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Articles 421 - 450 of 1646
Full-Text Articles in Mathematics
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.
Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, Richard B. Schneider
Irrational Philosophy? Kronecker's Constructive Philosophy And Finding The Real Roots Of A Polynomial, Richard B. Schneider
Rose-Hulman Undergraduate Mathematics Journal
The prominent mathematician Leopold Kronecker (1823 – 1891) is often relegated to footnotes and mainly remembered for his strict philosophical position on the foundation of mathematics. He held that only the natural numbers are intuitive, thus the only basis for all mathematical objects. In fact, Kronecker developed a complete school of thought on mathematical foundations and wrote many significant algebraic works, but his enigmatic writing style led to his historical marginalization. In 1887, Kronecker published an extended version of his paper, “On the Concept of Number,” translated into English in 2010 for the first time by Edward T. Dean, who …
Evaluating The Historical Accuracy Of Blackwork Embroidery With Fractal Analysis, Rhiannon Cire
Evaluating The Historical Accuracy Of Blackwork Embroidery With Fractal Analysis, Rhiannon Cire
Undergraduate Theses and Capstone Projects
The intricate monochromatic embroidery that graced the collars and cuffs of Renaissance nobility and domestic materials from that era has been little studied beyond the historical costuming and crafting communities. This style, known as blackwork, for it was traditionally done in black silk on white linen, exemplifies how complex and visually-appealing designs can arise from repetition of simple forms, often demonstrating the fractal property of self-similarity. Though most blackwork patterns are not true fractals, fractal analysis offers a means of objectively quantifying their complexity and new lens through which to examine this embroidery technique. The purpose of this study was …
The Agnostic Structure Of Data Science Methods, Domenico Napoletani, Marco Panza, Daniele Struppa
The Agnostic Structure Of Data Science Methods, Domenico Napoletani, Marco Panza, Daniele Struppa
MPP Published Research
In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within …
Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney
Collecting Works: A History Of The Euler Archive, Erik R. Tou, Christopher Goff, Michele Gibney
Euleriana
We give a brief history of the Euler Archive, an online database of the published works of Leonhard Euler (1707-1783). Furthermore, we describe the Archive's recent move to an academic repository, and the added functionality such a move allows.
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.
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 …
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 …
Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall
Mathematical Representations In Magazine Advertisements: Have The Messages Changed In A Decade?, Jennifer Hall
Journal of Humanistic Mathematics
Although people's ideas about mathematics and mathematicians often develop from their school and home experiences, such ideas also are influenced by interactions with popular media. In this article, I report on findings from a study in which I analyzed magazine advertisements for representations of mathematics and mathematicians. Data collection took place in two phases, approximately a decade apart. In each phase, I reviewed a year’s worth of issues in each of six diverse, popular magazines for mathematical representations in advertisements. The frequency of mathematical advertisements decreased from Phase 1 to Phase 2, but the initial frequency was already extremely low, …
Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski
Peer Motivation: Getting Through Math Together, Jessica Mean, Wes Maciejewski
Journal of Humanistic Mathematics
Students have a complex relationship with mathematics. Some love it, but more often than not, the feelings are less favorable. These feelings can lead to decreased motivation which makes it difficult for students to engage with the subject as the semester progresses. Instructors also have difficulty addressing this waning motivation. In this paper, we claim peers are better able to connect with the students and this can be leveraged to better motivate students. We present an approach to having peers motivate their students. These peer interactions integrated with a mandatory mathematics course might improve students’ motivation.
In How Many Days Will He Meet His Wife?, Dipak Jadhav
In How Many Days Will He Meet His Wife?, Dipak Jadhav
Journal of Humanistic Mathematics
In how many days will he meet his wife? This is a question asked at the end of each of two problems embedded in the verses of the last chapter of the Vyavahāra-gaṇita (‘Mathematics of Transaction’) of Rājāditya of 12th century. He infuses elegance in those two problems by choosing the charming idea of a husband’s meeting with his wife after their quarrel. This paper not only presents the algorithms offered by Rājāditya to solve them on their own terms as well as on modern terms and discusses the historicity of the categories of those two problems but also …
Raise The (Proportion) Bar!, Michael Waters
Raise The (Proportion) Bar!, Michael Waters
Journal of Humanistic Mathematics
This article, drawing mainly on references to teacher preparation textbooks, proposes proportion bars as a somewhat novel graphical approach to solving simple (direct) proportion problems and to illustrate the advantages of such an approach, which include accessibility with materials at early grade levels, allowance of students to better develop number sense and estimation, facilitation of setting up proportions, allowance for conceptual understanding and motivation of the procedure for solving direct proportions, assistance with part-to-part and part-to whole comparisons, and drawing of connections among mathematical topics. The emphasis is on teaching with understanding, rather than procedural knowledge.
“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner
“It’S All For The Best”: Optimization In The History Of Science, Judith V. Grabiner
Journal of Humanistic Mathematics
Many problems, from optics to economics, can be solved mathematically by finding the highest, the quickest, the shortest—the best of something. This has been true from antiquity to the present. Why did we start looking for such explanations, and how and why did we conclude that we could productively do so? In this article we explore these questions and tell a story about the history of optimization. Scientific examples we use to illustrate our story include problems from ancient optics, and more modern questions in optics and classical mechanics, drawing on ideas from Newton’s and Leibniz’s calculus and from the …
Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood
Humanistic Stem: From Concept To Course, Debra T. Bourdeau, Beverly L. Wood
Journal of Humanistic Mathematics
Blending perspectives from the humanities and STEM fosters the creativity of all students. The culturally implicit dichotomy between the two meta-disciplines can be overcome with carefully designed courses and programs intent on doing so. The why and how of doing so through an online course is described with qualitative evidence of the success. Future plans for a full slate of such course and a virtual community are discussed.
Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart
Ahab's Arithmetic: The Mathematics Of Moby-Dick, Sarah B. Hart
Journal of Humanistic Mathematics
In this article we explore mathematical allusions in Herman Melville’s novel Moby-Dick. We argue that both the quantity and sophistication of these allusions are evidence for Melville’s high level of mathematical knowledge and ability. We discuss some of the most compelling mathematical imagery, as well as giving background on the several mathematicians and mathematics books mentioned in the novel. We also include some biographical details supporting the assertion that Melville had an unusually good mathematical education.