Physical Sciences and Mathematics Commons^™

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 …

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 …

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.

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 …

Linking Mathematical Models And Trap Data To Infer The Proliferation, Abundance, And Control Of Aedes Aegypti, Jing Chen, Xi Huo, Andre B. B. Wilke, John C. Beier, Chalmers Vasquez, William Petrie, Robert Stephen Cantrell, Chris Cosner, Shigui Ruan

Mathematics Faculty Articles

Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this paper, we develop a deterministic mosquito population model, estimate model parameters by using local entomological and temperature data, and use the model to calibrate the mosquito trap data from 2017 to 2019. We further use the model to compare the Ae. aegypti population and evaluate the impact of rainfall intensity …

Developing Confidence And Interest In Teaching Relevant Mathematical Modeling Lessons, Jacy Beck

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

What is mathematical modeling and how can inservice and pre-service teachers develop the skills and competencies necessary to increase confidence and interest in teaching relevant mathematical modeling lessons? Mathematical modeling is “the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions” (CSSM, 2010, p. 72). By providing students with an opportunity to engage in relevant mathematical modeling prompts, we provide them with transferable skills and knowledge. The aim of this paper will be to provide insight into the relevance of teaching mathematical modeling, provide resources for integrating modeling …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Mentoring Undergraduate Research In Mathematical Modeling, Glenn Ledder

Department of Mathematics: Faculty Publications

In writing about undergraduate research in mathematical modeling, I draw on my 31 years as a mathematics professor at the University of Nebraska–Lincoln, where I mentored students in honors’ theses, REU groups, and research done in a classroom setting, as well as my prior experience. I share my views on the differences between research at the undergraduate and professional levels, offer advice for undergraduate mentoring, provide suggestions for a variety of ways that students can disseminate their research, offer some thoughts on mathematical modeling and how to explain it to undergraduates, and discuss the challenges involved in broadening research participation …

Three Questions From Cctm Teachers About Mathematical Modeling, Robyn Stankiewicz-Van Der Zanden, Rachel Levy

Colorado Mathematics Teacher

This article shares three questions and answers about mathematical modeling in the classroom from an April 2020 online conversation with participants of a CCTM webinar. We hope that the answers to these questions will motivate teachers to embrace the value of implementing math modeling tasks, help students see the math all around them in the world, and empower future professionals to reach for the mathematical tools in their pockets to make data-driven decisions.

Modeling Dewetting, Demixing, And Thermal Effects In Nanoscale Metal Films, Ryan Howard Allaire

Dissertations

Thin film dynamics, particularly on the nanoscale, is a topic of extensive interest. The process by which thin liquids evolve is far from trivial and can lead to dewetting and drop formation. Understanding this process involves not only resolving the fluid mechanical aspects of the problem, but also requires the coupling of other physical processes, including liquid-solid interactions, thermal transport, and dependence of material parameters on temperature and material composition. The focus of this dissertation is on the mathematical modeling and simulation of nanoscale liquid metal films, which are deposited on thermally conductive substrates, liquefied by laser heating, and subsequently …

Modeling And Design Optimization For Membrane Filters, Yixuan Sun

Dissertations

Membrane filtration is widely used in many applications, ranging from industrial processes to everyday living activities. With growing interest from both industrial and academic sectors in understanding the various types of filtration processes in use, and in improving filter performance, the past few decades have seen significant research activity in this area. Experimental studies can be very valuable, but are expensive and time-consuming, therefore theoretical studies offer potential as a cost-effective and predictive way to improve on current filter designs. In this work, mathematical models, derived from first principles and simplified using asymptotic analysis, are proposed for: (1) pleated membrane …

Social Distancing And Testing As Optimal Strategies Against The Spread Of Covid-19 In The Rio Grande Valley Of Texas, Kristina P. Vatcheva, Josef A. Sifuentes, Tamer Oraby, Jose Campo Maldonado, Timothy Huber, Cristina Villalobos

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

At the beginning of August 2020, the Rio Grande Valley (RGV) of Texas experienced a rapid increase of coronavirus disease 2019 (abbreviated as COVID-19) cases and deaths. This study aims to determine the optimal levels of effective social distancing and testing to slow the virus spread at the outset of the pandemic. We use an age-stratified eight compartment epidemiological model to depict COVID-19 transmission in the community and within households. With a simulated 120-day outbreak period data we obtain a post 180-days period optimal control strategy solution. Our results show that easing social distancing between adults by the end of …

Mathematical Modeling In Finance, Owen Sweeney

Honors Projects

Financial tools play an integral role in the day-to-day lives of individuals and businesses. Many of these tools use predefined formulas to calculate items such as loan payments, interest and capital structure components. These tools do not usually provide the flexibility needed when new parameters are introduced. By utilizing mathematical modeling, these standard formulas can be derived and even improved to provide the needed flexibility.

Mathematical Modeling Of The Candida Albicans Yeast To Hyphal Transition Reveals Novel Control Strategies, David J. Wooten, Jorge Gómez Tejeda Zañudo, David Murrugarra, Austin M. Perry, Anna Dongari-Bagtzoglou, Reinhard Laubenbacher, Clarissa J. Nobile, Réka Albert

Mathematics Faculty Publications

Candida albicans, an opportunistic fungal pathogen, is a significant cause of human infections, particularly in immunocompromised individuals. Phenotypic plasticity between two morphological phenotypes, yeast and hyphae, is a key mechanism by which C. albicans can thrive in many microenvironments and cause disease in the host. Understanding the decision points and key driver genes controlling this important transition and how these genes respond to different environmental signals is critical to understanding how C. albicans causes infections in the host. Here we build and analyze a Boolean dynamical model of the C. albicans yeast to hyphal transition, integrating …

Modeling The Ecological Dynamics Of A Three-Species Fish Population In The Chesapeake Bay, Iordanka N. Panayotova, Maila B. Hallare

CODEE Journal

We present an inquiry-based project that is designed for a mathematical modeling class of undergraduate junior or senior students. It discusses a three-species mathematical model that simulates the biological interactions among three important fish species in the Chesapeake Bay: the prey Atlantic menhaden and its two competing predators, the striped bass and the non-native blue catfish. The model also considers the following ecological issues related to these three species: the overfishing of menhaden, the invasiveness of the blue catfish, and the harvesting of blue catfish as a method to control the population. A series of modeling scenarios are considered based …

Modeling The Bidirectional Glutamine/ Ammonium Conversion Between Cancer Cells And Cancer-Associated Fibroblasts, Peter Hinow, Gabriella Pinter, Wei Yan, Shizhen Emily Wang

Mathematical Sciences Faculty Articles

Like in an ecosystem, cancer and other cells residing in the tumor microenvironment engage in various modes of interactions to buffer the negative effects of environmental changes. One such change is the consumption of common nutrients (such as glutamine/Gln) and the consequent accumulation of toxic metabolic byproducts (such as ammonium/NH⁴⁾. Ammonium is a waste product of cellular metabolism whose accumulation causes cell stress. In tumors, it is known that it can be recycled into nutrients by cancer associated fibroblasts (CAFs). Here we present monoculture and coculture growth of cancer cells and CAFs on different substrates: glutamine and ammonium. …

Mathematical Modeling Of Nonlinear Problem Biological Population In Not Divergent Form With Absorption, And Variable Density, Maftuha Sayfullayeva

Acta of Turin Polytechnic University in Tashkent

В работе установлены критические и двойные критические случаи, обусловленные представлением двойного нелинейного параболического уравнения с переменной плотностью с поглощением в "радиально-симметричной" форме.Такое представление исходного уравнения дало возможность легко построить решения типа Зельдовоч-Баренбатт-Паттл для критических случаев в виде функций сравнения.

Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke

Journal of Humanistic Mathematics

While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …

Phase-Adjusted Estimation Of The Covid-19 Outbreak In South Korea Under Multi-Source Data And Adjustment Measures: A Modelling Study, Xiaomei Feng, Jing Chen, Kai Wang, Lei Wang, Fengqin Zhang, Zhen Jin, Lan Zou, Xia Wang

Mathematics Faculty Articles

Based on the reported data from February 16, 2020 to March 9, 2020 in South Korea including confirmed cases, death cases and recovery cases, the control reproduction number was estimated respectively at different control measure phases using Markov chain Monte Carlo method and presented using the resulting posterior mean and 95% credible interval (C_rI). At the early phase from February 16 to February 24, we estimate the basic reproduction number R₀ of COVID-19 to be 4.79(95% C_rI 4.38 - 5.2). The estimated control reproduction number dropped rapidly to R_c ≈ 0.32(95% C_rI …

Comparison Of Non-Prosthetic And Prosthetic Strides In A Pendulum-Based Model, Catherine T. Cronister

Student Scholarship

In this paper, we explore the differences in a non-prosthetic and prosthetic single stride. We accomplish this by developing a model based on a forced, triple pendulum. We use this model to describe a single stride and alter where the internal force comes from to simulate a prosthetic and non-prosthetic stride. We numerically solve our model with Matlab. We find that our model qualitatively represents the energy gap between a prosthetic and non-prosthetic stride. Our model also agreed qualitatively with alterations of the prosthetic designed to decrease the energy gap between the two strides.

Making Real-World Connections In High School Mathematics: The Effectiveness Of A Professional Development Program In Changing Teachers’ Knowledge, Beliefs, And Practices, Thad Ludlam Wilhelm

Wayne State University Dissertations

The study aimed to assess the impact of a professional development workshop at changing secondary mathematics teachers’ knowledge, beliefs, and practices related to real-world applications of algebra. It also addressed gaps in the research literature related to teacher knowledge of how algebra is used by professionals in non-academic settings and their beliefs about the relevance of algebra to their students’ lives. The observational study employed mixed methods. Principal components analysis was conducted on responses to an online questionnaire. Pre-test vs. post-test comparisons were made for workshop participants. Treatment vs. control comparisons were also made using a nationally representative random sample …

Formation Of Escherichia Coli O157: H7 Persister Cells In The Lettuce Phyllosphere And Application Of Differential Equation Models To Predict Their Prevalence On Lettuce Plants In The Field, Daniel S. Munther, Michelle Q. Carter, Claude V. Aldric, Renata Ivanek, Maria T. Brandl

Mathematics and Statistics Faculty Publications

American Society for Microbiology. Escherichia coli O157:H7 (EcO157) infections have been recurrently associated with produce. The physiological state of EcO157 cells surviving the many stresses encountered on plants is poorly understood. EcO157 populations on plants in the field generally follow a biphasic decay in which small subpopulations survive over longer periods of time. We hypothesized that these subpopulations include persister cells, known as cells in a transient dormant state that arise through phenotypic variation in a clonal population. Using three experimental regimes (with growing, stationary at carrying capacity, and decaying populations), we measured the persister cell fractions in culturable EcO157 …

An Individual-Carcass Model For Quantifying Bacterial Cross-Contamination In An Industrial Three-Stage Poultry Scalding Tank, Zachary Mccarthy, Ben Smith, Aamir Fazil, Shawn D. Ryan, Jianhong Wu, Daniel Munther

Mathematics and Statistics Faculty Publications

No abstract provided.

Examining Students’ Covariational Reasoning Through Mathematical Modeling Activities Embedded In The Context Of The Greenhouse Effect, Debasmita Basu

Theses, Dissertations and Culminating Projects

The greenhouse effect is one of the most pressing environmental as well as social issues of the present age. In news media and weather reports, most of the essential information about the phenomenon is expressed in forms of graphs and pictures. However, the interpretation of such graphs is challenging for students; they often focus on the shape of the graphs, overlooking the covariational relationships between the concerned quantities. Building on the framework of critical mathematics literacy and social justice mathematics, in this study I aimed to explore the power of dynamic mathematical modeling activities for engaging students in covariational reasoning …

Ph Dependent C-Jejuni Thermal Inactivation Models And Application To Poultry Scalding, Zachary Mccarthy, Ben Smith, Aamir Fazil, Jianhong Wu, Shawn D. Ryan, Daniel Munther

Mathematics and Statistics Faculty Publications

Campylobacter jejuni related outbreaks and prevalence on retail poultry products pose threats to public health and cause financial burden worldwide. To resolve these problems, it is imperative to take a closer look at poultry processing practices and standards. Using available data (D-values) on the thermal inactivation of C. jejuni we develop a comprehensive inactivation model, taking into account the variation of strain-specific heat resistance, experimental method, and suspension pH. Utilizing our C. jejuni thermal inactivation model, we study the poultry scalding process. We present a mechanistic model of bacteria transfer and inactivation during a typical immersion scald in a high-speed …

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 …

Mathematical Modeling And Classroom Discourse: A Case For Modeling-Specific Discussion Strategies, Ashley Dorlack, Hyunyi Jung, Sarah Brand, Samuel Franklin Gailliot

Mathematical and Statistical Science Faculty Research and Publications

No abstract provided.

Mathematical Modeling Experiences: Narratives From A Preservice Teacher And An Instructor, Sarah Brand, Hyunyi Jung

Mathematical and Statistical Science Faculty Research and Publications

Regardless of the benefits of engaging in mathematical modeling, few preservice teachers (PTs) have experienced mathematical modeling firsthand. This study offers an example of how to make sense of the interaction between the teaching and learning of mathematical modeling by examining a teacher educator’s decision making, her analysis of 36 PTs’ learning, and an in-depth narrative from a PT. Findings show the value of engaging with structurally relevant mathematical modeling tasks and considering social issues via mathematical modeling, resulting in task designs which aim to deepen students’ understanding of society and mathematics.

Modeling The Spread Of Disease, James Hollister

Essential Studies UNDergraduate Showcase

Mathematically modeling the spread of disease in a population is a focus among epidemiologists. Using an SIR model (susceptible, infected, and recovered), we can create a system of differential equations to help better understand how a disease spreads in a simple environment. However, if we are to create a more realistic environment, computer simulations may be necessary. We can use the results from these simulations to try and find ways to eradicate the disease as efficiently as possible. In this poster, we will present the SIR model, present a system of differential equations that describe the movement of disease in …

Mathematical Models, Patty Wagner, Marnie Phipps

Mathematics Grants Collections

This Grants Collection for Mathematical Models was created under a Round Nine ALG Textbook Transformation Grant.

Affordable Learning Georgia Grants Collections are intended to provide faculty with the frameworks to quickly implement or revise the same materials as a Textbook Transformation Grants team, along with the aims and lessons learned from project teams during the implementation process.

Documents are in .pdf format, with a separate .docx (Word) version available for download. Each collection contains the following materials:

• Linked Syllabus
• Initial Proposal
• Final Report