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Articles 1 - 30 of 1171
Full-Text Articles in Physical Sciences and Mathematics
Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer
Mathematical Modeling, Analysis, And Simulation Of Patient Addiction Journey, Adan Baca, Diego Gonzalez, Alonso G. Ogueda, Holly C. Matto, Padmanabhan Seshaiyer
CODEE Journal
This paper aims to develop a mathematical model to study the dynamics of addiction as individuals go through their detox journey. The motivation for this work is three fold. First, there has been a significant increase in drug overdose and drug addiction following the COVID-19 pandemic, and addiction may be interpreted as a infectious disease. Secondly, the dynamics of infectious disease could be modeled via compartmental models described by differential equations and one can therefore leverage the existing analytical and numerical methods to model addiction as a disease. Finally, the work helps to inform how mathematical models governed by differential …
First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat
First Diffusion Course: "The Structure Of Language As A Connection Between Artificial Intelligence, Information And Ethics", Dioneia Monte-Serrat
Journal of Humanistic Mathematics
From August 22nd to November 21st, the first Diffusion Course on “The structure of language as a connection between artificial intelligence, information and ethics” will take place on a Thursday of each month, in Ribeirao Preto, Brazil. You are cordially invited to sign up for in-person classes and join other researchers and students on this course.
7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond
7th International Conference On Creative Mathematical Sciences Communication (Cmsc`24), Frances A. Rosamond
Journal of Humanistic Mathematics
The 7th International Creative Mathematical Sciences Communication (CMSC) conference is scheduled for October 2024 in Trier, Germany. Initiated in Darwin, Australia in 2013, CMSC aims to explore novel methods of imparting computational thinking to diverse audiences including non-specialists, modern citizens, and children. Participants from around the world and from various and interdisciplinary disciplines such as science, education, dance, drama, and visual arts convene to exchange ideas, present experimental approaches, and collaborate on engaging children in the exploration of ongoing, unresolved research challenges.
Oh Statistics!, Heather L. Cook
Oh Statistics!, Heather L. Cook
Journal of Humanistic Mathematics
This poem was written about statistics and the usefulness thereof.
Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat
Discordium Mathematica - A Symphony In Aleph Minor, Vijay Fafat
Journal of Humanistic Mathematics
How did Mathematics arise? Who created it? Why is it subject to Godel’s Incompleteness Theorems? And what does all this have to do with Coleridge’s poem, “Kubla Khan”, and “The Person from Porlock”? Here is a complete mythology of Mathematics set in an epic poetry format, fusing thoughts and verses from Western religions and Eastern mysticism… Those with immense patience and careful reading shall reap the fruit… (best read on a large screen or in printed form)
Love Is No Mean Thing: A Larkin Logarithm, Michael P.H. Stanley Md
Love Is No Mean Thing: A Larkin Logarithm, Michael P.H. Stanley Md
Journal of Humanistic Mathematics
This poem was recited at a marriage recently in Vermont. I met the groom in my freshman year. He was the first college friend I ever made, and he used to burst into the room like Cosmo Kramer and settle down in an easy-chair to think about math (my side of the dorm was quieter than his). I thought that was remarkable and delightful, and so, when the task came to write a matrimonial poem for him, I selected a mathematical conceit. The poem concludes with a mathematical paraphrasing of Philip Larkin's last line from Arundel Tomb.
Pi: A Perpetual Journey, Ravindra K. Bisht
Pi: A Perpetual Journey, Ravindra K. Bisht
Journal of Humanistic Mathematics
A brief history of the constant pi is presented with a poetic flavor.
Eighth Grade Algebra, Joseph Chaney
Eighth Grade Algebra, Joseph Chaney
Journal of Humanistic Mathematics
This is a poem about the affirming power of algebra in the life of a teenager.
Prime Motivation Of Eratosthenes, Pamela L. King
Prime Motivation Of Eratosthenes, Pamela L. King
Journal of Humanistic Mathematics
The sieve of Eratosthenes is used as a metaphor for the concept of people falling through the social safety net, and people who were once excluded, making efforts to increase inclusiveness.
Poems From The Series "At The Dimensional Border", Philip Fried
Poems From The Series "At The Dimensional Border", Philip Fried
Journal of Humanistic Mathematics
Poems about the border between the second and third dimensions, on geometry and the human condition.
Mathematical Graffiti: Bridges 2023 Clerihew Collection
Mathematical Graffiti: Bridges 2023 Clerihew Collection
Journal of Humanistic Mathematics
Clerihews are poems of a form invented by Edmund Clerihew Bentley around the turn of the 19th-20th century. The poems are typically biographical, humorous, and are made up of two couplets. The rhyming pattern is always aabb, but the meter of the two couplets is usually not the same. The first line is simply the name of the person, the other three lines relate to the subject, often in an absurd way. If the rhyme is slightly off, or the rhythm irregular or awkward, or the facts a bit confused, so much the better. The present collection of clerihews, written …
The Value Of Adding Nothing: A Call For Reform-Oriented Polynomial Division, Jonathan Clark, Jeneva Clark
The Value Of Adding Nothing: A Call For Reform-Oriented Polynomial Division, Jonathan Clark, Jeneva Clark
Journal of Humanistic Mathematics
The call to implement reform practices in schools reflects the historical turn away from the behaviorist theory of learning in education. Yet the praxis of this turn remains a significant challenge, particularly within mathematics classrooms where procedural memorization is emphasized. In this article, we show one means of how to advance our pursuit of meaningful mathematics into polynomial division. Building on the literature for reform-based division methods, an alternative to the long division algorithm will be explored that relies solely on adding zero and fundamental algebraic principles.
Book Review: How To Expect The Unexpected: The Science Of Making Predictions -- And The Art Of Knowing When Not To By Kit Yates, Mark Huber
Journal of Humanistic Mathematics
Humans think about the future all the time. Prediction is a part of how we prepare for the coming of both good and bad events in our lives. Kit Yates' book, How to expect the unexpected, concentrates primarily on the question of why prediction is difficult, and what mental shortcuts people take in prediction that can lead to incorrect results. Unfortunately, a lack of concern for details and several omissions undermine the quality of the book.
Geometric Shapes That Sing And Move: An Interdisciplinary Lesson With Pre-Service Teachers, Gladys Krause, Gustavo Velandia
Geometric Shapes That Sing And Move: An Interdisciplinary Lesson With Pre-Service Teachers, Gladys Krause, Gustavo Velandia
Journal of Humanistic Mathematics
Our work shares a practical example of an interdisciplinary lesson in which two teacher educators collaborated to integrate mathematics and music in an elementary mathematics methods course. This paper describes the process of collaboration in designing the lesson and shares original instructional resources to be used in the classroom. We also discuss what the pre-service teachers participating in the lesson shared about their learning experience, and what we, the teacher educators, learned from this experience. In presenting this work we aim to promote the opening of spaces in teacher preparation programs that allow pre-service teachers to develop their own instructional …
States Of Matter, Todd Sformo
States Of Matter, Todd Sformo
Journal of Humanistic Mathematics
This is a non-fiction essay overtly about three methods used in overwintering physiology, set in the context of my first learning them, along with associated thoughts and ideas as I began working on my PhD. The mathematics shows up mainly in the final section of the essay whose subtitle plays on a poem by Wallace Stevens called “Anecdote of the Jar”. This section is fable-like in its explanation of protein purification and begins with an impossible statement that is slowly adjusted to make sense by words and math.
Fibonacci-Inspired Spiral Quilts, Kathleen Offenholley, Sk Collins, David Radcliffe
Fibonacci-Inspired Spiral Quilts, Kathleen Offenholley, Sk Collins, David Radcliffe
Journal of Humanistic Mathematics
This article provides insight into the mathematics and designs of quilts inspired by Fibonacci and logarithmic spirals. We introduce the history and development of the Fibonacci number sequence and how to hand-draw a Fibonacci spiral. Further, we explain the relationship between the Fibonacci spiral and logarithmic spirals, the advantages of using logarithmic spirals to create designs, and how to produce digital spiral designs using Desmos, a free web-based graphing calculator. Finally, we discuss methods for designing spiral quilts or other triangle and spiral designs (such as collage or other media) and derive a formula for calculating the apex angles of …
Badass Women, Richard Delaware
Badass Women, Richard Delaware
Journal of Humanistic Mathematics
In this true story, one mathematics major supports another in an unexpected way.
Intuitive Explanations In Mathematical Education, Jerzy Pogonowski
Intuitive Explanations In Mathematical Education, Jerzy Pogonowski
Journal of Humanistic Mathematics
I discuss the role of intuitive explanations in the learning, teaching, and popularization of mathematics. Several examples of such explanations are presented, related to linguistic explanations, perception, empirical models, and internal explanations inside mathematics itself. I emphasize the fact that intuitive explanations in a sense transgress mere mathematical arguments. I also discuss in brief the role of paradox resolution in mathematical education.
Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller
Bootstraps And Scaffolds: What A Cognitive-Historical Analysis Of The Complex Number System Reveals About Numerical Cognition, Charles R. Card, Gary G. Miller
Journal of Humanistic Mathematics
The following investigation is a cognitive-historical analysis of the conceptual development of complex numbers. The history of this development spans nearly two millennia, from the earliest appearance of the square root of a negative quantity in the calculations of Heron of Alexandra (1st Century CE) to the full flowering of complex numbers in the first half of the 19th Century. The approach used for this analysis is Nersessian's, including her formulations of model-based reasoning and mental models. Additional aspects of the analysis feature the prominent roles played by process representations, including object-process complementarities, and by core numerical systems. Our analysis …
Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid
Building Communities Of Care For Equity, Justice, And Culturally Responsive Practice In Mathematics Education, Nicole Fletcher, B Waid
Journal of Humanistic Mathematics
Teaching is widely considered one of the “caring professions,” but conceptualizations of care and how care is put into practice in education are not universal. In this article, we draw from a range of perspectives on care that integrate supportive interpersonal relationships, high expectations, and culturally relevant theories of critical care, as well as Queer Theory and Disability Justice, to explore the application of these ideas in mathematics education. We identify key elements for building communities of care in mathematics education contexts: co-constructing community agreements, redefining participation, shifting traditional power structures, collaborative problem solving, and building networks of care beyond …
The Braids On Your Blanket, Michelle Cheng, Robert Uwe Laugwitz
The Braids On Your Blanket, Michelle Cheng, Robert Uwe Laugwitz
Journal of Humanistic Mathematics
In this expository essay, we introduce some elements of the study of groups by analysing the braid pattern on a knitted blanket. We determine that the blanket features pure braids with a minimal number of crossings. Moreover, we determine polynomial invariants associated to the links obtained by closing the braid patterns of the blanket.
Mathematical Models And Pedagogy Of Marxist Political Economy, Christopher Perez
Mathematical Models And Pedagogy Of Marxist Political Economy, Christopher Perez
Journal of Humanistic Mathematics
How can we teach people about the economics of labor and exploitation in mathematics courses? We define a mathematical model for describing the relationships embodied by commodities and labor. We then use this model to illustrate the exploitative nature of profit and the tendency for catastrophic chain-reactions that lead to market crashes. Lastly, we discuss applications to pedagogy in mathematics courses using a simplified version of the model.
What Is An Imaginary Number? The Plane And Beyond, Andrew W. Powell
What Is An Imaginary Number? The Plane And Beyond, Andrew W. Powell
Journal of Humanistic Mathematics
In this article I argue that i is a quantity associated with the two-dimensional real number plane, whether as a vector, a bi-vector, a point or a transformation (rotation). This position provides a foundation for the complex numbers and accounts for complex numbers in some equations of applied mathematics and physics. I also argue that complex numbers are fundamentally geometrical and can be described by geometric algebra, and that moreover the meaning of complex numbers in physics varies with dimension and geometry of the manifold.
Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson
Language Analysis Via The Run And Flattened Statistics On Permutations, Jennifer Elder, Pamela E. Harris, Anthony Simpson
Journal of Humanistic Mathematics
A permutation π in Sn can be decomposed into its runs π = τ1τ2 . . . τk, where a run of π is a maximal contiguous subsequence whose elements are in increasing order. If the first values of each run are in increasing order, then π is said to be flattened. Motivated by the study of flattened permutations, we study the words in the Danish, German, English, Spanish, French, Italian, Dutch, and Norwegian languages. In each language considered, our work provides the following: a list of the longest flattened words, histograms for the proportion …
Millions, Billions, Or Trillions: How To Partition Large Numbers Into Friendly Figures, Eryn Michelle Maher, Ha Nguyen, Cynthia Sanchez Tapia
Millions, Billions, Or Trillions: How To Partition Large Numbers Into Friendly Figures, Eryn Michelle Maher, Ha Nguyen, Cynthia Sanchez Tapia
Journal of Humanistic Mathematics
Communicating and making sense of large numbers — millions, billions, and trillions — is a persistent struggle in our society. Using large numbers is a learning requirement for elementary school children, but even adults struggle with it. Hence supporting future teachers in developing their own understanding of the concepts is valuable. To construct, enact, and revise an educational experience for preservice teachers, we apply three frameworks of teaching mathematics for social justice tasks, high cognitive demand tasks, and productive mathematics discussion. The context uses United States educational and defense spending, the national budget, and the gross domestic product. Preservice teachers …
The Modern Geometrician: Euclidean Construction For Digital Paper, Deborah A. Kent, David J. Muraki
The Modern Geometrician: Euclidean Construction For Digital Paper, Deborah A. Kent, David J. Muraki
Journal of Humanistic Mathematics
The emphasis on traditional hand-drawn compass and straight-edge geometrical constructions has been reduced in the core narrative of most current curricula. In response to this trend, this paper presents a virtual toolkit for producing precision geometrical figures within the popular note-taking app, Notability. These graphical procedures employ the app's stylus-based input and shape tools (for lines, circles and squares) to offer a modern take on classical geometrical construction. These procedures are adaptations of familiar textbook methods, necessary because the app's circle-drawing tool behaves differently from a standard compass. Beyond the familiar canon of elementary Euclidean constructions, such as angle bisectors …
Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl
Sociomathematical Norms And Automated Proof Checking In Mathematical Education: Reflections And Experiences, Merlin Carl
Journal of Humanistic Mathematics
According to a widely held view, mathematical proofs are essentially (indications of) formal derivations, and thus in principle mechanically checkable (this view is defended, for example, by Azzouni [3]). This should in particular hold for the kind of simple proof exercises typically given to students of mathematics learning to write proofs. If that is so, then automated proof checking should be an attractive option for math education at the undergraduate level. An opposing view would be that mathematical proofs are social objects and that what constitutes a mathematical proof can thus not be separated from the social context in which …
My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen
My Own Private World Of Non-Ordinary Associative Arithmetics, Marion D. Cohen
Journal of Humanistic Mathematics
A binary operation # on Z+ is said to be an associative arithmetic if both # and its iteration — the binary operation ∗ defined recursively by: x∗1 = x and x∗y = [x ∗ (y − 1)]#x — are associative. E. Rosinger [6] showed that under reasonable conditions an associative arithmetic must be ordinary addition. However, in the general case, there are associative arithmetics that are not ordinary addition. This paper gives examples of these as well as results towards a structure theorem for associative arithmetics. The paper also describes the role that this particular math problem has played …
Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali
Picturing Mathematics (Education) In New Ways, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.