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Articles 1 - 30 of 107
Full-Text Articles in Mathematics
Quik Church, Route 3.141592, Sarah Voss
Quik Church, Route 3.141592, Sarah Voss
Journal of Humanistic Mathematics
The following set of poems are from one of ten sections in a collection of poetry called Quik Church: Short Poems that Travel Far. Each section illustrates one of many “streets” which individuals often take on their spiritual journey through life, e.g., the Old Gods Path, Nature Trail, Memory Skyway, Mystic Avenue, Pastoral Lane, and so on. This one, Route 3.141592, is the route of mathematics and the science that depends on mathematics.
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Towards Ethical Ai: Mathematics Influences Human Behavior, Dioneia M. Monte-Serrat, Carlo Cattani
Journal of Humanistic Mathematics
Mathematics plays an important role in the linguistic structure of artificial in- telligence (AI). We describe the linguistic process as a unique structure present both in human cognition and in cognitive computing. The close relationship with both AI and human cognition is due to this unique structure, which paves the way for AI to interfere with the behavior of those who interact with it. We highlight the role of mathematicians in designing algorithms—the core of the AI linguistic process—and in defining steps and instructions for AI. Because al- gorithms, through AI, interfere with the thought of those who interact with …
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Synesthesia: 3.1415... Orange.Whiteperiwinklewhiteblue..., Shelly Sheats Harkness, Bethany A. Noblitt, Nicole Giesbers
Journal of Humanistic Mathematics
In this paper we address the questions: What is synesthesia? What support(s) can teachers provide for their students who have synesthesia? Nicole, a future mathematics teacher who possesses this synesthesia “superpower”, describes how it impacted her learning. We collected data for this case study through an audio-recorded and transcribed interview, as well as from subsequent email correspondence between the three authors. We asked Nicole three kinds of questions: questions she is frequently asked, questions she would like to be asked, and questions teachers (like Shelly and Beth) might ask. Results indicate that synesthesia may have helped Nicole learn English as …
#Disruptjmm: Online Social Justice Advocacy And Community Building In Mathematics, Rachel Roca, Carrie Diaz Eaton, Drew Lewis, Joseph Hibdon, Stefanie Marshall
#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 …
What Is A Number?, Nicholas Radley
What Is A Number?, Nicholas Radley
HON499 projects
This essay is, in essence, an attempt to make a case for mathematical platonism. That is to say, that we argue for the existence of mathematical objects independent of our perception of them. The essay includes a somewhat informal construction of number systems ranging from the natural numbers to the complex numbers.
Tribute To Gene Chase, Calvin Jongsma
Tribute To Gene Chase, Calvin Jongsma
Faculty Work Comprehensive List
Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.
Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma
Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma
Faculty Work Comprehensive List
Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.
The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak
The Theatre Of Math: The Stage As A Tool For Abstract Math Education, Blaine Hudak
Honors Projects
So often in the education of Mathematics does instruction solely consist of the lecture. While this can be an effective method of communicating the ideas of math, it leaves much to be desired in gathering the interest and intrigue of those who have not dedicated their lives to the study of the subject. Theatre, by contrast, is a tool that has been used in the past as means of teaching complicated and difficult to understand moral and emotional subjects. While Theatre and Mathematics have been used in combination many times in the past, it is most often done in the …
El Final Report: Undergraduate Summer Research Internships, Sophie Wu
El Final Report: Undergraduate Summer Research Internships, Sophie Wu
SASAH 4th Year Capstone and Other Projects: Publications
In her final report, Sophie Wu discusses her two Undergraduate Summer Research Internships at Western University: the first in the Statistics and Actuarial Science department, concerning microinsurance, and the second, in the Mathematics department, concerning computational neuroscience.
The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita
The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita
Journal of Humanistic Mathematics
We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.
The History Of The Enigma Machine, Jenna Siobhan Parkinson
The History Of The Enigma Machine, Jenna Siobhan Parkinson
History Publications
The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).
Mining The Soma Cube For Gems: Isomorphic Subgraphs Reveal Equivalence Classes, Edward Vogel, My Tram
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 …
In Mathematics, As In Art, Andrew Granville
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?
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Towards Pedagogy Supporting Ethics In Modelling, Marie Oldfield
Journal of Humanistic Mathematics
Education for concepts such as ethics and societal responsibility that are critical in building robust and applicable mathematical and statistical models do currently exist in isolation but have not been incorporated into the mainstream curricula at the school or university level. This is partially due to the split between fields (such as mathematics, statistics, and computer science) in an educational setting but also the speed with which education is able to keep up with industry and its requirements. I argue that principles and frameworks of socially responsible modelling should begin at school level and that this would mean that ethics …
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Foundational Mathematical Beliefs And Ethics In Mathematical Practice And Education, Richard Spindler
Journal of Humanistic Mathematics
Foundational philosophical beliefs about mathematics in the mathematical community may have an unappreciated yet profound impact on ethics in mathematical practice and mathematics education, which also affects practice. A philosophical and historical basis of the dominant platonic and formalist views of mathematics are described and evaluated, after which an alternative evidence-based foundation for mathematical thought is outlined. The dualistic nature of the platonic view based on intuition is then compared to parallel historical developments of universalizing ethics in Western thought. These background ideas set the stage for a discussion of the impact of traditional mathematical beliefs on ethics in the …
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Ethics And Mathematics – Some Observations Fifty Years Later, Gregor Nickel
Journal of Humanistic Mathematics
Almost exactly fifty years ago, Friedrich Kambartel, in his classic essay “Ethics and Mathematics,” did pioneering work in an intellectual environment that almost self-evidently assumed a strict separation of the two fields. In our first section we summarize and discuss that classical paper. The following two sections are devoted to complement and contrast Kambartel’s picture. In particular, the second section is devoted to ethical aspects of the indirect and direct mathematization of modern societies. The final section gives a short categorization of various philosophical positions with respect to the rationality of ethics and the mutual relation between ethics and mathematics.
A Non-Euclidean Story Or: How To Persist When Your Geometry Doesn’T, Rami Luisto
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 …
Alice’S Adventures In Wonderland: Carroll’S Symbolic Attack On Mathematical Symbolism, Firdous Ahmad Mala
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.
The Hamster Diaries, Pamela B. Pierce
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.
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Makers Do Math! Legitimizing Informal Mathematical Practices Within Making Contexts, Amber Simpson, Signe Kastberg
Journal of Humanistic Mathematics
In this paper, we argue that making activities within non-formal learning environments (e.g., museums, libraries) provide opportunities to engage youth in what we define as mathematical practices for making, everyday mathematical practices within the context of making activities. The mathematical practices identified from two non-formal school-based contexts highlighted three mathematical practices for making: informal measurement, spatial reasoning, and curiosity. These practices are identified in prior scholarship as being beneficial and foundational for the understanding of mathematical concepts. As educators and researchers turn to non-formal and informal contexts, with an eye toward understanding ways youth engage in the activity of making, …
Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler
Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler
Philosophy Faculty Publications
In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.
Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950, Andrew Beman-Cavallaro
Expansion Of The Department Of Mathematics At Princeton University And The Founding Of The School Of Mathematics At The Institute For Advanced Study: 1900-1950, Andrew Beman-Cavallaro
Graduate Review
From 1900 to 1950 Princeton, New Jersey, hosted two of the most prestigious institutions and provided a location for the expansive mathematical investigations taking place just before, during, and immediately after the Second World War. Princeton University and the Institute for Advanced Study housed, fed, and provided workspaces for an array of Mathematicians uncovering new research methodologies (resulting in the defeat of both the Nazi Party and the Empire of Nippon), the foundation for modern experimental Mathematics, and expansions of Theoretical and Applied Physics.
Fantasy At The Service Of Mathematics, Clara Ziskin, Esther Williams, Alla Shmukler
Fantasy At The Service Of Mathematics, Clara Ziskin, Esther Williams, Alla Shmukler
Journal of Humanistic Mathematics
This article aims to introduce the reader to a book published in 2016 under the title “Amazing Tales from the Magic Wood and Famous Problems of Mathematics” by Elli Shor and Clara Ziskin. The book offers an original method of presenting mathematical facts and history through a fantasy narrative. The book’s two authors, Clara Ziskin and Alla Shmukler (Elli Shor), together with consultant psychologist Esther Williams, share here several excerpts taken from the first part of the book as well as related illustrations and mathematical riddles, so that the reader can form an informed impression of the book, its structure, …
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Crocheting Mathematics Through Covid-19, Beyza C. Aslan
Journal of Humanistic Mathematics
As it is often said, something good often comes out of most bad situations. The time I spent during COVID-19, at home and isolated with my two children, brought out one secret passion in me: crocheting. Not only did it help me pass the time in a sane and productive way, but also it gave me a new goal in life. It connected my math side with my artistic side. It gave me a new perspective to look at math, and helped me help others see math in a positive way.
An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm
An Interdisciplinary Rendezvous Between Mathematics And Literature: Reflections On Beauty As A Perspective In Comparative Disciplinary Didactics And A Thematic Approach To Interdisciplinary Work In Upper Secondary School, Uffe Thomas Jankvist, Helle Rørbech, Jesper Bremholm
Journal of Humanistic Mathematics
In this paper we propose a thematic focus on aesthetics in the context of an interdisciplinary collaboration between mathematics and literature (Language Arts) as a way to further students’ reflections on and deeper understanding of what characterizes the two subjects. Furthermore, we argue that approaching aesthetics through the perspective of literacy can potentially strengthen students’ understanding of ways of thinking particular to specific (academic) disciplines; ways of thinking that are otherwise often hidden when teaching focuses on more pragmatic aspects. G. H. Hardy’s A Mathematician’s Apology from 1940 serves as the recurring illustrative example in our discussions of the pedagogical …
Mathematics And Magic Realism: A Study Of "The Raven Legend", Veselin Jungic
Mathematics And Magic Realism: A Study Of "The Raven Legend", Veselin Jungic
Journal of Humanistic Mathematics
This article demonstrates that “The Raven Legend”, a Haida myth transcribed by Franz Boas in 1888, is full of (ethno)mathematical concepts that Haida society used to make sense of the natural, real world. Calculus can be used to model several segments of the story since the narrative relied heavily on ideas that a mathematician would identify as the concepts of infinity and mathematical limits.
Perceiving Mathematics And Art, Edmund Harriss
Perceiving Mathematics And Art, Edmund Harriss
Mic Lectures
Mathematics and art provide powerful lenses to perceive and understand the world, part of an ancient tradition whether it starts in the South Pacific with tapa cloth and wave maps for navigation or in Iceland with knitting patterns and sunstones. Edmund Harriss, an artist and assistant clinical professor of mathematics in the Fulbright College of Arts and Sciences, explores these connections in his Honors College Mic lecture.
Changes And Deltas, Jim Wolper
Changes And Deltas, Jim Wolper
Journal of Humanistic Mathematics
Lecturing about Mathematics is like playing Jazz.
Using Departmental Publications To Foster Student Creativity In Mathematics, Zohreh Shahbazi, Parker Glynn-Adey
Using Departmental Publications To Foster Student Creativity In Mathematics, Zohreh Shahbazi, Parker Glynn-Adey
Journal of Humanistic Mathematics
This paper discusses the design and implementation of mathematical departmental publications. We argue that these publications foster students’ creativity and written communication skills.
Virtual Temari: Artistically Inspired Mathematics, Carl Giuffre, Lee Stemkoski
Virtual Temari: Artistically Inspired Mathematics, Carl Giuffre, Lee Stemkoski
Journal of Humanistic Mathematics
Technology can be a significant aide in understanding and appreciating geometry, beyond theoretical considerations. Both fiber art and technology have been employed as a significant aide and an inspiring vessel in education to explore geometry. The Japanese craft known as temari, or "hand-balls", combines important artistic, spiritual, and familial values, and provides one such approach to exploring geometry. Mathematically, the artwork of temari may be classified based on whether they are inspired by polyhedra and discrete patterns or by periodic functional curves. The resulting designs of these categories provide an ancient vantage for displaying spherical patterns. We illustrate a …