Mathematics Commons^™

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

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

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

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

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

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

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

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

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

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

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

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 …

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

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 20^th century philosophical ideas, particularly those of Georg Lukács. Szathmári’s portrayal of two …

Finding Direction, Finding Inspiration, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

A Closed-Form Solution To The Inverse Problem In Interpolation By A Bézier-Spline Curve, Le Phuong Quan, Thái Ahn Nhan

Mathematics and Computer Science

A geometric construction of a Bézier curve is presented by a unifiable way from the mentioned literature with some modification. A closed-form solution to the inverse problem in cubic Bézier-spline interpolation will be obtained. Calculations in the given examples are performed by a Maple procedure using this solution.

Positive And Generalized Positive Real Lemma For Slice Hyperholomorphic Functions, Daniel Alpay, Fabrizio Colombo, Izchak Lewkowicz, Irene Sabadini

Mathematics, Physics, and Computer Science Faculty Articles and Research

In this paper we prove a quaternionic positive real lemma as well as its generalized version, in case the associated kernel has negative squares for slice hyperholomorphic functions. We consider the case of functions with positive real part in the half space of quaternions with positive real part, as well as the case of (generalized) Schur functions in the open unit ball.

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 T_V 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 …

Exploring Mortality Rates For Major Causes Of Death In Korea, Hyo Jung Oh, Donng Min Yang, Chong Hyuck Kim, Jae Gyu Jeon, Nam Hyung Jung, Chan Young Kim, Jurgen Symanzik, Hyo Won Oh, Akugizibwe Edwin, Seong Ii Jo, Jeong Yong Ahn

Mathematics and Statistics Faculty Publications

Background: The trends and patterns of the mortality rates for causes of death are meaningful information. They can provide a basis for national demographic and health care policies by identifying the number, causes, and geographical distribution of deaths.

Objective: To explore and analyze the characteristics of the mortality rates for major causes of death in Korea.

Methods: Some common data analysis methods were used to describe the data. We also used some visualization techniques such as heat maps and line plots to present mortality rates by gender, age, and year.

Results: Our analysis shows the crude …