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Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn 2019 University of Kentucky

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 2019 Bowling Green State University

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 ...


On Mathematical Conjectures And Counterexamples, Ali Barahmand 2019 Department of Mathematics, Hamedan Branch, Islamic Azad University, Hamedan, Iran

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 2019 Independent researcher

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 2019 Bryant University

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 2019 University of Wisconsin - Stout

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 2019 Claremont Colleges

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 2019 George Mason University

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 2019 WW/English and Humanities

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 2019 University of Missouri - Kansas City

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 2019 University of Brighton

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 ...


Preparing Our Students To Read And Understand Mathematics, Melanie Butler 2019 Mount St. Mary's University

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 2019 University of Alaska Fairbanks

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 2019 Paderborn University

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 ...


The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli 2019 Adelphi University

The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli

Journal of Humanistic Mathematics

In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.


Sandor Szathmari's Kazohinia: Mathematics And The Platonic Idea, Susan J. Siggelakis 2019 The University of New Hampshire

Sandor Szathmari's Kazohinia: Mathematics And The Platonic Idea, Susan J. Siggelakis

Journal of Humanistic Mathematics

In this article I analyse Sándor Szathmári’s utopian, satiric novel, The Voyage to Kazohinia, as an exercise in the portrayal of Platonist ideas. Through a discussion specifically of Szathmári’s portrayal of the way mathematics is conceived in two different, imaginary societies, I aim to reveal his preoccupation with exploring a solution to the essential political and moral problem of the alienation of interests between the individual and the group. This analysis locates Szathmari’s ideas within the Platonic tradition as well as within the context of 20th century philosophical ideas, particularly those of Georg Lukács. Szathmári’s ...


Finding Direction, Finding Inspiration, Mark Huber, Gizem Karaali 2019 Claremont McKenna College

Finding Direction, Finding Inspiration, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.


Front Matter, 2019 Claremont Colleges

Front Matter

Journal of Humanistic Mathematics

No abstract provided.


Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil 2019 University Politehnica of Bucharest

Extending Set Functors To Generalised Metric Spaces, Adriana Balan, Alexander Kurz, Jiří Velebil

Mathematics, Physics, and Computer Science Faculty Articles and Research

For a commutative quantale V, the category V-cat can be perceived as a category of generalised metric spaces and non-expanding maps. We show that any type constructor T (formalised as an endofunctor on sets) can be extended in a canonical way to a type constructor TV on V-cat. The proof yields methods of explicitly calculating the extension in concrete examples, which cover well-known notions such as the Pompeiu-Hausdorff metric as well as new ones.

Conceptually, this allows us to to solve the same recursive domain equation X ≅ TX in different categories (such as sets and metric spaces) and we ...


Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga 2019 Marshall University

Local Lagged Adapted Generalized Method Of Moments: An Innovative Estimation And Forecasting Approach And Its Applications.Pdf, Olusegun M. Otunuga

Olusegun Michael Otunuga

In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, physical and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP ...


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