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Articles 31 - 60 of 69
Full-Text Articles in Physical Sciences and Mathematics
Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber
Markov Chains For Computer Music Generation, Ilana Shapiro, Mark Huber
Journal of Humanistic Mathematics
Random generation of music goes back at least to the 1700s with the introduction of Musical Dice Games. More recently, Markov chain models have been used as a way of extracting information from a piece of music and generating new music. We explain this approach and give Python code for using it to first draw out a model of the music and then create new music with that model.
The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak
The Math Games Seminar: A Mathematical Learning Community, Anthony Delegge, Ellen Ziliak
Journal of Humanistic Mathematics
Learning communities can be an effective means of engaging university students across disciplines. Games have always been a source of both enjoyment and interesting mathematics. Based on our own interest in games, and the deep, strategic discussions we found ourselves having with students when we played games with them, we decided to design a learning community around the mathematics of games. We hoped in particular that such a community could be a great pathway to introducing mathematical thinking to students not majoring in mathematics, and that they would gain a greater appreciation for our field. In this paper, we describe …
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 Heritage Project: An Exploration Empowering Students' Mathematical Identities, Siddhi Desai, Brianna Kurtz, Farshid Safi
Mathematics Heritage Project: An Exploration Empowering Students' Mathematical Identities, Siddhi Desai, Brianna Kurtz, Farshid Safi
Journal of Humanistic Mathematics
The International Study Group on Ethnomathematics (ISGEm) supports incorporating cultural diversity of mathematical practices to promote the teaching and learning of school mathematics. Through The Mathematics Heritage Project, students at a middle school in the southeastern United States developed unique creations to connect with the mathematics connected to their identities and self-identified cultural group. Upon reflection, students reported an increased awareness of the relevance of mathematics in their lives and a sense of ownership that is both meaningful and modern.
Logic And Biology: The Correspondence Between Alfred Tarski And Joseph H. Woodger, Paolo Mancosu
Logic And Biology: The Correspondence Between Alfred Tarski And Joseph H. Woodger, Paolo Mancosu
Journal of Humanistic Mathematics
This article makes available some early letters chronicling the relationship between the biologist Joseph H. Woodger and the logician Alfred Tarski. Using twenty-five unpublished letters from Tarski to Woodger preserved in the Woodger Papers at University College, London, I reconstruct their relationship for the period 1935-1950. The scientific aspects of the correspondence concern, among other things, Tarski’s reports on the work he is doing, his interests, and his --- sometimes critical but always well-meaning --- reactions to Woodger’s attempts at axiomatizing and formalizing biology using the system of Principia Mathematica. Perhaps the most interesting letter from a philosophical point …
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.
Seeing Mathematics In The World, Mark Huber, Gizem Karaali
Seeing Mathematics In The World, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Math In The Time Of Covid: An Open Call For Contributions, Mark Huber, Gizem Karaali
Math In The Time Of Covid: An Open Call For Contributions, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics invites submissions of essays, reflections, poetry, and artwork for an upcoming thematic folder tentatively titled Math in the Time of COVID and scheduled to appear in July 2021. Please send your submissions via email to the editors by May 1, 2021. Publication decisions will be made by June 15, 2021.
Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey
Special Issue Call For Papers: Ethics In Mathematics, Catherine Buell, Victor Piercey
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Ethics in Mathematics. Please send your abstract submissions via email to the guest editors by September 1, 2021. Initial submission of complete manuscripts is due December 1, 2021. The issue is currently scheduled to appear in July 2022.
Once Upon A Party - An Anecdotal Investigation, Vijay Fafat
Once Upon A Party - An Anecdotal Investigation, Vijay Fafat
Journal of Humanistic Mathematics
Mathematicians and Physicists attending let-your-hair-down parties behave exactly like their own theories. They live by their theorems, they jive by their theorems. Life imitates their craft, and we must simply observe the deep truths hiding in their party-going behavior...
Deterministic Republic, Kris H. Green
Deterministic Republic, Kris H. Green
Journal of Humanistic Mathematics
This story is an extension of the paper "Mathematics and Voter Choice" published in this same issue of the Journal of Humanistic Mathematics. It explores what elections and politics might look like from the voter perspective if some of the ideas from the paper were implemented. The story is also an attempt to highlight how mathematics and data science are done, much the way a colleague of mine refers to shows like CSI as recruiting tools that use "dramatic pipetting" in the labs to show day-to-day science in action. The story is, as you will no doubt see, heavily …
Iterations Of Emptying, Marian Christie
Iterations Of Emptying, Marian Christie
Journal of Humanistic Mathematics
Successive iterations of the Sierpinski carpet fractal are used to explore how we---our history, experiences, thoughts and memories---occupy spaces that we once inhabited.
Turing's Machine, Mike Curtis
Turing's Machine, Mike Curtis
Journal of Humanistic Mathematics
The musings of a Turing Machine.
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef
One Straight Line Addresses Another Traveling In The Same Direction On An Infinite Plane, Daniel W. Galef
Journal of Humanistic Mathematics
No abstract provided.
Proof Theory, Stan Raatz
Early Morning Mathematics Classes, Angelina Schenck
Early Morning Mathematics Classes, Angelina Schenck
Journal of Humanistic Mathematics
No abstract provided.
Permission To Add: Math-Teaching Limericks, Marion D. Cohen
Permission To Add: Math-Teaching Limericks, Marion D. Cohen
Journal of Humanistic Mathematics
Throughout my years and decades of being a teacher, I have written limericks about every course I’ve taught, and sometimes courses I haven’t taught but reviewed textbooks in. Here I share several of these limericks.
Peter Hilton En Passant, Richard Delaware
Peter Hilton En Passant, Richard Delaware
Journal of Humanistic Mathematics
This is a decades-long tale of my glancing friendship with distinguished mathematician and mathematics educator Peter Hilton and his constant collaborator Jean Pedersen. Peter’s wit, compassion, and support are in full display, though in truth I knew him only “in passing.”
The Number, Arati Nanda Pati
The Number, Arati Nanda Pati
Journal of Humanistic Mathematics
This is a story from the heart on COVID-19, penned around April 4, 2020, in the early days of the pandemic.
“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis
“You Will Remain Unwavering In Your Determination To Succeed No Matter How Long It Takes”: A Mathematico-Emotional Analysis Of A Guide To Higher Learning, Kathleen M. Clark, Oksana M. Rubis
Journal of Humanistic Mathematics
In this article we present an analysis of the multi-fold artist’s book, A Guide to Higher Learning (Chen, 2009). In our analysis, we propose different perspectives from which to view the mathematical and philosophical aspects found within the book. We explore aspects of “higher learning” by analyzing the complex mathematical equations and textual elements that readers meet in the book. Chen challenges the reader with: “This is a test. You will not be given any assistance or instructions on how to proceed. You will not be told when to begin or when to stop” (Chen, 2009). Thus, in our exploration …
Aligning Political Options And Aggregated Personal Opinions On The Issues, Kris H. Green
Aligning Political Options And Aggregated Personal Opinions On The Issues, Kris H. Green
Journal of Humanistic Mathematics
Much work has been done in studying how to aggregate voter opinions to decide a fair election. These models presuppose that each voter has a solid understanding of their choices and can express that opinion in the election process. We discuss why this is not always the case. Further, we explore some of the issues that arise when considering the multidimensional nature of both voter preference, with respect to the slate of issues in an election, and the platforms of the various candidates, with respect to the same slate of issues. In light of the complications we encounter and with …
How I First Heard About Calculus, Bradley J. Lucier
How I First Heard About Calculus, Bradley J. Lucier
Journal of Humanistic Mathematics
An attempt to motivate a class of engineering students leads to insights both personal and pedagogical.
Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg
Computational Thinking In Mathematics And Computer Science: What Programming Does To Your Head, Al Cuoco, E. Paul Goldenberg
Journal of Humanistic Mathematics
How you think about a phenomenon certainly influences how you create a program to model it. The main point of this essay is that the influence goes both ways: creating programs influences how you think. The programs we are talking about are not just the ones we write for a computer. Programs can be implemented on a computer or with physical devices or in your mind. The implementation can bring your ideas to life. Often, though, the implementation and the ideas develop in tandem, each acting as a mirror on the other. We describe an example of how programming and …
Teaching From The Unknown, Jon Jacobsen
Teaching From The Unknown, Jon Jacobsen
Journal of Humanistic Mathematics
The goal of teaching is to transform our students' understanding, much as the goal of acting is to transform the audience's reality. In this article we use the context of mathematics to explore connections between teaching and acting and how such connections can help our students learn not only mathematics, but about the nature of mathematics.
Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes
Using Mathematical Equations To Communicate And Think About Karma, Kien H. Lim, Christopher Yakes
Journal of Humanistic Mathematics
Two equations are presented in this article to communicate a particular understanding of karma. The first equation relates future experiences to past and present actions. Although the equation uses variables and mathematical symbols such as the integral sign and summation symbol, it reads more like a literal translation of an English sentence. Based on the key idea in the first equation, a second equation is then created to highlight the viability of using math to communicate concepts that are not readily quantifiable. Analyzing such equations can stimulate thinking, enhance understanding of spiritual concepts, raise issues, and uncover tensions between our …
Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza
Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza
Journal of Humanistic Mathematics
Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …
A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger
A Heart-Centered Stance: Receptivity To Algebra Teachers’ And Students’ Multidimensional Experiences, Nicole L. Fonger
Journal of Humanistic Mathematics
The algebra classroom in urban public high schools in the United States is a complex space, ripe with many challenges and opportunities. In this paper I introduce the notion of a heart-centered stance for the teacher and the educator, and a method of engaging in creative expression for reflection and introspection toward individual change in the rich context of the high school algebra classroom. My evolving relationships with two high school algebra teachers, observations of their classrooms, as well as my own self-study and professional growth, are incorporated into this paper as I introduce and exemplify two tenets of a …
A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli
A Holistic Mathematics Curriculum Revision: An Adelphi University Case Study, Salvatore J. Petrilli
Journal of Humanistic Mathematics
Join me as I take you on a journey with the faculty of the Department of Mathematics and Computer Science at Adelphi University during our two-year re-envisioning and implementation of our mathematics curriculum. From the beginning this involved a data-driven initiative that naturally led to the revisions. Here I describe in detail the process that our department followed. In closing I end with some recommendations for interesting research directions in the field of mathematics education.
The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia
The Prime Number Theorem As A Capstone In A Complex Analysis Course, Stephan Ramon Garcia
Journal of Humanistic Mathematics
We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem for a series of capstone lectures, a scaffold for a series of guided exercises, or as a framework for an inquiry-based course. We require almost no knowledge of number theory, for our aim is to make a complete proof of the prime number theorem widely accessible to complex analysis instructors and their students. In particular, we highlight the potential pitfalls and subtleties that may …