Physical Sciences and Mathematics Commons^™

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.

Eigenvalues And Approximation Numbers, Ryan Chakmak

CMC Senior Theses

While the spectral theory of compact operators is known to many, knowledge regarding the relationship between eigenvalues and approximation numbers might be less known. By examining these numbers in tandem, one may develop a link between eigenvalues and l^p spaces. In this paper, we develop the background of this connection with in-depth examples.

Gait And Postural Analysis In Healthy Young Adults And People With Parkinson's Disease, Aisha Joy Chen

CGU Theses & Dissertations

Postural analysis is the study of how the position of the body in any mode interacts with internal and external forces. This type of analysis is typically used to assess potential abnormalities in the balance control system and to understand how the balance control system changes with time. However, compared to other medical fields of study, postural analysis is relatively new [1]. In fact, although widely used in clinical and research studies, postural assessment methods are scientifically inaccurate, and some data collection methods are relatively expensive. A better understanding of the human balance control system could lead to more accurate …

Procuring Pediatric Vaccines In A Two-Economy Duopoly, Seongeun Lee, Susan E. Martonosi

Scripps Senior Theses

In this work, we aim to present an optimization model for vaccine pricing in a two-economy duopoly. This model observes the price dynamics between a high income country and a low income country that procure vaccinations through PAHO. This model is formulated to provide insights on optimal pricing strategy for PAHO to ultimately increase vaccine accessibility to low income countries. The objective is to satisfy the public demand at the lowest price possible, while providing enough profit for the vaccine manufacturers to stay in business. Using non-linear integer programming, the model results show that cross-subsidization occurs in PAHO vaccine procurement.

Radial Solutions To Semipositone Dirichlet Problems, Ethan Sargent

HMC Senior Theses

We study a Dirichlet problem, investigating existence and uniqueness for semipositone and superlinear nonlinearities. We make use of Pohozaev identities, energy arguments, and bifurcation from a simple eigenvalue.

Enhancing The Quandle Coloring Invariant For Knots And Links, Karina Elle Cho

HMC Senior Theses

Quandles, which are algebraic structures related to knots, can be used to color knot diagrams, and the number of these colorings is called the quandle coloring invariant. We strengthen the quandle coloring invariant by considering a graph structure on the space of quandle colorings of a knot, and we call our graph the quandle coloring quiver. This structure is a categorification of the quandle coloring invariant. Then, we strengthen the quiver by decorating it with Boltzmann weights. Explicit examples of links that show that our enhancements are proper are provided, as well as background information in quandle theory.

Mathematical Modeling Of Type 1 Diabetes, Gianna Wu

HMC Senior Theses

Type 1 Diabetes (T1D) is an autoimmune disease where the pancreas produces little to no insulin, which is a hormone that regulates blood glucose levels. This happens because the immune system attacks (and kills) the beta cells of the pancreas, which are responsible for insulin production. Higher levels of glucose in the blood could have very negative, long term effects such as organ damage and blindness.

To date, T1D does not have a defined cause nor cure, and research for this disease is slow and difficult due to the invasive nature of T1D experimentation. Mathematical modeling provides an alternative approach …

Free Market On The Free Way, Yuan Cheng

CGU Theses & Dissertations

Self-driving cars have the potential to decrease congestion and will probably become the future of efficient transportation. This dissertation presents a unique approach to implement sharing lanes on a freeway using the idea of option pricing. A macroscopic physical model (LWR) is implemented by adding noise to the speed which accounts for unexpected events. We then proceed to provide a fair price for lanes in real time.