Physical Sciences and Mathematics Commons^™

Proof Of The Kresch-Tamvakis Conjecture, John Caughman, Taiyo S. Terada

Mathematics and Statistics Faculty Publications and Presentations

In this paper we resolve a conjecture of Kresch and Tamvakis.

Pre-Calculus: Thinking Deeply About Simple Things, Jacob Carter

Graduate Research Showcase

“Pre-Calculus: Thinking Deeply About Simple Things” is a research-based creative endeavor focused on designing a high-school pre-calculus course. This course aims to foster deep, meaningful thinking, as well as an appreciation of the values of diversity, equity, and inclusion in the math classroom. The course leverages students’ funds of knowledge to employ culturally responsive teaching methods to connect mathematical concepts to the students’ backgrounds, interests, and real-life situations. This course also integrates social-emotional learning to create an engaging and supportive learning environment for all students. By combining Peter Liljedahl’s “Building Thinking Classroom in Mathematics” approach with problem-based learning, the course …

Benford’S Law And Its Applications To Accounting, Lucy Wilson

Mathematics Student Projects

In this paper, we introduce the concept of Benford’s Law, which is the mathematical observation that in many naturally occurring numerical datasets, the leading digits are not evenly distributed. We actually find that smaller leading digits appear more often than larger ones. We will explore when and why this phenomenon occurs and how we can use statistical tests to determine how well a dataset conforms to Benford’s Law. We will also see how Benford’s Law can be used by auditors in the accounting field to catch potential fraud.

The Traveling Salesman Problem At Taylor University, Jonathan Jinoo Pawley

Mathematics Student Projects

What is the shortest route to walk to every residence hall on campus, beginning and ending with the same hall? This question can be considered by applying the Traveling Salesman Problem, an easy to understand yet hard to solve problem in the realm of discrete combinatorial optimization. The Traveling Salesman Problem is useful as an introduction to optimization problems, and it also has immensely practical applications. This paper will serve as an introduction to the computational difficulty of the Traveling Salesman Problem and will also explore various approximation algorithms. We will subsequently apply our new understanding of the theory to …

Assessing Controls On Ice Dynamics At Crane Glacier, Antarctic Peninsula, Using A Numerical Ice Flow Model, Rainey Aberle, Ellyn M. Enderlin, Hans-Peter Marshall, Michal Kopera, Tate G. Meehan

Geosciences Faculty Publications and Presentations

The Antarctic Peninsula's widespread glacier retreat and ice shelf collapse have been attributed to atmospheric and oceanic warming. Following the initial post-collapse period of retreat, several former tributary glaciers of the Larsen A and B ice shelves have been slowly re-advancing for more than a decade. Here, we use a flowline model of Crane Glacier to gauge the sensitivity of former tributary glaciers to future climate change following this period of long-term dynamic adjustment. The glacier's long-term geometry and speed changes are similar to those of other former Larsen A and B tributaries, suggesting that Crane Glacier is a reasonable …

Engaging Students With High-Stakes Problems, Deepak Basyal

Mathematics and Statistics

Engaging students in meaningful mathematics problem-solving is the intention of many education stakeholders around the world. Research suggests that the implementation of high-stakes problems in mathematics teaching is one way to strengthen students’ conceptual understanding. Many carefully crafted open-ended problems constitute high-stakes problems, and proper use of such problems in teaching and learning not only encourages learners’ flexible thinking but also helps detect their misconceptions. However, what is less practiced and understood is: how exactly one should aim to implement such problems in a classroom setting. Teaching pre-service middle school teachers for a few years using high-stakes (mostly open-ended problems) …

Book Review Of Inside Mathforum.Org: Analysis Of An Internet Based Education Community., Jose Ponce

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Inside Mathforum.org: Analysis of an Internet-Based Education Community, Wesley Shumar, Cambridge University Press, September 7, 2017, 1st Edition, 204 pages, ISBN: 9781108518345 (e-book).

Tribute To Gene Chase, Calvin Jongsma

Faculty Work Comprehensive List

Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

Faculty Work Comprehensive List

Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

Defining Characteristics That Lead To Cost-Efficient Veteran Nba Free Agent Signings, David Mccain

Honors Projects in Mathematics

Throughout the history of the NBA, decisions regarding the signing of free agents have been riddled with complexity. Franchises are tasked with finding out what players will serve as optimal free agent signings prior to seeing them perform within the framework of their team. This study hypothesizes that the adequacy of an NBA free agent signing can be modeled and predicted through the implementation of a machine learning model. The model will learn the necessary information using training and testing data sets that include various player biometrics, game statistics, and financial information. The application of this machine learning model will …

Electric Vehicle Uptake: What Factors Are Motivating The Shift For College-Aged And Older Groups?, Jake Cardines

Honors Projects in Mathematics

Electric vehicles (EVs) arguably are the most quickly expanding form of transportation as the world races toward a greener future with advanced technology and reduced reliance on fossil fuels. This study analyzes various expected inputs to motivating consumers of particular age groups to purchase EVs, including examination of how the idea of EV ownership is currently perceived and testing which factors influence it positively and negatively. Data collected from 113 survey respondents serves as the basis for determining the responsiveness of potential future EV owners to variables such as vehicle brand and charging availability, electric range, costs associated with purchase …

El Final Report: Undergraduate Summer Research Internships, Sophie Wu

SASAH 4th Year Capstone and Other Projects: Publications

In her final report, Sophie Wu discusses her two Undergraduate Summer Research Internships at Western University: the first in the Statistics and Actuarial Science department, concerning microinsurance, and the second, in the Mathematics department, concerning computational neuroscience.

Changing Nfl Playoff Overtime Rules To Create Equal Opportunities To Win A Game, Matthew Silvia

Honors Projects in Mathematics

The NFL has attempted to create fair overtime rules over the course of the past decade; however, this study is interested in determining what playoff overtime rule (or rules) could the NFL implement to result in outcomes where both teams have a relatively equal chance of winning a game. This study aims to find which overtime rules work best at minimizing the differences between teams who possess the ball first versus teams that kick the ball off to start an overtime period. By collecting various NFL statistics from ESPN.com and FantasyOutsiders.com, this study hopes to run multiple simulations of different …

Match Results And The Equity Value Of Publicly Traded Soccer Teams, Ryan Bebyn

Honors Projects in Mathematics

This study aims to examine the relationship between the match performance of publicly traded European soccer clubs and their stock price returns. It is important for investors, owners, and fans to understand how competitive factors both on and off the field affect the equity value of European club soccer teams. Competitive factors such as basic match results (Win, Loss, or Draw), rivalry matches, and international matches will be evaluated against the daily stock prices of publicly traded soccer clubs. A sample of teams traded on public exchanges will be used to analyze the effects of their matches on the daily …

Using Game Theory To Model Tripolar Deterrence And Escalation Dynamics, Grace Farson

Honors Theses

The study investigated how game theory can been utilized to model multipolar escalation dynamics between Russia, China, and the United States. In addition, the study focused on analyzing various parameters that affected potential conflict outcomes to further new deterrence thought in a tripolar environment.

A preliminary game theoretic model was created to model and analyze escalation dynamics. The model was built upon framework presented by Zagare and Kilgour in their work ‘Perfect Deterrence’. The model is based on assumptions and rules set prior to game play. The model was then analyzed based upon these assumptions using a form of mathematical …

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

Faculty Work Comprehensive List

Reviewed Title: Generations of Reason: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Math Department 2022-2023 Newsletter, Mathematics Department

Mathematics Newsletter

Welcome to our annual Mathematics Department Newsletter. We had an exciting year with many activities and accomplishments. Our students have received awards, attended conferences, conducted research, and have really contributed to the life of the department. Our faculty have had many accomplishments in teaching and scholarship. We conducted several events such as Alumni Night, hosted a guest speaker for the university community, had our Pi Mu Epsilon induction and awards ceremony, and much more. We have heard from several alumni and are happy to report what they are doing. Our Math Club has been becoming more active. On the curriculum …

Utilizing Markov Chains To Estimate Allele Progression Through Generations, Ronit Gandhi

Honors Theses

All populations display patterns in allele frequencies over time. Some alleles cease to exist, while some grow to become the norm. These frequencies can shift or stay constant based on the conditions the population lives in. If in Hardy-Weinberg equilibrium, the allele frequencies stay constant. Most populations, however, have bias from environmental factors, sexual preferences, other organisms, etc. We propose a stochastic Markov chain model to study allele progression across generations. In such a model, the allele frequencies in the next generation depend only on the frequencies in the current one.

We use this model to track a recessive allele …

How The Perceived Value Of Education, Parental Influences, And Students' Perceived Success Affect Post-Graduate Decisions, Valerie Blanchard

Honors Projects in Mathematics

While technical education has been enhanced in many ways over the past few decades, college is still the preferred post-graduate path for many students and is the societal norm. This study will analyze the value that students view in their career path that leads them to make their post-graduate decisions. The goal of this research is to better understand why students pursue college and how these decisions come to be with specific attention paid to the impact of gender, interests, and self-efficacy. This understanding can educate others about the gravity of social norms and can start conversations about how to …

The History Of The Enigma Machine, Jenna Siobhan Parkinson

History Publications

The history of the Enigma machine begins with the invention of the rotor-based cipher machine in 1915. Various models for rotor-based cipher machines were developed somewhat simultaneously in different parts of the world. However, the first documented rotor machine was developed by Dutch naval officers in 1915. Nonetheless, the Enigma machine was officially invented following the end of World War I by Arthur Scherbius in 1918 (Faint, 2016).

Developing Awareness Around Language Practices In The Elementary Bilingual Mathematics Classroom, Gladys Krause, Melissa Adams Corral, Luz A. Maldonado Rodríguez

Teaching and Learning Faculty Publications and Presentations

This study contributes to efforts to characterize teaching that is responsive to children’s mathematical ideas and linguistic repertoire. Building on translanguaging, defined in this article as a pedagogical practice that facilitates students’ expression of their understanding using their own language practices, and on the literature surrounding children’s mathematical thinking, we present an example of a one-on-one interview and of the circulating portion of a mathematics class from a second grade classroom. We use these examples to foreground instructional practices, for researchers and practitioners, that highlight a shift from a simplified view of conveying mathematics as instruction in symbology and formal …

Applying Expansive Framing To An Integrated Mathematics-Computer Science Unit, Kimberly Evagelatos Beck, Jessica F. Shumway

Publications

In this research report for the National Council of Teachers of Mathematics 2022 Research Conference, we discuss the theory of Expansive Framing and its application to an interdisciplinary mathematics-computer science curricular unit.

Oer Ancient Egyptian Numerals And Arithmetic Activity, Cynthia Huffman Ph.D.

Faculty Submissions

Many people are fascinated with ancient Egypt. The amazing, unique culture influenced many other civilizations and cultures. If you study the history of math, you will see how this influence included mathematics. Ancient Egypt also lasted an incredibly long time – over 3000 years. According to Egyptologist Bob Brier, “No civilization lasted so long, contributed so much, or repeatedly amazed as did ancient Egypt.”

In this Open Educational Resource activity, students will have the opportunity to learn about ancient Egyptian numerals and basic arithmetic. For motivation, the setting is a scribal school with each student using a clipboard, paper, and …

The Executive’S Guide To Getting Ai Wrong, Jerrold Soh

Asian Management Insights

It’s all math. Really.

Topological Data Analysis And Ant Interaction Networks, Adam Banatwala, Esther Rønn

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Esther Rønn ’23, Majors: Physics and Mathematics
Faculty Mentor: Dr. Laura Murray, Mathematics and Computer Science

Our research group used topological data analysis (TDA) to quantify the movement and behavior of ants in a colony.

We extracted higher dimensional networks from point cloud data collected from Dr. James Waters’ lab. Varying the proximity parameter in this construction gives a sequence of networks. We analyzed the enduring topological features of these networks, and how these features evolve over time as the ants move in the colony. Both the experimental and null model simulation data …

Classifications Of Transformations Of Km#Tn And Pm#Tn Via Symmetry Groups, Adam Banatwala, Jensen Barry, Mackenzie Maude

Mathematics & Computer Science Student Scholarship

Adam Banatwala ’22, Majors: Mathematics and Finance
Jensen Barry ’22, Majors: Biology and Mathematics
Mackenzie Maude ’22, Majors: Mathematics and Art History
Faculty Mentor: Dr. C. Joanna Su, Mathematics and Computer Science

One of the main topics in topology is the classification and comparison of shapes and surfaces. Since Spring 2020, our research group has been using symmetry groups to classify the 1- and 2-dimensional orientable and non-orientable closed surfaces.

First, the group worked on the symmetry groups of the 1- and 2-dimensional orientable closed surfaces; namely, the classification on V?? 1 (the one-point adjoint of n circles) …

The Biggest Loser: How Tanking In Professional Sports Impacts Fan Perception, Julia Ayres

Honors Projects in Mathematics

Professional sports teams are adored nationwide for their talents and the pride they bring to their city for their efforts. However, not all teams take this responsibility seriously and will lose on purpose, or tank, to gain a higher draft pick in the future. Although the long-term goals of tanking are to help the organization, many people take issue with athletes not putting in their best efforts in every game. Teams in both the NBA and NFL are guilty of tanking to gain better draft picks but not all have found success in this process. This leads to important questions …

Lines On A Smooth Projective Surface, Jordan Demoura

Mathematics & Computer Science Student Scholarship

Jordan DeMoura ’22
Major: Mathematics
Faculty Mentor: Dr. Su-Jeong Kang, Math

This research is to investigate lines on a smooth projective surface. A quadric surface contains two families of planes that provide a ruling of the surface. A cubic surface contains twenty-seven lines, and we provide a complete description of these lines for a Fermat cubic surface. Furthermore, under the Plucker embedding, we show that each family of the lines on a quadric surface corresponds to plane conic curves lying on complementary planes in the projective space of dimension five.

Vampires And Other Diseases: Stochastic Infection Dynamics Of Small Populations, Marijn Jaarsma

Honors Projects in Science and Technology

Mathematical models are powerful tools often applied in the field of epidemiology. The type and shape of the model will differ between different types of diseases. In this study, stochastic dynamical models are applied to the entertaining example of vampires, and the results of this analysis are compared to real-life diseases with small populations of infected. The data used comes from pop-culture depictions of vampires in literature, television shows, movies, and fan pages associated with these depictions. The aim of this study is to serve as an educational tool for modeling diseases with small populations to predict and control the …

Applied Math In Introductory Chemistry, Ji Kim, Grace Pai

Open Educational Resources

Students, particularly those who are non-science majors, often struggle with college-level science courses required for graduation due to the applied mathematics needed to successfully complete the course. This resource includes four activities on the topics of units and measurements, dimensional analysis, density, and gases. These topics were specifically designed to teach the mathematics embedded in these topics in a culturally responsive way. Throughout the activities, we incorporate these four elements of culturally relevant pedagogy (Ladson-Billings, 2009) in order to engage students in successfully solving basic mathematics in chemistry while promoting their interest in learning chemistry.