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Full-Text Articles in Mathematics

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann Jan 2018

What Makes A Theory Of Infinitesimals Useful? A View By Klein And Fraenkel, Vladimir Kanovei, Karin Katz, Mikhail Katz, Thomas Mormann

Journal of Humanistic Mathematics

Felix Klein and Abraham Fraenkel each formulated a criterion for a theory of infinitesimals to be successful, in terms of the feasibility of implementation of the Mean Value Theorem. We explore the evolution of the idea over the past century, and the role of Abraham Robinson's framework therein.

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Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood Jan 2018

Mathematical Arguments In Favor Of Risk In Andy Weir's The Martian, Sarah C. Cobb, Jeff B. Hood

Journal of Humanistic Mathematics

In Andy Weir’s novel The Martian, the characters encounter high-stakes, life-or-death situations, in which they must make choices based on their assessment of risk and likely outcomes. They have different reactions to risky situations, based on their approaches to assessing risk and their perspectives on the stakes involved. In this paper, we examine the ways that characters in The Martian intuitively assess risk and compare them to mathematical analysis of the situations in the book.

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Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia Jan 2018

Mathematics, Writing, And Rhetoric: Deep Thinking In First-Year Learning Communities, Christine Von Renesse, Jennifer Digrazia

Journal of Humanistic Mathematics

Through the process of combining two seemingly unlikely bedfellows, mathematics and composition, two instructors explain how rhetoric connects the art of writing and the art of doing mathematics in an inquiry-based learning community. Combining these two courses in a learning community enables students and instructors to practice the deep thinking valued by each instructor and by a traditional liberal arts education while challenging both our and our students’ individual, disciplinary, and rhetorical conventions and beliefs. Using student writing from our course, our assignments from mathematics and composition, and survey evaluation results, we demonstrate how engaging in inquiry-based education provides unconventional …

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Ways Of Relating To The Mathematics Of The Past, Michael N. Fried Jan 2018

Ways Of Relating To The Mathematics Of The Past, Michael N. Fried

Journal of Humanistic Mathematics

Historians of mathematics, by definition, look at mathematics of the past. But mathematicians, too, often look at mathematics of the past; mathematicians of the past themselves often looked very closely at mathematics of their own past. Is their relationship to the past the same as that of the historians? Is every view of the past an historical view? Indeed, is every historical view historical in the same way? Or is it possible that there are different kinds of relationships to the mathematics of the past? This paper will suggest that there are in fact a variety of such relationships. It …

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Communicating Mathematics Across Time, Mark Huber, Gizem Karaali Jan 2018

Communicating Mathematics Across Time, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

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Front Matter Jan 2018

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

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Geometric Serendipity, Dakota Becker Jan 2018

Geometric Serendipity, Dakota Becker

AUCTUS: The Journal of Undergraduate Research and Creative Scholarship

The central focus of my practice is the serendipitous exploration into geometry, symmetry, design, and color. I have found more and more that the affinity I have for hard-edge geometric abstraction is a deeper reflection of the way in which I process my thoughts and surroundings. In the past year, I have sought to challenge myself by questioning the core of my practice and pushing it to go beyond its individual elements. In this way, I seek to create work that is more than its parts. As a result, I have become more purposeful with my designs and push both …

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How To Calculate Π: Machin's Inverse Tangents, A Mini-Primary Source Project For Calculus Ii Students, Dominic Klyve Jan 2018

How To Calculate Π: Machin's Inverse Tangents, A Mini-Primary Source Project For Calculus Ii Students, Dominic Klyve

Mathematics Faculty Scholarship

Almost every mathematical culture through history seems to have proved, trusted, or suspected that the area of a circle is a fixed constant times the square of its radius. It is maybe not surprising, then, that the last two millennia have seen a seemingly endless array of attempts to calculate this constant (today usually called π" role="presentation">π) with increasing precision.

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Discovering And Demonstrating Patterns, Maria Klawe Dec 2017

Discovering And Demonstrating Patterns, Maria Klawe

The Transdisciplinary STEAM+ Journal

Harvey Mudd College's President Maria Klawe shares her personal journey in combining a love of mathematics and art.

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Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas Dec 2017

Can Addressing Language Skills For Fifth Grade Ells In A Multiplication Curriculum Help Address The Achievement Gap In Math? A Multiplication Workbook For Big Kids, Michelle Douglas

Master's Projects and Capstones

Currently, the state of California has 1,332,405 students from grades k-12 who speak a language other than English at home (Caledfacts, 2016). When I started my first year teaching fifth grade with 95% of my students being English language learners (ELLs), I was surprised to see an achievement gap of two to three years in my student’s reading and math skills. I found that my student’s developmental language and math skills contributed to a lack of engagement during math time. Upon further research, I found that these three factors play a role in the wide achievement gaps between ELLs and …

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Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe, Martin Zwick, Joshua Hughes Oct 2017

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe, Martin Zwick, Joshua Hughes

Complex Systems Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

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Involute Analysis: Virtual Discourse, Memory Systems And Archive In The Involutes Of Thomas De Quincey, Kimberley A. Garcia Sep 2017

Involute Analysis: Virtual Discourse, Memory Systems And Archive In The Involutes Of Thomas De Quincey, Kimberley A. Garcia

Dissertations, Theses, and Capstone Projects

Thomas De Quincey’s involutes inform metaphysical thought on memory and language, particularly concerning multiplicity and the virtual, repetition and difference. When co-opting the mathematic and mechanic involute in Suspiria de Profundis, De Quincey generates an interdisciplinary matrix for the semiotics underpinning his philosophy of language and theory of memory and experience. Involutes entangle and reproduce. De Quincey’s involute exposes the concrete and actual through which all experience accesses the abstract or virtual. The materiality of their informatics and technics provides a literary model and theoretical precursor to a combination of archive and systems theory. The textuality of involute system(s)—both …

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Voices: Conference On Teaching Stem With Music, September 27-28, 2017, Gregory J. Crowther Jul 2017

Voices: Conference On Teaching Stem With Music, September 27-28, 2017, Gregory J. Crowther

Journal of Humanistic Mathematics

This first-of-its-kind, online-only conference will explore the use of music to teach STEM (science, technology, engineering, and mathematics) at the college level (including AP courses). Presentations will be live-streamed from the conference website, https://www.causeweb.org/voices. Online registrations (for only $10 apiece!) will be accepted at the conference website until the conclusion of the conference on September 28, 2017.

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Math In Seventeen Syllables: An Open Call For Mathematical Haiku, Mark Huber, Gizem Karaali Jul 2017

Math In Seventeen Syllables: An Open Call For Mathematical Haiku, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

The Journal of Humanistic Mathematics invites submissions of mathematical haiku for an upcoming poetry folder tentatively titled Math in Seventeen Syllables. Please send your submissions via email to the editors by November 1, 2017. Publication decisions will be made by December 15, 2017.

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One = Zero, Eric John Gofen Jul 2017

One = Zero, Eric John Gofen

Journal of Humanistic Mathematics

In this paper, I use Mathematics in addition to the three most pure sciences --- Physics, Chemistry, and Rap --- to prove that 1=0. The argument uses The Ideal Gas Law, Ohm's Law, the Definitions of Power and Velocity in addition to indefinite integrals, simple mathematical operations, and the 99 Problems Law. The intuition-crushing result can be applied to all branches of mathematics and sciences and will likely go down as one of the greatest discoveries of all time.

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Descartes Comes Out Of The Closet, Nora E. Culik Jul 2017

Descartes Comes Out Of The Closet, Nora E. Culik

Journal of Humanistic Mathematics

While “Descartes Comes Out of the Closet” is ostensibly about a young woman’s journey to Paris, the descriptive detail borrows language and images from Cartesian coordinate geometry, dualistic philosophy, neuroanatomy (the pineal), and projections of three dimensions onto planes. This mathematical universe is counterpointed in the natural language of the suppressed love story that locates the real in the human. Thus, at the heart of the story is the tension between competing notions of mathematics, i.e., as either an independent realm apart from history or as a culturally produced and historical set of practices. Of course, the central character proves …

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Disciple, Jessica K. Sklar Jul 2017

Disciple, Jessica K. Sklar

Journal of Humanistic Mathematics

This is a love poem for mathematics.

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Nostalgia For Quieter Times, Pedro Poitevin Jul 2017

Nostalgia For Quieter Times, Pedro Poitevin

Journal of Humanistic Mathematics

No abstract provided.

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A Calculus, Sandra Lindow Jul 2017

A Calculus, Sandra Lindow

Journal of Humanistic Mathematics

A poem that compares calculus to life.

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Book Review: Bridges 2013 Poetry Anthology And Bridges 2016 Poetry Anthology, Robin Chapman Jul 2017

Book Review: Bridges 2013 Poetry Anthology And Bridges 2016 Poetry Anthology, Robin Chapman

Journal of Humanistic Mathematics

Two collections of mathematical poetry edited by poet and mathematician Sarah Glaz are enthusiastically recommended to readers for the quality of the poetry, the diverse voices speaking in many modes—praise, elegy, philosophical musings, story-telling, humor, playfulness—and the variety of ways in which mathematical references are incorporated or illustrated. The work comes from participants in the Bridges conferences connecting mathematics, the arts, and the sciences over the last seven years.

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Uncovering Gems Of Mathematics, Asuman G. Aksoy, Ellis Cumberbatch Jul 2017

Uncovering Gems Of Mathematics, Asuman G. Aksoy, Ellis Cumberbatch

Journal of Humanistic Mathematics

Gateway to Exploring Mathematical Sciences (GEMS) is an outreach program offered by the six mathematics departments of the Claremont Colleges for eighth, ninth, and tenth graders. In this paper, we describe our program (in terms of format, participants, mathematical activities and topics involved) and share why we are so enthusiastic about it.

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Shakespeare, A Supernova, And A Little Green Man Walk Into A Mathematics Classroom, Sheila Kirstin Miller Jul 2017

Shakespeare, A Supernova, And A Little Green Man Walk Into A Mathematics Classroom, Sheila Kirstin Miller

Journal of Humanistic Mathematics

Creativity amidst constraints is a hallmark of the STEM researcher. It is precisely what is required to see what has never been seen. It is also at the core of creative mathematics, more commonly called “research”. We in the 21st century tell ourselves that science and story are separate enterprises. One goal of this article is to tell parts of the human story—featuring Shakespeare, Tycho Brahe, visiting stars, Little Green Men, and modern astrophysics—that might erode belief in that duality and illustrate why dissolving the artificial barriers between talents within individuals is to the benefit of ourselves, our students, …

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One + One > Two: The Effects Of Pair Quizzes On Student Attitudes And Perceptions, Harrison W. Straley, Lauren Dupee Jul 2017

One + One > Two: The Effects Of Pair Quizzes On Student Attitudes And Perceptions, Harrison W. Straley, Lauren Dupee

Journal of Humanistic Mathematics

Pair Quizzes are cooperative pop quizzes, taken by a pair of students working together for the same grade. The first author, Chuck, had used pair quizzes in many of his courses through his tenure teaching and was interested in determining their perceived effect on student learning and attitude toward mathematics.To this end, we designed a questionnaire and distributed it to all students currently taking and who had taken two different mathematics courses within a span of four years. Responses from those who chose to complete the survey seem to indicate that the pair quizzes had a positive effect on students’ …

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A Generalised Song, Will Turner Jul 2017

A Generalised Song, Will Turner

Journal of Humanistic Mathematics

We consider parallels between words and music. We call a triple of structures, one verbal, one musical, and one mathematical, in which the mathematical structure is related to the verbal and musical structures, a generalised song. With the intention of exhibiting the potential of this form, we describe a generalised song called ‘Cube’.

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They Say She Was Good -- For A Woman: Poetry And Musings, Joanne Growney Jul 2017

They Say She Was Good -- For A Woman: Poetry And Musings, Joanne Growney

Journal of Humanistic Mathematics

These pages contain ideas and verses that consider the roles of women in mathematics. Details of the life of Amalie “Emmy” Noether inspired a poem and the poem, in turn, led to the poet’s growth and awareness of her self and her voice.

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A Mathematician Reads Plutarch: Plato's Criticism Of Geometers Of His Time, John B. Little Jul 2017

A Mathematician Reads Plutarch: Plato's Criticism Of Geometers Of His Time, John B. Little

Journal of Humanistic Mathematics

This essay describes the author's recent encounter with two well-known passages in Plutarch that touch on a crucial episode in the history of the Greek mathematics of the fourth century BCE involving various approaches to the problem of the duplication of the cube. One theme will be the way key sources for understanding the history of our subject sometimes come from texts that have much wider cultural contexts and resonances. Sensitivity to the history, to the mathematics, and to the language is necessary to tease out the meaning of such texts. However, in the past, historians of mathematics often interpreted …

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Mathematics In The Mind's Eye: Michael Schultheis Paints Poetic And Conceptual Geometries, Patricia Grieve Watkinson Jul 2017

Mathematics In The Mind's Eye: Michael Schultheis Paints Poetic And Conceptual Geometries, Patricia Grieve Watkinson

Journal of Humanistic Mathematics

Michael Schultheis is an established artist and a formally-educated mathematician. In his practice the two disciplines are inextricably linked. His large-scale lyrical paintings at first glance seem to focus on the effects of light and atmospheres, representing cloudscapes or waterscapes in resonant color. Yet moving through these mists are decidedly mathematical references --- drawn geometric shapes and hand-written equations. These are employed by Schultheis to represent the physical world or to express feelings (or both). For example, he may examine the structure of a pine cone or reflect on human relationships or do both at the same time. The resulting …

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On French Pudding And A German Mathematician, Amy Shoemaker Jul 2017

On French Pudding And A German Mathematician, Amy Shoemaker

Journal of Humanistic Mathematics

At the turn of the 19th century, mathematics developed the rigor that is now considered essential to the field. Mathematicians began going back and proving theorems and statements that had been taken to be true on face value, ensuring the underpinnings of mathematics were solid. This era of mathematics was characterized not only by setting foundations, but also by pushing the boundaries of new ideas. In 1830, Bolzano found an example of a function that was nowhere differentiable, despite being continuous. Thirty years later, Cellerier and Riemann each discovered another example of such a pathological function. The first everywhere …

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Multifaceted Mathematicians, Juan M. Sepulcre Jul 2017

Multifaceted Mathematicians, Juan M. Sepulcre

Journal of Humanistic Mathematics

This report attempts to provide an overview of some of the mathematicians who have combined their mathematical knowledge with other academic and non-academic specialities. The various examples given, many of them included in the well-known MacTutor History of Mathematics archive, corroborate the fact that although the idea of the typical polymath has receded with the passage of time, until the end of the Renaissance, most well-known mathematicians were also well-versed in a number of different sciences such as philosophy, astronomy, and physics. We also highlight other, less common combinations of knowledge, in famous mathematicians who were experts in other disciplines …

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Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou Jul 2017

Some Thoughts On The Epicurean Critique Of Mathematics, Michael Aristidou

Journal of Humanistic Mathematics

In this paper, we give a comprehensive summary of the discussion on the Epicurean critique of mathematics and in particular of Euclid's geometry. We examine the methodological critique of the Epicureans on mathematics and we assess whether a 'mathematical atomism' was proposed, and its implications. Finally, we examine the Epicurean philosophical stance on mathematics and evaluate whether it was on target or not.

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