# Physical Sciences and Mathematics Commons™

Articles 1 - 30 of 6699

## Full-Text Articles in Physical Sciences and Mathematics

Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau Jan 2024

#### Polygon Quadrature And Dodecagonal Tessellation With Pattern Blocks, Gunhan Caglayan, Ben Kamau

##### Journal of Humanistic Mathematics

The age-old challenge of polygon quadrature involves converting a polygon into a square of equal area. In this educational resource, we utilize pattern blocks, commonly employed instructional aids in K-12 education across the United States, to visually demonstrate the transformation of different equilateral and regular pattern block polygons into squares. This is achieved through the application of the area conservation principle and geometric congruence/similarity reasoning.

Jan 2024

#### Seating Groups And 'What A Coincidence!': Mathematics In The Making And How It Gets Presented, Peter J. Rowlett

##### Journal of Humanistic Mathematics

Mathematics is often presented as a neatly polished finished product, yet its development is messy and often full of mis-steps that could have been avoided with hindsight. An experience with a puzzle illustrates this conflict. The puzzle asks for the probability that a group of four and a group of two are seated adjacently within a hundred seats, and is solved using combinatorics techniques.

Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett Jan 2024

#### Undergraduate Mathematics Students Question And Critique Society Through Mathematical Modeling, Will Tidwell, Amy Bennett

##### Journal of Humanistic Mathematics

Mathematics can be used as a tool to question and critique society and, in doing so, give us more information about the world around us and how it operates. This however, is not a common perspective that is conveyed to students during their undergraduate mathematics coursework. This paper contributes to the understanding of how undergraduate mathematics students question and critique society via mathematical modeling tasks. In two courses at two universities, 27 mathematics majors and secondary preservice teachers engaged in the modeling process situated in authentic contexts to learn specific concepts and make mathematical connections across domains and disciplines. Both …

Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter Jan 2024

#### Sharing Four Biscuits Between Three People: An Illustrative Example Of How Mathematics Is Intertwined With Human Values, Lovisa Sumpter, David Sumpter

##### Journal of Humanistic Mathematics

Despite convincing arguments by mathematicians, philosophers, sociologists and machine learning practitioners to the contrary, there remains a widespread notion amongst many members of the general public (and some practitioners) that mathematics is neutral, that it is free from human values. One reason why this notion persists is that we lack clear-cut examples that demonstrate how mathematics and values are intertwined. In this paper, we offer one such example. In particular, we show that when sharing four biscuits between three people, several possible mathematical and ethical frameworks can be used. We demon- strate that different solutions—hiding one biscuit, arbitrarily sharing the …

Jan 2024

#### Gödel's Theorem In The Continuing Education Of Mathematics Teachers, Ana J. Lemes

##### Journal of Humanistic Mathematics

The notion of dépaysement épistémologique (epistemological disorientation) aims to capture the sense of disorientation when a learner is led to question their prior assumptions and understandings, generating uncertainty in a context in which they thought they had certain knowledge. This article describes an activity used with a group of practicing mathematics teachers in Uruguay that integrates elements of the history of mathematics related to Gödel’s incompleteness theorem, with the aim of provoking in the participants the experience of dépaysement épistémologique. Results show that several of the teachers participating in the activity felt dépaysement épistémologique, and this feeling triggered …

Jan 2024

#### Finding Your Mathematical Roots: Inclusion And Identity Development In Mathematics, Linda Mcguire

##### Journal of Humanistic Mathematics

This paper details a semester-long course project that has been successfully adapted for use in mathematics courses ranging from introductory level, general-education classes to advanced courses in the mathematics major. Through creating aspirational mathematical family trees and writing mathematical autobiographies, this assignment is designed to help battle belonging uncertainty, to challenge students to self-situate in relation to the history of mathematical and scientific knowledge, and to make visible a student’s developing identity in mathematics and, more broadly, in STEM.

The construction and scaffolding of the project, assignments, examples of student work, foundational readings, assessment and outcomes, and adaptation strategies for …

#### Full Issue - Engaging The World: Differential Equations Can Influence Public Policies

##### CODEE Journal

This is the full issue (front matter and all papers) of the Third CODEE Special Issue, with the theme, "Engaging the World: Differential Equations can Influence Public Policies."

#### Special Issue On Public Policy: Front Matter

##### CODEE Journal

The Front Matter contains the Editor-in-Chief's Foreword, a Dedicatory by Associate Editor Douglas Meade, a Preface by the Special Editors Bev West and Samer Habre, and the Table of Contents.

Seeing Eye To Eye? Comparing Faculty And Student Perceptions Of Biomolecular Visualization Assessments, Josh T. Beckham, Daniel R. Dries, Bonnie L. Hall, Rarchel M. Mitton-Fry, Shelly Engelman, Charmita Burch, Roderico Acevedo, Pamela S. Mertz, Didem Vardar-Ulu, Swati Agrawal, Kristin M. Fox, Shane Austin, Margaret A. Franzen, Henry V. Jakubowski, Walter R. P. Novak, Rebecca Roberts, Alberto I. Roca, Kristen Procko Jan 2024

#### Seeing Eye To Eye? Comparing Faculty And Student Perceptions Of Biomolecular Visualization Assessments, Josh T. Beckham, Daniel R. Dries, Bonnie L. Hall, Rarchel M. Mitton-Fry, Shelly Engelman, Charmita Burch, Roderico Acevedo, Pamela S. Mertz, Didem Vardar-Ulu, Swati Agrawal, Kristin M. Fox, Shane Austin, Margaret A. Franzen, Henry V. Jakubowski, Walter R. P. Novak, Rebecca Roberts, Alberto I. Roca, Kristen Procko

##### Chemistry Faculty Publications

While visual literacy has been identified as a foundational skill in life science education, there are many challenges in teaching and assessing biomolecular visualization skills. Among these are the lack of consensus about what constitutes competence and limited understanding of student and instructor perceptions of visual literacy tasks. In this study, we administered a set of biomolecular visualization assessments, developed as part of the BioMolViz project, to both students and instructors at multiple institutions and compared their perceptions of task difficulty. We then analyzed our findings using a mixed-methods approach. Quantitative analysis was used to answer the following research questions: …

Jan 2024

#### Nonlinear Dynamics Of Mountain Pine Beetle Populations: Discussion Of Forestry Policy, A Survey Of Existing Mathematical Models, And Code Base Demonstration, Scott A. Strong, Maya Maes-Johnson

##### CODEE Journal

This article presents existing mathematical models associated with mountain pine beetle populations in lodgepole pine forests, whose reproductive cycle requires the destruction of colonized host trees, decreasing timber availability/quality, and providing fuel sources for wildfires. With the existence of a positive-feedback loop with environmental warming, the need for intervention and management is clear. However, the legislative responses to the focusing events from our 2000-2010 North American epidemics are characterized as under-leveraged. While the reasons for this are multifaceted, increasing the capacity of STEM-informed individuals to take part in quantitative modeling of the underlying ecosystem generates awareness and provides pathways connecting …

#### Solar Panels, Euler’S Method And Community-Based Projects: Connecting Differential Equations With Climate Change, Victor J. Donnay

##### CODEE Journal

How does mathematics connect with the search for solutions to the climate emergency? One simple connection, which can be explored in an introductory differential equations course, can be found by analyzing the energy generated by solar panels or wind turbines. The power generated by these devices is typically recorded at standard time intervals producing a data set which gives a discrete approximation to the power function \$P(t)\$. Using numerical techniques such as Euler’s method, one can determine the energy generated. Here we describe how we introduce the topic of solar power, apply Euler’s method to determine the energy generated, and …

Jan 2024

#### Blue Whale And Krill Populations Modeling, Li Zhang

##### CODEE Journal

We present an intriguing topic in an undergraduate mathematical modeling course where predator-prey models are taught to our students. We describe modeling activities and the use of technology that can be implemented in teaching this topic. Through modeling activities, students are expected to use the numerical and graphical methods to observe the qualitative long-term behavior of predator and prey populations. Although there are other choices of predators and prey, we find that using blue whales and krill as predator and prey, respectively, would be most beneficial in strengthening our students' awareness of protecting endangered species and its impact on climate …

Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr Jan 2024

#### Odes And Mandatory Voting, Christoph Borgers, Natasa Dragovic, Anna Haensch, Arkadz Kirshtein, Lilla Orr

##### CODEE Journal

This paper presents mathematics relevant to the question whether voting should be mandatory. Assuming a static distribution of voters’ political beliefs, we model how politicians might adjust their positions to raise their share of the vote. Various scenarios can be explored using our app at https: //centrism.streamlit.app/. Abstentions are found to have great impact on the dynamics of candidates, and in particular to introduce the possibility of discontinuous jumps in optimal candidate positions. This is an unusual application of ODEs. We hope that it might help engage some students who may find it harder to connect with the more customary …

To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses, Christina Joy Edholm, Maryann Hohn, Nicole Lee Falicov, Emily Lee, Lily Natasha Wartman, Ami Radunskaya Jan 2024

#### To Open Or Not To Open: Developing A Covid-19 Model Specific To Small Residential Campuses, Christina Joy Edholm, Maryann Hohn, Nicole Lee Falicov, Emily Lee, Lily Natasha Wartman, Ami Radunskaya

##### CODEE Journal

In May 2020, administrators of residential colleges struggled with the decision of whether or not to open their campuses in the Fall semester of 2020. To help guide this decision, we formulated an ODE model capturing the dynamics of the spread of COVID-19 on a residential campus. In order to provide as much information as possible for administrators, the model accounts for the different behaviors, susceptibility, and risks in the various sub-populations that make up the campus community. In particular, we start with a traditional SEIR model and add compartments representing relevant variables, such as quarantine compartments and a hospitalized …

Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum Jan 2024

#### Fitting A Covid-19 Model Incorporating Senses Of Safety And Caution To Local Data From Spartanburg County, South Carolina, D. Chloe Griffin, Amanda Mangum

##### CODEE Journal

Common mechanistic models include Susceptible-Infected-Removed (SIR) and Susceptible-Exposed-Infected-Removed (SEIR) models. These models in their basic forms have generally failed to capture the nature of the COVID-19 pandemic's multiple waves and do not take into account public policies such as social distancing, mask mandates, and the ``Stay-at-Home'' orders implemented in early 2020. While the Susceptible-Vaccinated-Infected-Recovered-Deceased (SVIRD) model only adds two more compartments to the SIR model, the inclusion of time-dependent parameters allows for the model to better capture the first two waves of the COVID-19 pandemic when surveillance testing was common practice for a large portion of the population. We find …

Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?, Carrin Goosen, Mark I. Nelson, Mahime Watanabe Jan 2024

#### Applying The Sir Model: Can Students Advise The Mayor Of A Small Community?, Carrin Goosen, Mark I. Nelson, Mahime Watanabe

##### CODEE Journal

This is an account of a modelling scenario that uses the sir epidemic model. It was used in a third year applied mathematics subject. All students were enrolled in a mathematics degree of some type. Students are presented with the results of a test carried out on 100 individuals in a community containing 3000 people. From this they determined the number of infectious and recovered individuals in the population. Given the per capita recovery rate and making a suitable assumption about the number of infectious individuals at the start of the epidemic, they then estimate the infectious contact rate and …

#### Differential Equations For A Changing World:How To Engage Students In Learning And Applying Differential Equations, Biyong Luo

##### CODEE Journal

In this article, I share my decade-long experience teaching an intensive five-week summer Differential Equation course covering complex topics and tips for creating an interactive and supportive learning environment to optimize student engagement. This article provides my detailed approach to planning and teaching an asynchronous course with rigor and flexibility for each student. An interactive teaching approach and variety of learning activities will augment students’ mathematical fluency and appreciation of the importance of differential equations in modeling a wide variety of real-world situations with special attention to ways differential equations can be relevant to creating public policy.

Jan 2024

#### Raising Student Awareness Of Environmental Issues Via Writing Assignments With Differential Equations, Michelle L. Ghrist

##### CODEE Journal

In this paper, I discuss two environmentally-focused writing assignments that I developed and implemented in recent integral calculus and differential equations courses. These models of carbon storage and PCB’s in a river provide interesting applications of one-compartment mixing problems. The assignments were intended to focus student attention on sustainability concerns while also developing other essential skills. I discuss these assignments and their effect on my students’ technical writing and environmental awareness. Detailed introductory instructions and mostly complete solutions to these assignments appear in the appendices, to include sample student work.

Modeling Aircraft Takeoffs, Catherine Cavagnaro Jan 2024

#### Modeling Aircraft Takeoffs, Catherine Cavagnaro

##### CODEE Journal

Real-world applications can demonstrate how mathematical models describe and provide insight into familiar physical systems. In this paper, we apply techniques from a first-semester differential equations course that shed light on a problem from aviation. In particular, we construct several differential equations that model the distance that an aircraft requires to become airborne. A popular thumb rule that pilots have used for decades appears to emanate from one of these models. We will see that this rule does not follow from a representative model and suggest a better method of ensuring safety during takeoff. Aircraft safety is definitely a matter …

Ode Models Of Wealth Concentration And Taxation, Bruce Boghosian, Christoph Borgers Jan 2024

#### Ode Models Of Wealth Concentration And Taxation, Bruce Boghosian, Christoph Borgers

##### CODEE Journal

We refer to an individual holding a non-negligible fraction of the country’s total wealth as an oligarch. We explain how a model due to Boghosian et al. can be used to explore the effects of taxation on the emergence of oligarchs. The model suggests that oligarchs will emerge when wealth taxation is below a certain threshold, not when it is above the threshold. The underlying mechanism is a transcritical bifurcation. The model also suggests that taxation of income and capital gains alone cannot prevent the emergence of oligarchs. We suggest several opportunities for students to explore modifications of the model.

Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier Jan 2024

#### Using A Sand Tank Groundwater Model To Investigate A Groundwater Flow Model, Christopher Evrard, Callie Johnson, Michael A. Karls, Nicole Regnier

##### CODEE Journal

A Sand Tank Groundwater Model is a tabletop physical model constructed of plexiglass and filled with sand that is typically used to illustrate how groundwater water flows through an aquifer, how water wells work, and the effects of contaminants introduced into an aquifer. Mathematically groundwater flow through an aquifer can be modeled with the heat equation. We will show how a Sand Tank Groundwater Model can be used to simulate groundwater flow through an aquifer with a no flow boundary condition.

#### Coalescence: A Carnivore Coexistence Curriculum That Braids Indigenous & Western Ecological Knowledge Into A Relevant And Experiential Learning Opportunity For Youth, Stephanie Anne Barron

##### Graduate Student Theses, Dissertations, & Professional Papers

As grizzly bears (Ursus arctos horriblis) begin to reoccupy more of their historic range, and as humans and large carnivore populations continue to increase, incidences of human carnivore conflict are on the rise. A decolonial curriculum designed in collaboration with the Confederated Salish and Kootenai Tribe’s wildlife biologists stands to increase awareness of Indigenous ecological knowledge and teach youth about the importance of coexistence with carnivores. Additionally, this project could greatly influence youth perceptions of grizzly bears and other large carnivores. This research project examines the development and implementation of a carnivore coexistence curriculum for youth that is guided by …

Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage Dec 2023

#### Analyzing A Smartphone Battle Using Bass Competition Model, Maila Hallare, Alireza Hosseinkhan, Hasala Senpathy K. Gallolu Kankanamalage

##### CODEE Journal

Many examples of 2x2 nonlinear systems in a first-course in ODE or a mathematical modeling class come from physics or biology. We present an example that comes from the business or management sciences, namely, the Bass diffusion model. We believe that students will appreciate this model because it does not require a lot of background material and it is used to analyze sales data and serve as a guide in pricing decisions for a single product. In this project, we create a 2x2 ODE system that is inspired by the Bass diffusion model; we call the resulting system the Bass …

Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia Dec 2023

#### Reducing Food Scarcity: The Benefits Of Urban Farming, S.A. Claudell, Emilio Mejia

##### Journal of Nonprofit Innovation

Urban farming can enhance the lives of communities and help reduce food scarcity. This paper presents a conceptual prototype of an efficient urban farming community that can be scaled for a single apartment building or an entire community across all global geoeconomics regions, including densely populated cities and rural, developing towns and communities. When deployed in coordination with smart crop choices, local farm support, and efficient transportation then the result isn’t just sustainability, but also increasing fresh produce accessibility, optimizing nutritional value, eliminating the use of ‘forever chemicals’, reducing transportation costs, and fostering global environmental benefits.

Imagine Doris, who is …

Dec 2023

#### How To Intercept A High-Speed Rocket With A Pair Of Compasses And A Straightedge?, Yagub N. Aliyev

##### CODEE Journal

In this paper a nonlinear differential equation arising from an elementary geometry problem is discussed. This geometry problem was inspired by one of the proofs of the first remarkable limit discussed in a typical first semester undergraduate Calculus course. It is known that the involved differential equation can be reduced to Abel’s differential equation of the first kind. In this paper the problem was solved using an approximate geometric method which constructs a piecewise linear solution approximation for the curve. The compass tool of GeoGebra was extensively used for these constructions. At the end of the paper, some generalizations are …

Dec 2023

#### Centering Equity In Stem Teaching: Stem Ideas That Change The World, Ileana Vasu

##### Feminist Pedagogy

No discussion on equity/inequity makes sense without bringing power into that discussion. As instructors we need to ask questions such as “who decides and controls what knowledge is”, “whose identities are empowered and whose are erased”, “who has access and opportunity and who doesn’t”. Traditional teaching in STEM, including mathematics, assumes knowledge is objective, transmittable, repeatable to everyone. When educators follow a traditional curriculum, just like their teachers before them, they do so thinking their methods ensure equality and objectivity. These practices not only deny the role that Western patriarchal cultures have played in creating these so-called equitable practices, but …

Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price Dec 2023

#### Building Community, Competency, And Creativity In Calculus 2: Summary Of A Pilot Year Of Project Implementation, Jennifer Beichman, Candice R. Price

##### Feminist Pedagogy

In light of the COVID-19 pandemic, instructional modes at our institution moved to fully online and remote, then fully online but on campus, and back to in-person learning in fall 2021. To combat perceived issues in student engagement, we piloted using group projects in place of exams at the natural content break points in Calculus 2.

The Underrepresentation Of Black Females In Cybersecurity, Makendra Latrice Crosby Dec 2023

#### The Underrepresentation Of Black Females In Cybersecurity, Makendra Latrice Crosby

The significance of cybersecurity methods, strategies, and programs in protecting computers and electronic devices is crucial throughout the technological infrastructure. Despite the considerable growth in the cybersecurity field and its expansive workforce, there exists a notable underrepresentation, specifically among Black/African American females. This study examines the barriers hindering the inclusion of Black women in the cybersecurity workforce such as socioeconomic factors, limited educational access, biases, and workplace culture. The urgency of addressing these challenges calls for solutions such as education programs, mentorship initiatives, creating inclusive workplace environments, and promoting advocacy and increased awareness within the cybersecurity field. Additionally, this paper …

(R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun . Dec 2023

#### (R2054) Convergence Of Lagrange-Hermite Interpolation Using Non-Uniform Nodes On The Unit Circle, Swarnima Bahadur, Sameera Iqram, Varun .

##### Applications and Applied Mathematics: An International Journal (AAM)

In this research article, we brought into consideration the set of non-uniformly distributed nodes on the unit circle to investigate a Lagrange-Hermite interpolation problem. These nodes are obtained by projecting vertically the zeros of Jacobi polynomial onto the unit circle along with the boundary points of the unit circle on the real line. Explicitly representing the interpolatory polynomial as well as establishment of convergence theorem are the key highlights of this manuscript. The result proved are of interest to approximation theory.

#### Southern Rio Grande Rift Kinematics And Geochronology, Big Bend Fold Geometry, And The Use Of Real Data In Geoscience Education: Contributions To The Understanding Of Big Bend Geology And To Public Geoscientific Literacy, Jessica Kelsch

##### Open Access Theses & Dissertations

The Big Bend region of Trans-Pecos Texas preserves a rich record of Rio Grande rifting and Laramide-age contraction that provide intrigue to national and state park visitors and field trips for undergraduate geology students. Despite its well-exposed geologic record, the Big Bend region remains an underutilized natural laboratory for studying these two tectonic events. This dissertation combines structural studies of Rio Grande rift and Laramide structures with public outreach and geoscience education studies focused on the Big Bend region. In Chapter 2, existing extensional-kinematic studies from parts of this region are compiled with new fault kinematic and U-Pb geochronologic data …