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Claremont Colleges

2022

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Articles 1 - 30 of 121

Full-Text Articles in Physical Sciences and Mathematics

The Eu's Capacity To Lead The Transatlantic Alliance In Ai Regulation, Varun Roy, Vignesh Sreedhar Oct 2022

The Eu's Capacity To Lead The Transatlantic Alliance In Ai Regulation, Varun Roy, Vignesh Sreedhar

Claremont-UC Undergraduate Research Conference on the European Union

In the face of Chinese advances in AI in terms of technological prowess and influence, there has been a call for collaboration between the EU and the US to create a foundation for AI governance based on shared democratic beliefs. This paper maps out the EU, US, and Chinese approaches to AI development and regulation as we analyze the capacity of the US and EU to establish international standards for AI regulation through channels such as the TTC. As the EU rolled out a proportionate and risk-based approach to ensure stricter regulation for high-risk AI technologies, it laid the foundation …

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A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook Sep 2022

A Generalized Method Of Undetermined Coefficients, James S. Cook, William J. Cook

CODEE Journal

The method of undetermined coefficients is used to solve constant coefficient nonhomogeneous differential equations whose forcing function is itself the solution of a homogeneous constant coefficient differential equation. In this paper, we show that the classical methods for tackling constant coefficient equations, including the method of undetermined coefficients, generalize to much wider class linear differential equations which, for example, include Cauchy-Euler type equations. This general method includes an explicit construction of the fundamental solution sets of such equations. We also briefly consider where this method can be applied by producing the most general second and third order differential equations that …

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Mathematical Constants Beyond The Half-Circle: An Open Call For Poetry, Mark Huber, Gizem Karaali Jul 2022

Mathematical Constants Beyond The Half-Circle: An Open Call For Poetry, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of mathematical poetry for an upcoming poetry folder tentatively titled Mathematical Constants Beyond the Half-Circle. Please send your submissions via email to the editors by November 1, 2022. Publication decisions will be made by December 31, 2022. The folder is expected to appear in January 2023.

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Squate, Tom Blackford Jul 2022

Squate, Tom Blackford

Journal of Humanistic Mathematics

This is the story of a middle school student who befriends an irrational number, the square root of eight.

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A Topologist’S Broken Heart, Josh Hiller Jul 2022

A Topologist’S Broken Heart, Josh Hiller

Journal of Humanistic Mathematics

A poem about a topologist's broken heart.

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Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat Jul 2022

Perturbation - For Nature Computes On A Straight Line (In Seven Balancing Acts), Vijay Fafat

Journal of Humanistic Mathematics

What if all of our Reality is a simulation? What, perhaps, are the unintended artifacts if we are an "approximate" simulation because God could not muster sufficient computational power for the Equations capturing the ultimate Theory of Everything? Are life and Sentience something She intended, a problem with the simulation's code, or an irreducible, teleological inevitability in Creation?

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Spurious Correlation Sestina, Jules Nyquist Jul 2022

Spurious Correlation Sestina, Jules Nyquist

Journal of Humanistic Mathematics

This is a sestina poem about Spurious Correlations with a magical realism angle for beginning students learning statistics for the first time during the COVID pandemic.

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Doughnut At The End Of Space, Deborah Coy Jul 2022

Doughnut At The End Of Space, Deborah Coy

Journal of Humanistic Mathematics

No abstract provided.

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Scientists Confirm Euler's Identity Is Math's Most Beautiful Expression, John F. Donoghue Jul 2022

Scientists Confirm Euler's Identity Is Math's Most Beautiful Expression, John F. Donoghue

Journal of Humanistic Mathematics

The poem is an exploration of the natures of mathematical and artistic beauty.

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Ode To Delta, Evandro Il Cinico Jul 2022

Ode To Delta, Evandro Il Cinico

Journal of Humanistic Mathematics

No abstract provided.

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Circular Meditations, Kevin Farey Jul 2022

Circular Meditations, Kevin Farey

Journal of Humanistic Mathematics

Circular Meditations is a sequence of seventeen interconnected poems pertaining to mathematics, science, history, politics, religion, and spirituality.

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Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos Jul 2022

Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos

Journal of Humanistic Mathematics

We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …

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Ramanujan Cab Numbers: A Recreational Mathematics Activity, Soumya Banerjee Jul 2022

Ramanujan Cab Numbers: A Recreational Mathematics Activity, Soumya Banerjee

Journal of Humanistic Mathematics

In this paper, I introduce teaching activities about Ramanujan’s cab numbers and related software that can inspire people and help them enjoy these beautiful mathematical creations.

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Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova Jul 2022

Academic Hats And Ice Cream: Two Optimization Problems, Valery F. Ochkov, Yulia V. Chudova

Journal of Humanistic Mathematics

This article describes the use of computer software to optimize the design of an academic hat and an ice cream cone!

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Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram Jul 2022

Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram

Journal of Humanistic Mathematics

Soma cubes are an example of a dissection puzzle, where an object is broken down into pieces, which must then be reassembled to form either the original shape or some new design. In this paper, we present some interesting discoveries regarding the Soma Cube. Equivalence classes form aesthetically pleasing shapes in the solution set of the puzzle. These gems are identified by subgraph isomorphisms using SNAP!/Edgy, a simple block-based computer programming language. Our preliminary findings offer several opportunities for researchers from middle school to undergraduate to utilize graphs, group theory, topology, and computer science to discover connections between computation and …

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Creative Writing That Combines Mathematics And Literature, Hsueh-Chen Lee Jul 2022

Creative Writing That Combines Mathematics And Literature, Hsueh-Chen Lee

Journal of Humanistic Mathematics

In early 2015, the Mathematics-Literature Creativity Award was offered through competition for technological and vocational college students in Taiwan. This paper focuses on the two winning works, the poem Parabola and the flash-fiction, Love Letters of a Science Student, by analyzing the mathematical notions involved and their uses to enhance literary expression. The introduction surveys briefly the various ways of combining mathematics and literature in a piece of creative writing that enriches and supports communication in both disciplines.

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Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark Jul 2022

Calculus Iii: Under The Influence Of Peer Instruction, Alan Von Herrmann, L. Jeneva Clark

Journal of Humanistic Mathematics

In peer Instruction, students engage with core course concepts and then explain those concepts to one another in small groups. Unlike in lecture format, peer instruction involves every student in the class. In Spring 2019, the first authot began using a modified version of peer instruction in Calculus III classes. He started each class by discussing important Calculus III concepts from three standpoints (the formula, the geometry behind the formula, and the physics behind the formula). During the last 20 minutes of each 50-minute class session, he polled the students using questions in the “Goldilocks Zone” – not too hard …

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The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells Jul 2022

The Fractal Geometry Of Mathematics Classrooms: Navigating Classroom Environments In Factory-Model Schools, Cacey L. Wells

Journal of Humanistic Mathematics

Mathematics education has a diverse and complex history. After decades of national reform, mathematics classrooms today are still in desperate need of change. This article examines the current state of factory-model schooling through the lens of Mandelbrot's The Fractal Geometry of Nature in order to rethink pedagogic practices.

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Irruption Of The New: Truth, Events, History, Parallels, Fidelity, David L. Neel Jul 2022

Irruption Of The New: Truth, Events, History, Parallels, Fidelity, David L. Neel

Journal of Humanistic Mathematics

A historical meditation on non-Euclidean geometry, three Jesuits, a radical egalitarian mathematical philosopher, and the atom bomb, structured by word-count with attention to divisors of 441 and the Fano plane.

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In Mathematics, As In Art, Andrew Granville Jul 2022

In Mathematics, As In Art, Andrew Granville

Journal of Humanistic Mathematics

The artist’s vision helps decide what should be created; the mathematician’s insight what can be created. Yet most people view art as merely decoration, or a reflection of existing reality, while they think of mathematics as just a tool for accurate scientific description. Can more people learn to value and enjoy both art and mathematics? And spend a lifetime exploring them and appreciating them for their own sakes?

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The Aleph Of Borges And The Paradise Of Cantor, Raffaella Mulas Jul 2022

The Aleph Of Borges And The Paradise Of Cantor, Raffaella Mulas

Journal of Humanistic Mathematics

The mathematician Georg Cantor, the writer Jorge Luis Borges, and the protagonist of Borges' short story The Aleph, Carlos Argentino Daneri, are seen here as three pieces of a single puzzle. We put these pieces together and we look at the surprising figure that we obtain.

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Mathematical Counterpoint: A Short Essay On The Point, Ruža Jeličić Jul 2022

Mathematical Counterpoint: A Short Essay On The Point, Ruža Jeličić

Journal of Humanistic Mathematics

The dot is the simplest graphic symbol, and in the most diverse areas of human thought it signifies the original principle. At the point as a symbol lies the basis of antinomy in the corresponding areas; as the beginning of everything, the point is and is not. The dot represents emptiness, but also fullness. It is imagined on the border of being and non-being, either as a place of transition from what we consider reality in everyday life -- to its negation, or, on the contrary, as a transition from otherworldly reality to nothingness here. In any case, the point …

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Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman Jul 2022

Higher Meanings: A Speaker Series Connecting Mathematics And Religion, Lawrence M. Lesser, Patricia S. Barrientos, Ben Zeidman

Journal of Humanistic Mathematics

An innovative grant-funded general adult audiences international speaker series on connections between mathematics and religion yielded six 2021 (now archived) presentations. We share reflections and lessons learned, informed by two sets of surveys.

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Conic Diagrams, David Pierce Jul 2022

Conic Diagrams, David Pierce

Journal of Humanistic Mathematics

Textbooks may say that the so-called conic sections can be obtained from cones, but this is rarely proved. However, diagrams of the proof require no intuition for solids and can be read as flat. We construct the diagrams with ruler and compass and derive from them basic properties of conic sections as established by Apollonius of Perga, though again in a way that does not require a third dimension. The construction inevitably involves choices that give play to one’s aesthetic sense.

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Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae Jul 2022

Navigating Mathematics Teacher Preparation During A Time Of Crisis, Zareen G. Rahman, Rani Satyam, Younggon Bae

Journal of Humanistic Mathematics

In this paper we highlight the experience of a mathematics teacher educator (MTE) and their prospective teachers (PTs) in a middle school mathematics methods course during the 2020 shift to online instruction due to the COVID-19 pandemic. We believe it is valuable to report how the MTE reflected on their instructional decision-making in response to this massive transition to remote instruction. We also report that PTs needed support and guidance to employ new teaching practices they had learned in the methods course instead of reverting to familiar teaching methods.

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What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher Jul 2022

What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher

Journal of Humanistic Mathematics

We describe students’ learning practices in an online asynchronous PreCalculus course during Fall 2020, the first complete semester of distance learning induced by the COVID-19 pandemic. Results were compiled using a thematic analysis of a questionnaire administered to 43 students enrolled in PreCalculus at a university in the Midwest (United States). Students were given opportunities for active learning and various synchronous Q&A sessions, yet they primarily learned through watching videos and reading worked examples, minimizing interactions with the instructor and available tutors. The questionnaire results show that students knew active learning was helpful, but they were unable to curtail unproductive …

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Social Justice And Exponential Functions: Using Pandemic Data To Increase Student Understanding, Jane Friedman Jul 2022

Social Justice And Exponential Functions: Using Pandemic Data To Increase Student Understanding, Jane Friedman

Journal of Humanistic Mathematics

This paper describes a class activity based on real data about COVID-19 death rates in California. The activity helps students learn about exponential functions while providing an opportunity to integrate social justice concerns into the mathematics classroom.

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Beyond Ethics: Considerations For Centering Equity-Minded Data Science, Nathan Alexander, Carrie Diaz Eaton, Anelise H. Shrout, Belin Tsinnajinnie, Krystal Tsosie Jul 2022

Beyond Ethics: Considerations For Centering Equity-Minded Data Science, Nathan Alexander, Carrie Diaz Eaton, Anelise H. Shrout, Belin Tsinnajinnie, Krystal Tsosie

Journal of Humanistic Mathematics

In this paper, we utilize duoethnography - a research method in which practitioners discursively interrogate the relationships between culture, context, and the mechanisms which shape individual autobiographical experiences - to explore what may be beyond ethics in the context of data science. Although ethical frameworks have the ability to reflect cultural priorities, a singular view of ethics, as we explore, often fails to speak to the multiple and diverse priorities held both within and across institutional spaces. To that end, this paper explores multiple perspectives, epistemologies, and worldviews that can collectively push researchers towards considerations of a data science education …

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Stewardship Of Mathematics: Essential Training For Contributors To, And Users Of, The Practice Of Mathematics, Rochelle E. Tractenberg Jul 2022

Stewardship Of Mathematics: Essential Training For Contributors To, And Users Of, The Practice Of Mathematics, Rochelle E. Tractenberg

Journal of Humanistic Mathematics

A steward of the discipline was originally defined as an individual to whom “we can entrust the vigor, quality, and integrity of the field”, and more specifically, as “someone who will creatively generate new knowledge, critically conserve valuable and useful ideas, and responsibly transform those understandings through writing, teaching, and application” [8]. Originally articulated for doctoral education, in 2019 the construct of stewardship was expanded so that it can also be applied to non-academic practitioners in any field, and can be initiated earlier than doctoral education [18]. In this paper, we apply this construct to the context of mathematics, and …

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A Mini-Seminar: Teaching Ethics In Mathematics In An Hour A Week, Allison N. Miller Jul 2022

A Mini-Seminar: Teaching Ethics In Mathematics In An Hour A Week, Allison N. Miller

Journal of Humanistic Mathematics

This article describes a one-credit class on ethics in mathematics, which met once a week for an hour and discussed topics in cryptography, algorithms and big data, and the role of mathematics in public life. I offer anecdotal evidence that even a course with relatively little time commitment for both students and faculty can have a significant impact on students' understanding of and interest in ethics in mathematics. I also collect recommendations and resources in the hopes of encouraging others to consider teaching such a course.

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