Physical Sciences and Mathematics Commons^™

Self-Reference And Diagonalisation, Joël A. Doat

Journal of Humanistic Mathematics

This poem is an exercise on self-reference and diagonalisation in mathematics featuring Turing’s proof of the undecidability of the halting problem, Cantor’s cardinality argument, the Burali-Forti paradox, and Epimenides' liar paradox.

Wartime Logic, Tony Bedenikovic

Journal of Humanistic Mathematics

No abstract provided.

Book Review: Algebra The Beautiful: An Ode To Math’S Least-Loved Subject By G. Arnell Williams, Judith V. Grabiner

Journal of Humanistic Mathematics

In his book Algebra the Beautiful, G. Darnell Williams has undertaken a challenging job – to show the importance, deep structure, intellectual connections, and sheer beauty of classroom algebra. This review describes some of the questions the book raises, the historical and cultural context it provides, and the intellectual apparatus it deploys.

Poetry Folder: Mathematical Constants Beyond The Half-Circle

Journal of Humanistic Mathematics

In our July 2022 issue, we announced an open call for poetry about mathematical constants other than pi. And you delivered. This folder contains five eclectic poems celebrating those constants beyond the half-circle, written by Robin Chapman, John Donoghue, Kevin Farey, Lawrence M. Lesser, and E. R. Lutken.

Enjoy!

Anneli Lax: They Think, Therefore We Are, Elena Anne Corie Marchisotto

Journal of Humanistic Mathematics

No abstract provided.

Walking Alone: My Career In Mathematics, Maohua Le, Yongzhong Hu

Journal of Humanistic Mathematics

In this article, dictated by Maohua Le and arranged by Yongzhong Hu, Professor Le briefly recounts his legendary experience of self-study mathematics, which reflects the life experiences of his generation of Chinese people.

Blending Mathematics Teaching With Kindness, Kien H. Lim, Anthony Matsuura

Journal of Humanistic Mathematics

Mathematics can be intellectually demanding, engaging, and fulfilling. Learning mathematical concepts adequately warrants an environment where students can err without penalty, shame, or hurtful consequences. Teaching mathematics efficaciously depends on the trusting relationship between the teacher and the students. We advocate blending mathematics teaching with kindness because it benefits the teacher, the students, and society. Kindness, niceness, caring, and benevolence are interrelated but not synonymous. We outline four progressive levels of kindness: conditional, superficial, optimal, and genuine. Blending mathematics teaching and kindness effectively requires the teacher to decenter from their own perspectives and adopt the student’s perspective as the student …

Mathaphor As A Literary Tool, Sarah Voss

Journal of Humanistic Mathematics

Drawing from one of my recent sermons, I chart the path of mathaphor (metaphor drawn from mathematics) as a literary tool. Following a short history of the concept, I detail contemporary author Colum McCann’s significant use of a geometric term to unveil and encourage compassion.

Figure-Ground Perception: A Poem Proof, Richard Delaware

Journal of Humanistic Mathematics

This is a proof, in poetic form, of a bit of real analysis, more specifically involving the topology of accumulation points, that exploits the human optical phenomenon of figure-ground perception. Sometimes it is not a change in content, but a snap shift in point of view that yields a proof.

Using Bloom's Taxonomy For Math Outreach Within And Outside The Classroom, Manmohan Kaur

Journal of Humanistic Mathematics

Not everyone is a great artist, but we don’t often hear, “I dislike art.” Most people are able to appreciate visual arts, music and sports, without necessarily excelling in it themselves. On the other hand, the phrase “I dislike math” is widely prevalent. This is especially ironic in our current society, where mathematics affects our day-to-day activities in essential ways such as e-commerce and e-mail. This paper describes the opportunity to popularize mathematics by focusing on its fun and creative aspects, and illustrates this opportunity through a brief discussion of interdisciplinary topics that expose the beauty, elegance and value of …

The Mathematics Of The Harp: Modeling The Classical Instrument And Designing Futuristic Ones, Cristina Carr, Daniel Chioffi, Maya Glenn, Stefan O. Nita, Vlad N. Nita, Bogdan G. Nita

Journal of Humanistic Mathematics

We analyze and model the neck of the classical harp based on the length of the strings, their tension and density. We then use the results to design new and innovative harp shapes by adjusting the parameters of the model.

Lessons From Human Experience: Teaching A Humanities Course Made Me A Better Math Teacher, Erin Griesenauer

Journal of Humanistic Mathematics

As a professor at a Liberal Arts college, I recently taught a General Education course called Human Experience. Far from my normal experiences in the mathematics classroom, in Human Experience I was tasked with teaching topics from the humanities, including art, philosophy, history, and political science. Teaching this course was challenging, but it was also transformative. Teaching a course so far from my background gave me the opportunity to experiment with different pedagogical techniques and to reflect on how I set up my math classes. I learned many lessons that I have brought back to my math classes—lessons that have …

The Nothing That Really Matters, Szilárd Svitek

Journal of Humanistic Mathematics

Zero has (a) special role(s) in mathematics. In the current century, we take negative numbers and zero for granted, but we should also be aware that their acceptance and their emergence in mathematics, and their ubiquity today, have not come to happen as rapidly as, for example, that of natural numbers. Students can quickly become confused by the question: is zero a natural number? The answer is simple: a matter of definition. The history of zero and that of negative numbers are closely linked. It was in the calculations of debts that the negative numbers first appeared, where the state …

The Use And Development Of Mathematics Within Creative Literature, Toby S C Peres

Journal of Humanistic Mathematics

This paper presents a study on the extent to which creative literature been used as a vessel to carry forward the development of mathematical thought. The role of mathematics as a driving force for literature is highlighted, and while many examples exist that clearly show an attempt to disperse mathematical ideas, with Lewis Carroll, OuLiPo and ancient poetry considered, the argument that the sole purpose of the writings was for the sake of mathematical development is not clear-cut.

The Genesis Of A Theorem, Osvaldo Marrero

Journal of Humanistic Mathematics

We present the story of a theorem's conception and birth. The tale begins with the circumstances in which the idea sprouted; then is the question's origin; next comes the preliminary investigation, which led to the conjecture and the proof; finally, we state the theorem. Our discussion is accessible to anyone who knows mathematical induction. Therefore, this material can be used for instruction in a variety of courses. In particular, this story may be used in undergraduate courses as an example of how mathematicians do research. As a bonus, the proof by induction is not of the simplest kind, because it …

Where Do Babies Come From?, Marcio Luis Ferreira Nascimento

Journal of Humanistic Mathematics

According to European folklore, popularized by a fairy tale, storks are responsible for bringing babies to new parents. This probably came from observation in certain European countries, such as Norway, Netherlands or Germany, that storks nesting on the roofs of households were believed to bring good luck, as the possibility of new births. People love stories, but correlation simply means that there is a relationship between two factors that tells nothing about the direction of said relationship, if any. Another possibility is simple coincidence. Let us say that it’s possible that one factor causes another. It’s also possible that the …

Teaching Mathematics After Covid: A Conversation Not A Discussion, Wendy Ann Forbes, Joyce Mgombelo

Journal of Humanistic Mathematics

Inspired by Brent Davis' conceptualization of listening and conversation in his book Teaching Mathematics: Toward a Sound Alternative, we propose how we as a mathematics education community may move forward by continuing in the conversation that emerged from COVID. We encourage all involved to listen rather than assume a discussion-oriented stance. Using an enactivist lens, we look at the pandemic learning space, give an overview of the education conversation that emerged in Ontario, and offer a way to rethink Mathematics Education within the frame of a conversation. We believe that if mathematics education is to engage learners in a meaningful …

Human-Machine Collaboration In The Teaching Of Proof, Gila Hanna, Brendan P. Larvor, Xiaoheng (Kitty) Yan

Journal of Humanistic Mathematics

This paper argues that interactive theorem provers (ITPs) could play an important role in fostering students’ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that …

A Classification Of Musical Scales Using Binary Sequences, Thomas Hillen

Journal of Humanistic Mathematics

Every beginning music student has gone through the four main musical scales: major, natural minor, harmonic minor, and melodic minor. And some might wonder, why those four and not five, or six, or just three? Here we show that a mathematical classification can be used to identify these scales as representatives of certain scale families. Moreover, the classification reveals another scale family, which is much less known: the harmonic major scale. We find that each scale family contains exactly seven scales, which include the modes (dorian, phrygian,...) and other scales such as the Romanian, …

The Merchant And The Mathematician: Commerce And Accounting, Graziano Gentili, Luisa Simonutti, Daniele C. Struppa

Journal of Humanistic Mathematics

In this article we describe the invention of double-entry bookkeeping (or partita doppiaas it was called in Italian), as a fertile intersection between mathematics and early commerce. We focus our attention on this seemingly simple technique that requires only minimal mathematical expertise, but whose discovery is clearly the result of a mathematical way of thinking, in order to make a conceptual point about the role of mathematics as the humus from which disciplines as different as operations research, computer science, and data science have evolved.

The Roles Of Mathematical Metaphors And Gestures In The Understanding Of Abstract Mathematical Concepts, Omid Khatin-Zadeh, Zahra Eskandari, Danyal Farsani

Journal of Humanistic Mathematics

When a new mathematical idea is presented to students in terms of abstract mathematical symbols, they may have difficulty to grasp it. This difficulty arises because abstract mathematical symbols do not directly refer to concretely perceivable objects. But, when the same content is presented in the form of a graph or a gesture that depicts that graph, it is often much easier to grasp. The process of solving a complex mathematical problem can also be facilitated with the use of a graphical representation. Transforming a mathematical problem or concept into a graphical representation is a common problem solving strategy, and …

From A Doodle To A Theorem: A Case Study In Mathematical Discovery, Juan FernáNdez GonzáLez, Dirk Schlimm

Journal of Humanistic Mathematics

We present some aspects of the genesis of a geometric construction, which can be carried out with compass and straightedge, from the original idea to the published version (Fernández González 2016). The Midpoint Path Construction makes it possible to multiply the length of a line segment by a rational number between 0 and 1 by constructing only midpoints and a straight line. In the form of an interview, we explore the context and narrative behind the discovery, with first-hand insights by its author. Finally, we discuss some general aspects of this case study in the context of philosophy of mathematical …

Where Does Mathematics Come From? Really, Where?, Mark Huber, Gizem Karaali

Journal of Humanistic Mathematics

No abstract provided.

Front Matter

Journal of Humanistic Mathematics

No abstract provided.

Post-Quantum Hermite-Jensen-Mercer Inequalities, Martin Bohner, Hüseyin Budak, Hasan Kara

Mathematics and Statistics Faculty Research & Creative Works

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals.

Towards Carbon Neutrality: Prediction Of Wave Energy Based On Improved Gru In Maritime Transportation, Zhihan Lv, Nana Wang, Ranran Lou, Yajun Tian, Mohsen Guizani

Machine Learning Faculty Publications

Efficient use of renewable energy is one of the critical measures to achieve carbon neutrality. Countries have introduced policies to put carbon neutrality on the agenda to achieve relatively zero emissions of greenhouse gases and to cope with the crisis brought about by global warming. This work analyzes the wave energy with high energy density and wide distribution based on understanding of various renewable energy sources. This study provides a wave energy prediction model for energy harvesting. At the same time, the Gated Recurrent Unit network (GRU), Bayesian optimization algorithm, and attention mechanism are introduced to improve the model's performance. …

Galfit-Ing Agn Host Galaxies In Cosmos: Hst Versus Subaru, Callum Dewsnap, Pauline Barmby, Sarah C. Gallagher, C. Megan Urry, Aritra Ghosh, Meredith C. Powell

Physics and Astronomy Publications

The COSMOS field has been extensively observed by most major telescopes, including Chandra, HST, and Subaru. HST imaging boasts very high spatial resolution and is used extensively in morphological studies of distant galaxies. Subaru provides lower spatial resolution imaging than HST but a substantially wider field of view with greater sensitivity. Both telescopes provide near-infrared imaging of COSMOS. Successful morphological fitting of Subaru data would allow us to measure morphologies of over 104 known active galactic nucleus (AGN) hosts, accessible through Subaru wide-field surveys, currently not covered by HST. The morphological parameters indicate the types of galaxies that host AGNs. …

Sexual Selection As A Tool To Improve Student Reasoning Of Evolution, Sarah K. Spier, Joseph Dauer

School of Natural Resources: Faculty Publications

There is an emphasis on survival-based selection in biology education that can allow students to neglect other important evolutionary components, such as sexual selection, reproduction, and inheritance. Student understanding of the role of reproduction in evolution is as important as student understanding of the role of survival. Limiting instruction to survival- based scenarios (e.g., effect of food on Galapagos finch beak shape) may not provide students with enough context to guide them to complete evolutionary reasoning. Different selection forces can work in concert or oppose one another, and sexual selection can lead to the selection of trait variants that are …

Enhanced Convolutional Neural Network For Non-Small Cell Lung Cancer Classification, Yahya Tashtoush, Rasha Obeidat, Abdallah Al-Shorman, Omar Darwish, Mohammad A. Al-Ramahi, Dirar Darweesh

Computer Information Systems Faculty Publications

Lung cancer is a common type of cancer that causes death if not detected
early enough. Doctors use computed tomography (CT) images to diagnose
lung cancer. The accuracy of the diagnosis relies highly on the doctor's
expertise. Recently, clinical decision support systems based on deep learning
valuable recommendations to doctors in their diagnoses. In this paper, we
present several deep learning models to detect non-small cell lung cancer in
CT images and differentiate its main subtypes namely adenocarcinoma,
large cell carcinoma, and squamous cell carcinoma. We adopted standard
convolutional neural networks (CNN), visual geometry group-16 (VGG16),
and VGG19. Besides, we …

Drone Detection Using Yolov5, Burchan Aydin, Subroto Singha

Faculty Publications

The rapidly increasing number of drones in the national airspace, including those for recreational and commercial applications, has raised concerns regarding misuse. Autonomous drone detection systems offer a probable solution to overcoming the issue of potential drone misuse, such as drug smuggling, violating people’s privacy, etc. Detecting drones can be difficult, due to similar objects in the sky, such as airplanes and birds. In addition, automated drone detection systems need to be trained with ample amounts of data to provide high accuracy. Real-time detection is also necessary, but this requires highly configured devices such as a graphical processing unit (GPU). …