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Full-Text Articles in Physical Sciences and Mathematics

Hockey Card Statistics Are Stagnant And Stale, Egan J. Chernoff Jan 2024

Hockey Card Statistics Are Stagnant And Stale, Egan J. Chernoff

Journal of Humanistic Mathematics

The purchase of a coffee at a Canadian institution, Tim Hortons, turned into an informal investigation into hockey card statistics. Turns out, hockey card statistics are stagnant and stale. This was disappointing to see because the game of hockey has changed, the statistics used to keep track of the game have changed. Even the cards have changed. Well, not the back of the cards, which do not well enough paint a statistical picture of the hockey player photographed on the front of the card.


The Limits Of Data Science, David E. Drew Jan 2024

The Limits Of Data Science, David E. Drew

Journal of Humanistic Mathematics

Data science can contribute valuable predictions in diverse fields. But I write to express some concerns and red flags. I suggest that data science is being oversold. This article contains three questions that I believe data science must address as this new discipline matures. Is data science significantly different from statistics? This is a question that has haunted the field since the term first was introduced. By creating algorithms based on current societal decision rules that may be biased, even bigoted, does data science lock in and exacerbate inequality? Scholars have identified a continuum from data to information to knowledge …


Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau Jan 2024

Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau

Journal of Humanistic Mathematics

The age-old challenge of polygon quadrature involves converting a polygon into a square of equal area. In this educational resource, we utilize pattern blocks, commonly employed instructional aids in K-12 education across the United States, to visually demonstrate the transformation of different equilateral and regular pattern block polygons into squares. This is achieved through the application of the area conservation principle and geometric congruence/similarity reasoning.


Reflections On Teaching Mathematics In Prisons, Matthew Junge Jan 2024

Reflections On Teaching Mathematics In Prisons, Matthew Junge

Journal of Humanistic Mathematics

I started teaching math in prison ten years ago during my PhD studies. Since then, I have taught for three different college-in-prison programs across the country. The goal of this piece is to communicate my experiences with the hopes of encouraging more mathematicians to get involved.


Benefits Of Risk-Taking In Teaching Mathematics, Mehmet Kirmizi, Abigail Quansah, Zafer Buber Jan 2024

Benefits Of Risk-Taking In Teaching Mathematics, Mehmet Kirmizi, Abigail Quansah, Zafer Buber

Journal of Humanistic Mathematics

In this paper, we, a group of graduate students in mathematics education, discuss some of the metacognitive benefits of the non-traditional teaching methods we observed employed by one of our professors. This professor’s methods challenge the common belief that well-managed class time is key for positive learning outcomes. Instead, he orients his teaching to share the exploration and sense-making phases of doing mathematics. The goal of his teaching is to share the idea that learning mathematics is a process of “refining our mathematical thinking”. We argue that this approach to teaching helps students see that mathematics is a human endeavor, …


The Frankensteinian Nature Of Mathematics, Ali Barahmand Jan 2024

The Frankensteinian Nature Of Mathematics, Ali Barahmand

Journal of Humanistic Mathematics

Frankenstein is a story about a scientist who creates a sapient creature that gets out of control and horrifies its creator by its unexpected behavior. In this note, we show that this type of undesirable behavior can reflect a part of the nature of mathematics, and that its origin is related to the ontological question of whether mathematics is invented or discovered. Based on a review of the relationship be- tween discovery and invention, we demonstrate that mathematics has similarities and differences with both discovery and invention. In the natural sciences, new instruments have to be invented to discover new …


Does Chatgpt Know Calculus?, Kris H. Green Jan 2024

Does Chatgpt Know Calculus?, Kris H. Green

Journal of Humanistic Mathematics

Academics and educators across the world are grappling with how OpenAI’s new software, ChatGPT, will impact teaching and learning. This essay explores ChatGPT’s response to a typical calculus problem as a way of illustrating its functionality and limitations.


Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett Jan 2024

Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.


Logical Or Epistemological? A Study On Kepler’S 3m Cosmological Model, Po-Hung Liu Jan 2024

Logical Or Epistemological? A Study On Kepler’S 3m Cosmological Model, Po-Hung Liu

Journal of Humanistic Mathematics

Kepler published Mysterium Cosmographicum in 1597 constructing his cosmo- logical model based on the five regular polyhedra. Such a creative but weird idea was almost consistent with empirical evidence. Furthermore, following the Pythagorean belief about the connection between music and astronomy, Kepler delved into looking for what things having to do with the planetary movements have the harmonic consonances. This article claims that Kepler’s model is a 3M (mathematical, musical, and metaphysical) model and demonstrates how it had been constructed. Furthermore, I explore the reasons behind Kepler’s departure from the 3M model and his subsequent consideration of a non-circular orbit, …


On Parallels Between Words And Music, Will Turner Jan 2024

On Parallels Between Words And Music, Will Turner

Journal of Humanistic Mathematics

A generalised song is a means of drawing parallels between words and music. The parallels are encoded in a mathematical structure, which is interpreted in a verbal structure and a musical structure. Here we develop a number of new techniques for drawing such parallels, in giving two examples of generalised songs, `Relation', and `Merge/Split'.

The first five partials of a note played on a piano are roughly 0,12,19,24,28 semitones above the fundamental.`Relation' is a generalised song, whose musical part is played on a piano, constructed from the mathematical relation 4.28 = 3.12 + 4.19.

`Merge/Split' is a generalised song whose …


Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett Jan 2024

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett

Journal of Humanistic Mathematics

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …


Aesthetic Approaches To Symmetric Functions, John M. Campbell Jan 2024

Aesthetic Approaches To Symmetric Functions, John M. Campbell

Journal of Humanistic Mathematics

Symmetry is often regarded as an integral aspect about aesthetics. This motivates the pursuit of interdisciplinary studies based on the use of subjects in mathematics concerned with symmetry in conjunction with aesthetics. What is referred to as a symmetric function in the field of algebraic combinatorics is an abstraction based on polynomials that exhibit a symmetric property, and this leads us to pursue an algebraic combinatorics-inspired exploration based on aesthetics. In particular, we use different bases and transitions between them to create aesthetically pleasing visualizations of symmetric functions. We see that these visualizations in turn raise new and interesting questions.


Mathematicians Going East, Pasha Zusmanovich Jan 2024

Mathematicians Going East, Pasha Zusmanovich

Journal of Humanistic Mathematics

I survey emigration of mathematicians from Europe, before and during WWII, to Russia. The emigration started at the end of 1920s, the time of “Great Break”, and accelerated in 1930s, after the introduction in Germany of the “non-Aryan laws”. Not everyone who wanted to emigrate managed to do so, and most of those who did spent a relatively short time in Russia, being murdered or deported, or fleeing the Russian regime. After 1937, the year of “Great Purge”, only a handful of emigrant mathematicians remained, and even fewer managed to leave a trace in the scientific milieu of their new …


Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter Jan 2024

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demonstrate that different solutions—hiding one biscuit, arbitrarily sharing the extra …


The Automathography: A Humanistic Autobiographical Writing Assignment For Mathematics Courses, Colton Sawyer, Ron Buckmire Jan 2024

The Automathography: A Humanistic Autobiographical Writing Assignment For Mathematics Courses, Colton Sawyer, Ron Buckmire

Journal of Humanistic Mathematics

In this article, we discuss an autobiographical writing assignment that we call an “automathography” which can be used in different types of mathematics and mathematics education courses, and by extension, in other disciplines as well. This assignment can enhance student-instructor interactions, develop student communication skills, and provide outlets for student creativity by leveraging the lived experiences of students. We have deployed the assignment in different kinds of classes (general education [service] courses and major-only seminars) at different kinds of institutions (a private, open-admission, large university on the East Coast and a private, highly selective, small liberal arts college on the …


Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes Jan 2024

Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …


Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire Jan 2024

Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …


Our Histories, Our Values, Our Mathematics, Mark Huber, Gizem Karaali Jan 2024

Our Histories, Our Values, Our Mathematics, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.


Front Matter Jan 2024

Front Matter

Journal of Humanistic Mathematics

No abstract provided.


Life Beyond The Horizon: The Universe Was Born In A Black Hole, Zahria Patrick Jan 2024

Life Beyond The Horizon: The Universe Was Born In A Black Hole, Zahria Patrick

Undergraduate Research Symposium

It is a widely accepted fact that obtaining information about a black hole is a near-impossible task without being stretched like a spaghetti noodle and trapped in one due to its strong gravitational pull. If the universe exists in a black hole, however, it will mean that it could be possible to survive after crossing its inescapable borders. As surprising as all of this may seem, this theory has existed for quite a while amongst a few different physicists. One person that has shed light on and expanded people’s knowledge of this frightening theory is theoretical physicist, Nikodem Poplawski. The …


The Effect Of Variation Of N-Substituents On Oxidopyridinium Ions In (4+3) Cycloadditions, Zahria Patrick, Madison Clark Jan 2024

The Effect Of Variation Of N-Substituents On Oxidopyridinium Ions In (4+3) Cycloadditions, Zahria Patrick, Madison Clark

Undergraduate Research Symposium

The aim of this research project is to expand the scope of 4 + 3 cycloadduct chemistry by varying functional groups attached to the prerequisite oxidopyridinium ion for each respective cycloadduct product. While N-substitution of the pyridinium precursor is known to proceed smoothly if alkylated by a lone methyl group, we evaluated the effect a larger alkyl group would have on the overall yield of the 4 + 3 cycloadduct product.

Isobutyl triflate, generated from the known reaction between isobutyl alcohol and triflic anhydride, was reacted with ethyl 5-hydroxy-nicotinate to generate the respective N-isobutyl oxidopyridinium ion in quantitative …


Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich Jan 2024

Total Variation Flow In R^N Dimensions With Examples Relating To Perimeters Of Level Sets, Luis Schneegans, Victoria Shumakovich

Undergraduate Research Symposium

In this project, we explore radial solutions to the Total Variation Flow (TVF) equation with the help of the Sign Fast Diffusion Equation (SFDE) and prior results in the 1-dimensional case. Specifically for radial solutions, we derive equations and explicit solutions relating to the n-dimensional case. Lastly, we look at how level sets and (time) profiles change.


The Roaring Lion Of Berlin: The Life, Thought, And Influence Of Eugen Dühring, Arden Roy Jan 2024

The Roaring Lion Of Berlin: The Life, Thought, And Influence Of Eugen Dühring, Arden Roy

Undergraduate Research Symposium

The life and influence of 19th-century German polymath Eugen Dühring remain but a mere footnote in the history of ideas, being primarily relegated to the status of little more than a theoretical rival to Marxism in the German socialist movement and the occasional object of Freidrich Nietzsche's rhetorical flogging. Despite the current consensus on the subject, Eugen Dühring was a scholar of vast, remarkable learnedness, contributing greatly to philosophy, economics, and the natural sciences. The aim of this talk will be to clear the fog surrounding the life and work of the controversial blind scholar and give an account of …


Etherification Of Propargylic Alcohol Using Ferrocenium Ions, Cody Amann, Sai Anvesh Bezawada, Eike B. Bauer Jan 2024

Etherification Of Propargylic Alcohol Using Ferrocenium Ions, Cody Amann, Sai Anvesh Bezawada, Eike B. Bauer

Undergraduate Research Symposium

Etherification of Propargylic Alcohol using Ferrocenium Ions

Cody Amann, Sai Anvesh Bezawada and Eike B. Bauer*

Department of Chemistry and Biochemistry, University of Missouri-St.Louis, MO 63121

Our research efforts are directed toward the improvement of iron-based catalyst systems. The Bauer research group recently found that the ferrocenium cation is a catalytically active in the etherification of propargylic alcohols. My research was to compare the effect of two different counteranions of the ferrocenium cation on the catalytic activity. Etherification test reactions were performed using 2-methyl-2-phenol-propargylic alcohol and n-butanol to afford the corresponding propargylic ether substitution products. The complexes used …


Determination Of Antibody Affinity For The Alzheimer’S Amyloid-Β Protein, Bree Carlton Jan 2024

Determination Of Antibody Affinity For The Alzheimer’S Amyloid-Β Protein, Bree Carlton

Undergraduate Research Symposium

Alzheimer's Disease (AD) is a common form of dementia that is characterized by inflammation, loss of brain mass, and loss of motor function and memory. One of the pathological hallmarks of AD is the accumulation of Amyloid-β (Aβ) in the brain as senile plaques. Aβ is formed from a large protein called Amyloid Precursor Protein (APP) when specific enzymes cut a segment of the protein into a shorter polypeptide chain, Aβ. Different aggregation species were used in this project, specifically monomers and protofibrils. Monomers are naturally occurring and nontoxic, while protofibrils are neurotoxic and neuroinflammatory. One way that Aβ can …


On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t Jan 2024

On The Qualitative Analysis Of Nonlinear Q-Fractional Delay Descriptor Systems, Abdullah Yi̇ği̇t

Turkish Journal of Mathematics

In this manuscript, we obtain some sufficient conditions for a nonlinear q fractional integro singular system with constant delays to be asymptotically admissible and a nonlinear q fractional non-singular system to be asymptotically stable. We use Lyapunov-Krasovskii functionals and some inequalities to obtain these conditions. At the same time, we present some numerical examples that confirm the sufficient conditions we obtained theoretically, with their annotated solutions and graphs.


Quantifying The Relative Importance Of Boat Wakes In Fetch-Limited Environments, Abigail Maria Carswell Jan 2024

Quantifying The Relative Importance Of Boat Wakes In Fetch-Limited Environments, Abigail Maria Carswell

Electronic Theses and Dissertations

Wind waves and wave-generated currents are known to contribute to shoreline change, but there is increasing evidence that vessel-generated waves (i.e., boat wakes) may be responsible for erosion of shorelines in fetch-limited environments. Depending on vessel type and speed of operation, boat wakes have also been shown to be capable of resuspending sediment, degrading habitat, and water quality, and causing damage to shoreline infrastructure. The number of cottages and recreational boats on inland lakes has been steadily increasing in recent decades in Ontario, Canada, which has resulted in a growing perception that boat wakes are detrimental to the environment, infrastructure, …


Rewilding Our Story: Using Storytelling To Combat Climate Change, Calli Lambard Jan 2024

Rewilding Our Story: Using Storytelling To Combat Climate Change, Calli Lambard

Sustainability Research & Practice Seminar Presentations

Calli Lambard, WCU Office of Sustainability, Rewilding Our Story: Using Storytelling to Combat Climate Change


Bmfou Pilot Project Rfc - Request For Change, Nikia Greene, Daryl Reed Jan 2024

Bmfou Pilot Project Rfc - Request For Change, Nikia Greene, Daryl Reed

Silver Bow Creek/Butte Area Superfund Site

No abstract provided.


Some Estimates On The Spin−Submanifolds, Serhan Eker Jan 2024

Some Estimates On The Spin−Submanifolds, Serhan Eker

Turkish Journal of Mathematics

In this paper, an optimal lower bound is given for the Submanifold Dirac operator in terms of the trace of an Energy−Momentum tensor, scalar curvature and mean curvature. In the equality case, it is proven that the submanifold is Einstein if the normal bundle is flat. Key words: Spin geometry, eigenvalues,