would it help?

Exploring Set-Theoretic Practices Of Youth Engagement In Connective Journalism: What We Lose In School-Mathematical Descriptions, Alexandra R. Aguilar, Emma C. Gargroetzi, Lynne M. Zummo, Emma P. Bene

Journal of Humanistic Mathematics

Analyzing youth video submissions regarding COVID-19 to KQED’s ‘Let’s Talk About the Election’ website, we explore the mathematics these youth engaged in through their submissions without creating any explicit connection to school mathematical concepts or standards. Our focus is the students’ construction of sets (e.g. sets of nurses, doctors, American workers), as a means of creating connection with voters and other media authors through Marchi and Clark’s (2021) construct of connective journalism. We observe these youth constructing sets of varying sizes and reflecting on how these sets are contextualized within a larger political dialogue. We also attempt to rewrite part …

Students’ Mathematical Learning During The Covid-19 Pandemic, Jessica Mean, Shilpa Dasgupta

Journal of Humanistic Mathematics

This paper discusses our new approach to assessing students’ learning. This approach includes the use of a final project rather than a final cumulative exam. We suggest that students taking a deep dive into one particular math concept and being able to make connections between that concept and the real world are educational achievements during this pandemic. We also argue that there is value in online learning because students who learn online choose to use library resources and develop their own interests by attending office hours, all of which benefit their learning.

No Simple Formula: Navigating Tensions In Teaching Postsecondary Social Justice Mathematics, Alexa W. C. Lee-Hassan

Journal of Humanistic Mathematics

Instructors of Social Justice Mathematics (SJM) have shared important insights into the powerful potential of connecting classroom mathematics with authentic data about social justice topics, but they have also warned about the harm such teaching can cause when done poorly. In this article, I consider what is necessary to teach SJM at the postsecondary level. I share research that has supported me in learning to teach SJM and highlight challenges that are particular to doing this work in postsecondary contexts. I then describe my experiences navigating the central tensions of this work while honoring its complexity.

Critical Co-Investigators Of Math Trails: Reflections From A Student And Teacher, Benjamin Dickman, Julia Feinberg

Journal of Humanistic Mathematics

In this article, a K-12 mathematics educator and a recent (2020) high school graduate discuss curricular work related to math trails, which are based around the idea of mathematizing potential discoveries along a physical walk. The intersection of math trails with the realities of schooling amid the COVID pandemic is described, along with ways in which math trail learning has ramified beyond classroom walls. This collaboration serves not only to draw attention to the under-researched topic of math trails, but also to exhibit how students and teachers can, in the language of Freire, work together as critical co-investigators.

Math And Democracy, Kimberly A. Roth, Erika L. Ward

Journal of Humanistic Mathematics

Math and Democracy is a math class containing topics such as voting theory, weighted voting, apportionment, and gerrymandering. It was first designed by Erika Ward for math master’s students, mostly educators, but then adapted separately by both Erika Ward and Kim Roth for a general audience of undergraduates. The course contains materials that can be explored in mathematics classes from those for non-majors through graduate students. As such, it serves students from all majors and allows for discussion of fairness, racial justice, and politics while exploring mathematics that non-major students might not otherwise encounter. This article serves as a guide …

Responsible Data Science For Genocide Prevention, Victor Piercey

Journal of Humanistic Mathematics

The term "genocide" emerged out of an effort to describe mass atrocities committed in the first half of the 20th century. Despite a convention of the United Nations outlawing genocide as a matter of international law, the problem persists. Some organizations (including the United Nations) are developing indicator frameworks and “early-warning” systems that leverage data science to produce risk assessments of countries where conflict is present. These tools raise questions about responsible data use, specifically regarding the data sources and social biases built into algorithms through their training data. This essay seeks to engage mathematicians in discussing these concerns.

#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall

Journal of Humanistic Mathematics

In 2019, \#DisruptJMM, a Twitter hashtag, began circulating after an Inclusion/Exclusion blog by Dr. Piper H pointing to the need to make commonplace conversations about human suffering in the Joint Mathematics Meetings (JMM). While the \#DisruptJMM hashtag has been used since 2019, the vast majority of use was in the JMM 2020 meetings. Twitter hashtags are used by activists to push forward conversations, join communities around a single idea, and create change. In this article, we draw on frameworks from community building seen in other equity and inclusion advocacy hashtags such as \#GirlsLikeUs [7] to qualitatively code and analyze tweets …

On Definitions Of "Mathematician", Ron Buckmire, Carrie Diaz Eaton, Joseph Hibdon, Katherine M. Kinnaird, Drew Lewis, Jessica Libertini, Omayra Ortega, Rachel Roca, Andrés R. Vindas Meléndez

Journal of Humanistic Mathematics

The definition of who is or what makes a “mathematician” is an important issue to be addressed in the mathematics community. Too often, a narrower definition of who is considered a mathematician (and what is considered mathematics) is used to exclude people from the discipline—both explicitly and implicitly. However, using a narrow definition of a mathematician allows us to highlight, examine, and challenge systemic barriers that exist in certain spaces of the community. This paper analyzes and illuminates tensions between narrow and broad definitions and how they can be used to promote both inclusion and exclusion simultaneously. In this article, …

Mathematics And Society: Towards Critical Mathematics Research And Education, Tian An Wong, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez

Journal of Humanistic Mathematics

No abstract provided.

Mathematics And Society, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Special Case Of Partial Fraction Expansion With Laplace Transform Application, Laurie A. Florio, Ryan D. Hanc

CODEE Journal

Partial fraction expansion is often used with the Laplace Transforms to formulate algebraic expressions for which the inverse Laplace Transform can be easily found. This paper demonstrates a special case for which a linear, constant coefficient, second order ordinary differential equation with no damping term and a harmonic function non-homogeneous term leads to a simplified partial fraction expansion due to the decoupling of the partial fraction expansion coefficients of s and the constant coefficients. Recognizing this special form can allow for quicker calculations and automation of the solution to the differential equation form which is commonly used to model physical …

Modeling Immune System Dynamics During Hiv Infection And Treatment With Differential Equations, Nicole Rychagov

CODEE Journal

An inquiry-based project that discusses immune system dynamics during HIV infection using differential equations is presented. The complex interactions between healthy T-cells, latently infected T-cells, actively infected T-cells, and the HIV virus are modeled using four nonlinear differential equations. The model is adapted to simulate long term HIV dynamics, including the AIDS state, and is used to simulate the long term effects of the traditional antiretroviral therapy (ART). The model is also used to test viral rebound over time of combined application of ART and a new drug that blocks the reactivation of the viral genome in the infected cells …

Regular Solutions To Elliptic Equations, Alfonso Castro, Jon T. Jacobsen

All HMC Faculty Publications and Research

A review of results and techniques on the existence of regular radial solutions to second order elliptic boundary value problems driven by linear and quasilinear operators is presented. Of particular interest are results where the solvability of a given elliptic problem can be analyzed by the relationship between the spectrum of the operator and the behavior of the nonlinearity near infinity and at zero. Energy arguments and Pohozaev type identities are used extensively in that analysis. An appendix with a proof of the contraction mapping principle best suited for using continuous dependence to ordinary differential equations on initial conditions is …

An Undergraduate Consortium For Addressing The Leaky Pipeline To Computing Research, James C. Boerkoel Jr., Mehmet Ergezer

All HMC Faculty Publications and Research

Despite an increasing number of successful interventions designed to broaden participation in computing research, there is still significant attrition among historically marginalized groups in the computing research pipeline. This experience report describes a first-of-its-kind Undergraduate Consortium (UC; https://aaai-uc.github.io/about) that addresses this challenge by empowering students with a culmination of their undergraduate research in a conference setting. The UC, conducted at the AAAI Conference on Artificial Intelligence (AAAI), aims to broaden participation in the AI research community by recruiting students, particularly those from historically marginalized groups, supporting them with mentorship, advising, and networking as an accelerator toward graduate school, AI research, …

Collaboration Between Science And Art Through A Special International Symposium For Ecosystem Health And Sustainability, Changwoo Ahn Dr.

The Transdisciplinary STEAM+ Journal

The collaborations between ecosystem restoration and art practices was epitomized by the eco-artist Jackie Brookner who said: “it is not a matter of the scientists providing the hard-core research and artists the soft outreach; rather, the dynamics engendered in the space between disciplines is full of information necessary to solve complex problems at the systemic level”. This paper reviews and summaries the goals, activities, and lessons learned from a special symposium, which was held at the 12^th INTECOL (International Congress of Ecology) conference in Beijing, China, August 21 through 25, 2017, where about 3000 people attended from 70 countries. …

Students Arts Participation Increases Stem Motivation Via Self-Efficacy, Stephen M. Dahlem

The Transdisciplinary STEAM+ Journal

This work found that there exists a correlation between student motivation in science, technology, engineering and mathematics (STEM) and student participation in the arts during high school with self-efficacy being a mediator. STEM is an important component of student success from a broad, national, perspective, as well as from a domain-specific point of view. The results of this work may provide aid to teachers, parents, administrators, and even students seeking to find ways to increase student motivation and performance in the STEM subjects. Additionally, this work may be of interest to advocates of the arts. This quantitative correlational study was …

Challenge-Based Learning & Steam Curriculum, Diana Lockwood

The Transdisciplinary STEAM+ Journal

STEAM education is being integrated into elementary schools as a way to engage more students in creativity, hands-on learning, and problem-based learning also referred to as Challenge-Based-Learning (CBL). This article focuses on elementary educators’ curriculum design for STEAM and presenting students with open-ended questions phrased as a challenge as a way to raise student interest and achievement (DeJarnette, 2018; Hunter-Doniger, 2018). When students received challenges to solve, they felt more open to sharing their ideas since there was more than one potential right answer (DeJarnette, 2018; Drake, 2012). When implementing CBL, teachers act as facilitators using a constructivist approach as …

Stable Trace Ideals And Applications, Haydee Lindo, Hai Long Dao

All HMC Faculty Publications and Research

We study stable trace ideals in one dimensional local Cohen–Macaulay rings and give numerous applications.

Between Heaven And Earth! A Poem-Collage Pair About Hypatia Of Alexandria, Sarah Glaz, Mark Sanders

Journal of Humanistic Mathematics

The poem-collage pair presented here is a work of collaboration between the mathematician and poet, Sarah Glaz, and the collage and ceramic artist, Mark Sanders. The piece is part of their larger joint poem-collage project involving the history of mathematics. Included as background is a brief discussion on the history and mathematics involved, and a reflection on several landmark locations and some of the relevant imagery appearing in the poem and the collage.

The Babelogic Of Mathematics, Vijay Fafat

Journal of Humanistic Mathematics

How would the Bible written about a Mathematical God start, describing the Creation of Mathematics and Logic? How would Rigveda's "Nasadiya sukta" read if it were describing the Void before mathematics was "born"? Here is an attempt at a partial answer, one which takes the original Genesis chapter and the Nasadiya sukta and makes suitable changes to create a fairly consistent, if somewhat anachronistic narrative (with the slight mixing up of Bertrand Russell and Lobachevsky / Bolyai attributable to "Babelogic"), along with a new ending to the Beginning...

Astor Place Barber, Audrey Nasar

Journal of Humanistic Mathematics

"Astor Place Barber" is a short story about a math professor and a barber. It plays with the logical concept of a paradox via the Barber's Paradox, which, made famous by Bertrand Russell, tells the story of a barber who both shaves himself and does not shave himself.

Locked In Functions: A Short Poem For Robert Langlands, Virgilio A. Rivas

Journal of Humanistic Mathematics

This short poem is inspired by Robert Langlands, recipient of the 2018 Abel Prize. The poem tries to sum up in poetic language, as brief but substantial as it can be, the philosophical and rhetorical connotation of his contributions to mathematics, from automorphic forms to number theory, and the famous Langlands programme, among others. Also partly inspired by Edward Frenkel's tribute to Langlands, the book Love and Mathematics, the poem seeks to capture the philosophical beauty of mathematics that privileges the importance of 'functions' over 'passions', consistent with Langlands' purely mathematical side.

Unsolved Haiku, Scott W. Williams

Journal of Humanistic Mathematics

This poem describes the still unsolved 1937 conjecture of Lloyd Collatz: Do repeated applications of the algorithm described yield the number 1?

Mathematics, Kim Regnier Jongerius

Journal of Humanistic Mathematics

Inspired by the song "Memories" from the musical Cats, this work describes some of the frustrations and joys inherent in mathematical work.