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Articles 481 - 510 of 708
Full-Text Articles in Mathematics
Using Hidden Markov Modeling For Biogeographical Ancestry Analysis, Melvin R. Currie
Using Hidden Markov Modeling For Biogeographical Ancestry Analysis, Melvin R. Currie
Journal of Humanistic Mathematics
This paper describes a methodology for analyzing X-chromosome data to establish biogeographical contributions to the author’s X chromosome. We present an exposition of how Hidden Markov Modeling (HMM) can be used as a black box for ancestry analysis and focus on a set of conditions that are not universal but fairly common. The first condition is that the ancestral populations are drawn from regions that have had very little or no contact with each other since prehistoric times. The second condition is that the number of possible ancestral populations is small. In this analysis, we assume that the ancestral populations …
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Choose Your Own Adventure: An Analysis Of Interactive Gamebooks Using Graph Theory, D'Andre Adams, Daniela Beckelhymer, Alison Marr
Journal of Humanistic Mathematics
"BEWARE and WARNING! This book is different from other books. You and YOU ALONE are in charge of what happens in this story." This is the captivating introduction to every book in the interactive novel series, Choose Your Own Adventure (CYOA). Our project uses the mathematical field of graph theory to analyze forty books from the CYOA book series for ages 9-12. We first began by drawing the digraphs of each book. Then we analyzed these digraphs by collecting structural data such as longest path length (i.e. longest story length) and number of vertices with outdegree zero (i.e. number …
Engaging Crisis: Immersive, Interdisciplinary Learning In Mathematics And Rhetoric, Meredith L. Greer, Stephanie Kelley-Romano
Engaging Crisis: Immersive, Interdisciplinary Learning In Mathematics And Rhetoric, Meredith L. Greer, Stephanie Kelley-Romano
Journal of Humanistic Mathematics
This paper describes an interdisciplinary activity that crosses over between Mathematics and Rhetoric. The professors who created this activity both sought active-learning opportunities for their students, a sense of realism--even urgency--in what can otherwise be perceived as abstract material, and a meaningful liberal arts experience. Evidence of the power of this experience is seen in the media coverage, both from our college and from the Portland Press Herald newspaper. Both courses described in this paper are at the elective level, taken by majors or minors in their respective disciplines. Students have moderate to extensive backgrounds in their subject areas. However, …
Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking
Visual Teaching Of Geometry And The Origins Of 20th Century Abstract Art, Stephen Luecking
Journal of Humanistic Mathematics
As a group, the artists educated near the turn of the 19th and 20th centuries possessed greater mathematical knowledge than expected of artists today, especially regarding constructive skills in Euclidean geometry. Educational theory of the time stressed such skills for students in general, who needed these to enter the workplace of the time. Mathematics teaching then stressed the use of manipulatives, i.e., visual and interactive aids thought to better fix the student’s acquisition of mathematical skills. This visual training, especially in geometry, significantly affected the early development of abstraction in art. This paper presents examples of this visual …
Anschaulich: Visualization, Imagination, Mathematics, Mark Huber, Gizem Karaali
Anschaulich: Visualization, Imagination, Mathematics, Mark Huber, Gizem Karaali
Journal of Humanistic Mathematics
No abstract provided.
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily Cilli-Turner, Gail Tang, Gulden Karakok, Houssein El Turkey
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.
What The Wasp Said, Hugh C. Culik
What The Wasp Said, Hugh C. Culik
Journal of Humanistic Mathematics
On a bright spring day, the ancient building housing the English and Logic Departments begins to slowly collapse on itself, trapping McMann (an inept English professor) and Lucy Curt (a logician) in the office they share. As the Fibonacci repetitions of the building’s brickwork slowly peel away, McMann seizes the moment to tell Lucy stories about skunks, stories whose recurrent pattern finally leads to the unrecognized connection between a “message” burned into his ear by a wasp and the orderly universe for which he cannot find a language. At last, he looks up only to see Lucy descending a ladder, …
An 1883 Faery Tale, Scott W. Williams
An 1883 Faery Tale, Scott W. Williams
Journal of Humanistic Mathematics
A poem about the construction of Georg Cantor's famous set.
Irrational Infinity, Ricky Chen
Irrational Infinity, Ricky Chen
Journal of Humanistic Mathematics
A short whimsical poem on the cardinality of irrational numbers.
Cosmology, Craig W. Steele
A Mathematician's Travel Memories, Michael Holcomb
A Mathematician's Travel Memories, Michael Holcomb
Journal of Humanistic Mathematics
No abstract provided.
Geometry Of Night, Jenny Patton
Geometry Of Night, Jenny Patton
Journal of Humanistic Mathematics
No abstract provided.
Ecstatic Syllabi: Four Poems, Mary Peelen
Ecstatic Syllabi: Four Poems, Mary Peelen
Journal of Humanistic Mathematics
Four poems with mathematical themes. Poems are entitled: Algebra I, Algebra II, Plane Geometry, Number Theory.
A Selection Of Poems From Ode To Numbers, Sarah Glaz
A Selection Of Poems From Ode To Numbers, Sarah Glaz
Journal of Humanistic Mathematics
My first poetry collection, Ode to Numbers, was published by Antrim House in September 2017 (http://www.antrimhousebooks.com/glaz.html). The book contains poems written over a quarter of a century and inspired by mathematics and my life as a mathematician. The poems in this folder are a small selection from the book—a series of seven poems focusing on events from the history of mathematics.
Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye
Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye
Journal of Humanistic Mathematics
This review explores the issues surrounding mathematics poetry and its role in challenging stereotypes about mathematics and mathematicians. In Ode to Numbers Sarah Glaz takes us from her childhood in Romania to her work as a professor at the University of Connecticut in the USA, with the constant thread of her love of mathematics. It is an intense emotional journey through time and place, arriving at mature reflection. The reader will encounter a wide range of poetic forms; some traditional, others inspired by mathematics. Glaz writes with originality, courage, insight, and generosity and this collection secures her reputation as an …
Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn
Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn
Journal of Humanistic Mathematics
Many colleges and universities offer a course in the history of mathematics. While the potential benefits for students taking such a course might be apparent, it is often less clear how teaching a history of mathematics course can be a transformational experience for faculty. We present a dialogue between the authors regarding their experiences teaching history of mathematics courses, including their motivation for doing so, the impact these experiences have had on their classroom practices and assessment methods, and the opportunities history of mathematics courses offer for incorporating social justice, equity, and inclusion into the study of mathematics. Our goal …
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren
Journal of Humanistic Mathematics
The logos or rational language of the fifth-century BCE teacher, Gorgias, as contained in the fragment On the Nonexistent, challenges a reader to understand the relationship between the existent and the nonexistent; yet the text also offers an accessible idea of logos. Inspired by William M. Priestley's approach to the study of logos through ratios, and by Ivor Grattan-Guinness's recommendation to broaden the study of historical texts in the history of mathematics and mathematics education, and pursue their significance in a heritage sense, this article suggests that this ancient non-mathematics text by Gorgias may inspire and refresh elementary mathematics educators' …
On Mathematical Conjectures And Counterexamples, Ali Barahmand
On Mathematical Conjectures And Counterexamples, Ali Barahmand
Journal of Humanistic Mathematics
This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of number-theoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of long-term attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor.
Cartegory Theory: Framing Aesthetics Of Mathematics, Maria Mannone
Cartegory Theory: Framing Aesthetics Of Mathematics, Maria Mannone
Journal of Humanistic Mathematics
Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy …
Fun With Math On Valentine's Day, Kristin T. Kennedy
Fun With Math On Valentine's Day, Kristin T. Kennedy
Journal of Humanistic Mathematics
This article describes various love-themed activities the department of mathematics at Bryant University hosted during a college-wide celebration of love called "The Arts and Science of Love", held during Valentine's Day 2018. Inspired by Susan D'Agustino's article "To Fall in Love with Math, Do This" [1], Bryant mathematicians came up with many creative and engaging activities that brought mathematics and its practitioners closer to the students on campus. Much fun was had.
Incorporating Philosophy, Theology, And The History Of Mathematics In An Introduction To Proof Course, Steven Deckelman
Incorporating Philosophy, Theology, And The History Of Mathematics In An Introduction To Proof Course, Steven Deckelman
Journal of Humanistic Mathematics
In this article I describe a project activity for an undergraduate introduction to proof course aimed at mathematics and computer science majors that combines logic and philosophy with a significant dimension of writing. Pedagogically, the project involves a broader range of critical thinking skills than is usual in such courses. Undergraduate students analyze Anselm of Canterbury's and Kurt Gödel's proofs of the existence of God using modal logic.
Spirit-Wise Math: Two Examples From A Collection Of Mathaphors, Sarah Voss
Spirit-Wise Math: Two Examples From A Collection Of Mathaphors, Sarah Voss
Journal of Humanistic Mathematics
This article consists of two examples of loosely spiritual insights drawn from mathematics, both of which are from a work-in-progress -- a collection of mathematical metaphors.
Comforting With Mathematics: A Case Study, Michael J. Goldstein
Comforting With Mathematics: A Case Study, Michael J. Goldstein
Journal of Humanistic Mathematics
Death by suicide often leaves behind grieving family members with unanswered questions. Of these concerns, fear that their loved one suffered or felt regret is common. When the method of suicide was jumping from height, that answer can easily be determined using basic kinematics. Despite the perception that mathematics is a cold, calculating field, it can provide a clear, definitive answer and comfort those left behind.
What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood
What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood
Journal of Humanistic Mathematics
Getting students who are planning on technical careers to value their general education courses, particularly in the humanities, is not an easy task. The experiences of two professors from disciplines that cross the so-called divide between STEM and Humanities motivate not only a series of courses blending the two to the advantage of their own students but also a virtual pedagogical community to support efforts taking place elsewhere.
Out Of The Vacuum: A Hidden Assumption, Richard Delaware
Out Of The Vacuum: A Hidden Assumption, Richard Delaware
Journal of Humanistic Mathematics
In writing a proof, a student surprises her sense of reality and logic.
Untangling Knots: Embodied Diagramming Practices In Knot Theory, Kate Mccallum
Untangling Knots: Embodied Diagramming Practices In Knot Theory, Kate Mccallum
Journal of Humanistic Mathematics
The low visibility and specialised languages of mathematical work pose challenges for the ethnographic study of communication in mathematics, but observation-based study can offer a real-world grounding to questions about the nature of its methods. This paper uses theoretical ideas from linguistic pragmatics to examine how mutual understandings of diagrams are achieved in the course of conference presentations. Presenters use shared knowledge to train others to interpret diagrams in the ways favoured by the community of experts, directing an audience’s attention so as to develop a shared understanding of a diagram’s features and possible manipulations. In this way, expectations about …
Preparing Our Students To Read And Understand Mathematics, Melanie Butler
Preparing Our Students To Read And Understand Mathematics, Melanie Butler
Journal of Humanistic Mathematics
This article gives techniques and tips for college mathematics instructors to increase students’ ability to read and comprehend mathematics. The article also includes some relevant history of reading instruction and some motivation for incorporating these ideas into courses.
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Journal of Humanistic Mathematics
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
From Solvability To Formal Decidability: Revisiting Hilbert’S “Non-Ignorabimus”, Andrea Reichenberger
Journal of Humanistic Mathematics
The topic of this article is Hilbert’s axiom of solvability, that is, his conviction of the solvability of every mathematical problem by means of a finite number of operations. The question of solvability is commonly identified with the decision problem. Given this identification, there is not the slightest doubt that Hilbert’s conviction was falsified by Gödel’s proof and by the negative results for the decision problem. On the other hand, Gödel’s theorems do offer a solution, albeit a negative one, in the form of an impossibility proof. In this sense, Hilbert’s optimism may still be justified. Here I argue that …