Physical Sciences and Mathematics Commons^™

So Long My Friend, Bryan Mcnair

Journal of Humanistic Mathematics

No abstract provided.

A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto

Journal of Humanistic Mathematics

Too little mathematics has been written in prose. Thus we prove here, via a fantasy novellette, that a locally L-bilipschitz mapping f : X → Y between uniformly Ahlfors q-regular, complete and locally compact path-metric spaces X and Y is an L-bilipschitz map when Y is simply connected. The motivation for such a result arises from studying the asymptotic values of BLD-mappings with an empty branch set.

As far as the author is aware, the result is new, even though it would not be hard for specialists in the field to prove. The proof is essentially a modest extension of …

Heuristic Or Stochastic?, E Laura Golberg

Journal of Humanistic Mathematics

This is a poem about laying odds on the outcome of weddings.

The Solipsist’S First Paper, Sabrina Sixta

Journal of Humanistic Mathematics

The angst of a graduate student who has not yet written a paper, but really wants to.

What's So Great About Non-Orientable Manifolds?, Michael Mccormick

Journal of Humanistic Mathematics

No abstract provided.

Wrong Way, Joseph Chaney

Journal of Humanistic Mathematics

No abstract provided.

Poetry In The Glade: Bridges 2021 Fib Collection

Journal of Humanistic Mathematics

A Fibonacci poem follows the Fibonacci sequence to any length in its count of syllables per line, or words per line, or lines per stanza, or any other countable thing connected with the poem. A Fib is a special case of Fibonacci poem, a poem of 6 lines whose syllable line count follows the first 6 numbers of the Fibonacci sequence: 1; 1; 2; 3; 5; 8. The present collection of Fibs arose out of the Bridges poetry community in response to the Bridges organization’s efforts to make the Bridges 2021 conference more interactive.

An Urgent Plea For More Graduate Programs In Statistics Education, David Eli Drew, Sam Behseta, Cherie L. Ichinose

Journal of Humanistic Mathematics

Lately, much has been written about the importance of amplifying statistics-related content in the K-12 curricula. This can be viewed in parallel or as an addendum to the existing mathematics curricula in the United States. Nevertheless, a key component of this debate is the lack of robust and cutting-edge academic programs in statistics education. In this piece, we emphasize the urgent need for investing in creating strong statistics education programs, which would significantly contribute to nurturing quantitative literacy as well as preparing a more informed citizenry in the 21^st century.

Mathematics For The Masses: Door-To-Door Missionaries Of Math And Twelve-Step Recovery Programs, Daniel S. Helman

Journal of Humanistic Mathematics

Conversion of strangers, or proselytizing, is a feature of a range of groups for religious, organizational and other aims. In twelve-step recovery programs, such as Alcoholics Anonymous, belief in a higher power is a requirement for working the steps to recovery. People are encouraged to find a higher power of their own understanding. This paper presents a model for using mathematics as a higher power, and shows how recovery works with mathematics in that role instead of a more traditional higher power such as God. A contemplative definition of math is given along with a description of a three-categoried epistemology: …

A Reflection On Growth Mindset And Meritocracy, Rachel L. Petrik, Julianne Vega, Andrés R. Vindas-Meléndez

Journal of Humanistic Mathematics

As mathematicians working in higher education we reflect on meritocracy and growth mindset with a focus on the relationship between the two. We also note the subtle differences between growth mindset and grit. Our reflection ends with suggestions for how to move forward in the math classroom and throughout the collegiate level.

Life Of A Working Ramsey Theorist: Conversation With Thomas C. Brown, Kyle Singh, Veselin Jungic, Jun Bo Mei

Journal of Humanistic Mathematics

This interview, conducted in November 2020, explores the fascinating life and work of Ramsey theorist Thomas Craig Brown. We hope, through our conversation with Dr. Brown, to show that mathematics is not a discipline that is only concerned with numbers, but that it is, in a fundamental way, also about people and connections.

Decisions, Decisions: How Should The Votes Be Counted?, Michael J. Caulfield

Journal of Humanistic Mathematics

It is a simple matter for the members of a group to decide among two options. When there are three or more options among which to choose, the situation is much more complicated. This is precisely what faces the electorate each time there are more than two candidates running for a single office. And while there is debate over which voting method should be used, there is wide agreement over the method that should not be used: plurality, the most common approach taken in the United States. This article presents a simple classroom activity which provides students the opportunity to …

A Cognitive View Of "Pandemic Meditation" (A Mathematical Visual Poem), Kazmier Maslanka

Journal of Humanistic Mathematics

Mathematical visual poetry is a poetic genre whereby metaphorical expressions are created using mathematical structures. Within the structure, the poetics are understood by the cross-mapping of numerous conceptual domains including visual, lexical, and mathematical. Here I focus on one particular mathematical visual poetic structure: what I call a Similar Triangles Poem or Proportional Poem. To illustrate the ideas discussed, I present "Pandemic Meditations," a mathematical visual poem; in particular I discuss how this mathematical poem uses the mechanisms of poetic metaphor in the context of the embodied mind. The intent of this paper is not to explain "Pandemic Meditation," …

Twisting The Cube: Art-Inspired Mathematical Explorations, Lingguo Bu

Journal of Humanistic Mathematics

A cube can be twisted in a playful manner for visual and algebraic insights. The twisting process and the resulting ruled surfaces can be demonstrated using 3D modeling tools (e.g., GeoGebra® and Autodesk Fusion 360®) or elastic cords on a 3D-printable scaffold. The twisted cube is aesthetically appealing, posing interesting questions that are worthwhile at multiple levels. Algebraically, the volume of the twisted cube is shown to be two-thirds of the reference cube. The twisted faces are parts of hyperbolic paraboloids, whose implicit and parametric equations can be established from diverse perspectives in support of further dynamic explorations and discussions …

Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala

Journal of Humanistic Mathematics

In 2009, a literature scholar, Melanie Bayley, proposed that Lewis Carroll's famous books about Alice visiting the magical and illogical Wonderland were attempts to mock and critique the modern mathematics of the day. In this short paper, I aim to support Bayley's thesis and expound upon Carroll's artful use of symbolism to attack excessive use of symbolism in mathematics.

Accidental World Teacher, Richard Delaware

Journal of Humanistic Mathematics

When the College Algebra and Calculus I video courses I created were posted on my university’s YouTube channel in 2009, I suddenly began to receive dozens of heartfelt emails from students around the world thanking me. Here I tell the story of the creation of those videos and sample the effect they seem to have had over the last decade, as I accidentally became a teacher available to the entire planet.

The Nature Of Numbers: Real Computing, Bradley J. Lucier

Journal of Humanistic Mathematics

While studying the computable real numbers as a professional mathematician, I came to see the computable reals, and not the real numbers as usually presented in undergraduate real analysis classes, as the natural culmination of my evolving understanding of numbers as a schoolchild. This paper attempts to trace and explain that evolution. The first part recounts the nature of numbers as they were presented to us grade-school children. In particular, the introduction of square roots induced a step change in my understanding of numbers. Another incident gave me insight into the brilliance of Alan Turing in his paper introducing both …

The Problem Of Words: Learning To Teach Mathematics When Numbers And Languages Mix, Gladys Krause

Journal of Humanistic Mathematics

In this piece I propose a perspective shift, from a simplified view of mathematics story problems to a more academically rigorous perspective that integrates mathematical proficiency and language practices crucial for educating bilingual students. The data presented in this article provide a window into what preparing bilingual pre-service teachers to teach mathematics might involve. I discuss issues that arise in the context of preparing Spanish-English bilingual pre-service teachers in a way that can inform their practice in linguistically and culturally diverse classrooms.

An Amends Letter From A Recovering Mean Professor, Feryal Alayont

Journal of Humanistic Mathematics

The following is an amends letter written by a recovering professor enrolled in a twelve-step program for mean professors. The letter is directed to current and past students who have been hurt by the insensitive behavior of the professor in response to the students' mathematical anxiety and other emotional defenses in their learning. As common in twelve-step programs, the purpose of an amends letter is for the recovering person to clearly identify their hurtful actions and the effects on their victims, and to take responsibility for them. By sharing this letter openly, the professor, identified by their twelve-step program name …

Lessons Learned From The Disorder Of Operations, Egan J. Chernoff

Journal of Humanistic Mathematics

The purpose of this article, in general, is to explore certain possible outcomes associated with an underaged gambler attempting to collect his rightful winnings. More specifically, this article is a thought experiment investigating the union of (1) skill testing questions, (2) the equation that recently broke/divided the internet, and (3) how different outcomes render different elements of the thought experiment moot. For example, when the final arbiter has total dominion over a particular outcome, the mathematics of a skill testing question is rendered moot. The article concludes with a discussion revealing how disorder of operations could be considered the teaching …

In Search Of Star Clusters: An Introduction To The K-Means Algorithm, Marcio Nascimento

Journal of Humanistic Mathematics

This article is a gentle introduction to K-means, a mathematical technique of processing data for further classification. We begin with a brief historical introduction, where we find connections with Plato’s Timæus, von Linné’s binomial classification, and the star clustering concept of Mary Sommerville and collaborators. Artificial intelligence algorithms use K-means as a classification methodology to learn about data in a very accurate way, because it is a quantitative procedure based on similarities.

A Note On A Mathematician-Cyclist: Anna Kiesenhofer, Man Keung Siu

Journal of Humanistic Mathematics

This short note offers some reflections on the teaching and learning of mathematics inspired by the news about a feat accomplished by the Austrian mathematician-cyclist Anna Kiesenhofer in the Summer Olympic Games held in Tokyo in 2021.

Extremal Mathematicians, Carlos A. Alfaro

Journal of Humanistic Mathematics

We report on the top ten mathematicians with the highest number of articles, citations, and students, based on data from MathSciNet and the Mathematics Genealogy Project.

Navigating A Calculus Course During A Pandemic: A Usma Perspective, Shane K. Smith, Tyson H. Walsh, Lee Evans

Journal of Humanistic Mathematics

In this article we analyze publications written about different teaching modalities and evaluate how each applies to a calculus class during the on-going COVID-19 pandemic. We focus on the positives and negatives of teaching and learning in a virtual, classroom, or HyFlex environment. Although arguments could be made for each environment, especially given different institutional objectives, this work aims to explain why we eventually preferred teaching our Fall 2020 multivariable calculus course in a face-to-face classroom setting at the United States Military Academy at West Point. We also offer measures of performance to compare the current COVID-19 semester with previous …

On The Mathematics Of Social Distancing, Robert Haas

Journal of Humanistic Mathematics

Early in the COVID-19 pandemic, when spring began to make itself felt, photos showed New Yorkers enjoying the outdoors, while properly socially distanced, by sitting on the grass in a square lattice of circles. But the planners should have consulted a mathematician for the design, because significantly more people (over 15% more) could enjoy the same area safely if the circles were closer packed into a hexagonal lattice.

Covid-19, Vaccines, And Decision Theory, Michael A. Lewis

Journal of Humanistic Mathematics

In this piece, I delve into some thoughts I've had about decision theory. These have been inspired by the vaccine rollout phase of the COVID-19 Pandemic. I focus on decision making under uncertainty, as it relates to the decision to get vaccinated or not.

The Hamster Diaries, Pamela B. Pierce

Journal of Humanistic Mathematics

When the pandemic hits, the author acquires a hamster, who provides some humorous anecdotes and some much-needed inspiration.

Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu

Journal of Humanistic Mathematics

We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through …

Unmotivated, Depressed, Anxious: Impact Of The Covid-19 Emergency Transition To Remote Learning On Undergraduates’ Math Anxiety, Melinda Lanius, Tiffany Frugé Jones, Samantha Kao, Tynan Lazarus, Alex Farrell

Journal of Humanistic Mathematics

In summer 2020, we invited the 6761 undergraduate students who took a Spring 2020 math course at the University of Arizona to participate in a survey, with 13% responding. We asked about their experience with the emergency transition to remote learning and measured their math anxiety before and after the transition using the well-established Abbreviated Math Anxiety Scale(AMAS). “Unmotivated, depressed, anxious” are the words one undergraduate used to describe their emergency transition to remote learning. Our results indicate that limited access to quality technology and inadequate communication with an instructor were the two greatest predictors for an increase in math …

Nilpotents Leave No Trace: A Matrix Mystery For Pandemic Times, Eric L. Grinberg

Journal of Humanistic Mathematics

Reopening a cold case, Inspector Echelon, high-ranking in the Row Operations Center, is searching for a lost linear map, known to be nilpotent. When a partially decomposed matrix is unearthed, he reconstructs its reduced form, finding it singular. But were its origins nilpotent?