15-minute talks are invited from all attendees on any mathematical topic. Papers submitted to Contributed Papers will be organized by subject as best as possible and scheduled during the Friday afternoon and Saturday morning paper sessions.
Please consider looking at the Special Sessions first to see if your paper would fit well into one of those sessions.
This paper investigates the impacts of automation technology on the employment rates of customer service representatives in the United States. While automation is recognized as a significant driver of economic growth, enhancing productivity and living standards, it simultaneously poses substantial challenges for the workforce. This duality raises public concerns regarding job displacement and the potential for increased unemployment in low-skilled positions. Utilizing R software for data analysis, the study draws on employment figures from the U.S. Bureau of Labor Statistics(https://www.bls.gov/oes/current/oes434051.htm) covering May 2011 to May 2022. The research focuses on the Business Support Service Industry, where customer service roles are prevalent, and analyzes percentage changes in employment figures to assess the risks associated with automation. Preliminary findings indicate a projected decline of 5% in customer service employment from 2022 to 2032. The paper underscores the critical need for upskilling and reskilling initiatives to prepare the workforce for the challenges posed by advancing automation technology and suggests that proactive measures are essential to mitigate the adverse effects on employment.
View Submission
There are multiple interpretations for the linear regression coefficients, ci, that result from the linear approximation of an output vector y based on multiple input vectors xi (i = 1 to n). A concise mathematical interpretation for the ci can be obtained by decoupling the input/output system via the techniques of random data analysis. In such case, each ck can be reinterpreted as the correlation coefficient resulting from the linear approximation of the conditioned output for y based solely on the conditioned input for xk. Here, conditioning refers to the removal of the linear contributions of the remaining inputs from both xk and y. In other words, ck is the correlation coefficient resulting from the single input/output system consisting of the residual of xk and the residual of y when the linear contributions of the remaining variables xi (i ≠ k) are eliminated from the system.
View Submission
While studying some inequalities of fractions, we encounters a new value. For fractions
View Submission
As a math faculty member in an art and design school, I find the task of making mathematics accessible, relevant, and maybe even fun to our students to be uniquely challenging. This is especially true in our department’s MATH 100 course, which many students use to fulfill the math and natural science requirements for majors ranging from painting and illustration to fashion marketing and jewelry design. Unsurprisingly, hands-on projects and student-centered activities encouraging inquiry-based exploration help students connect math with their respective creative disciplines and overcome the math-related anxiety many of them bring to the classroom. I will share two projects I used in our MATH 100 and math 104 classes, indicating how these projects can be adapted to suit the needs of students in general education math classes at various institutions.
View Submission
This research delves into how climate change can affect Belize's sugar cane industry, increasing market, environmental, and credit risks. Belize is a small Caribbean country whose geographical location makes it vulnerable to various climatic events. This study aims to inform its audiences of the impact these natural phenomena have on the country's agricultural sector through an examination of the sugar cane industry. By utilizing a combination of historical data, case studies, and industry research, the research aims to assess the resultant market risks. By integrating quantitative assessments and qualitative perspectives, the study seeks to quantify and qualify the implications of these market dynamics. The outcomes of this research can reignite the discussion on minimizing the impact these storms have on the farmers and overall industry.
View Submission
The standard U.S. voting methods of plurality and ranked choice (or instant runoff) voting are susceptible to significant voting failures, including Condorcet and majority failures as well as monotonicity and no-show paradoxes. We investigate alternative ranked choice voting systems relating to the points-based Borda count which avoid monotonicity paradoxes, particularly variations based on how partial ballots are counted and on extending the values of the points assigned to each rank in the ballot. In this talk, we will discuss which voting failures are possible for each variation and then present an empirical study of 421 U.S. ranked choice elections from 2004 to 2023 where we determined the frequency of voting failures when using five Borda variations.
View Submission
I spoke at this meeting in 2024 on properties of the Fibonacci sequence in regards to a Math for the Arts class project. This year, I have a follow up regarding properties of the Tribonacci sequence: a recursive sequence in which the next term is the sum of the previous three terms, as opposed to the previous two for the Fibonacci sequence. In this talk I will go over properties of the Fibonacci sequence and show how some generalize to the Tribonacci sequence. This is join work with undergraduate student Logan Moore.
View Submission
A digraph
View Submission
The Astronomical Clock at Prague was built in 1410, with later additions, and is beautifully preserved and fully functioning. It shows time “by the sun,” as marked on an astrolabial dial, and also time “metronomically,” with an hand going round once every twenty-four hours. After explaining the (admirable) features of the astronomical clock, we list the sequence of departures from scientific sensibility that gave rise to the (not so admirable) modern clock as we know it now.
View Submission
In this session, we will share effective strategies for fostering active student engagement in introductory math courses at Georgia State University. Many of our students, primarily from early college backgrounds, are eager to pursue their major programs but often struggle to connect with prerequisite math courses. To bridge this gap, we have developed and implemented a range of dynamic teaching methods, both in and outside the classroom, that cultivate a community spirit and foster a deeper connection to the material. We will spotlight two proven, in-class techniques that have successfully maintained student engagement and motivation throughout the semester. Attendees will leave with actionable insights and practical strategies to transform their own classrooms into interactive, inspiring environments that support student success and enthusiasm for learning.
View Submission
We propose a CUSUM-based testing procedure to sequentially monitor structural changes in Autoregressive Distributed Lag (ARDL) models using a penalized algorithm. Initially, this approach leverages historical panel data to simultaneously perform variable selection and estimation through a penalization method applied to the ARDL model. To detect any change point when new data is introduced, we conduct tests based on the CUSUM statistics. The consistency of this method, along with the oracle property of the resulting regularized estimators, is thoroughly examined. Additionally, we establish the asymptotic properties of the test statistics under both the null and alternative hypotheses. Simulations are carried out to demonstrate the effectiveness of the proposed method, and a real data application is presented to illustrate the detection procedure.
View Submission
Should faculty be concerned about cheating in online math classes? Is it worth our time and energy? Issues can range from students sharing information to having someone else take the class completely. We look at research on how serious the problem is, and we look at ways to discourage cheating and promote academic integrity. We discuss the pros and cons of proctoring using LockDown Browser and similar tools and examine alternative assessment methods.
View Submission
A configuration space models
View Submission
This talk investigates the enumeration of spanning forests in complete graphs, where each tree contains a fixed set of vertices. We begin with an overview of how the Tree function (Lambert W function) can be used to count spanning forests with a single fixed vertex per tree. Building on this foundation, we demonstrate how this approach can be extended to more complex fixed vertex sets, potentially revealing broader implications of the method. (This work was done in collaboration with Daniel Pinzon and Daniel Pragel at GGC.)
View Submission
A spanning forest of a graph G is an acyclic spanning subgraph of G. When a spanning forest has a single connected component, it is referred to as a spanning tree. A well known theorem from Kirchhoff uses the Laplacian Matrix of G to count the number of spanning trees of G. We extend this method to spanning forests.
View Submission
We recently developed a learning assistants pilot program in which we train and mentor a team of undergraduate learning assistants to provide additional support for students in our calculus 1 and introductory statistics courses. The learning assistants attend each class to help facilitate active learning, promote metacognitive approaches, and help students adapt to new technologies in the courses. They also run weekly supplemental instruction sessions that provide structured and peer-led review of course content. After two semesters, feedback on the pilot program has been very positive, with students, learning assistants, and professors all reporting high satisfaction. In an end-of-semester survey, 60% of students who attended supplemental instruction sessions reported them being very helpful and 93% said they were at least somewhat helpful. Students largely said they would recommend sections with learning assistants and attendance of supplemental instruction sessions to future students. In this talk we discuss how we created the program and share further survey results demonstrating the positive impact that this program is having on calculus 1 and introductory statistics students at our university.
View Submission
In a course graded with Standards-Based Grading, students are given multiple opportunities to demonstrate proficiency in the course standards, often on exams where each problem is labeled with which standard it assesses. One drawback of Standards-Based Grading is that even though each problem is easier to grade than when using points-based grading, the increased number of exams can lead to a significant burden on the instructor’s time. Another concern with Standards-Based Grading is that since there is no partial-credit, students who have a basic but not a deep understanding of many of the standards may not meet enough standards to earn a passing grade. To address both of these issues, I chose a selection of standards to become “Double-M standards,” which are standards that appear twice on each exam, allowing for fewer total exams. Often, one of the problems would focus more on the basics of the standard and the other require a deeper understanding. In order to earn an A, students would sometimes need to answer both problems, to show they had a deeper understanding of the material. In this presentation, I will discuss how I implemented this strategy and how it worked out during the Fall 2024 semester in my Precalculus courses.
View Submission
The author will present a small collection of strategies for face-to-face and synchronous online courses that run in half-session, summer half-session, May-mester, and other shortened formats. All strategies can help mitigate the "drinking from a firehose" effect of accelerated content pacing and long class meetings. These strategies range from big to small, including a game-changing structural shift in content delivery, a few ways to help students manage their progress and feel empowered, and some "grab-and-go" ideas that can be implemented easily in any course.
View Submission
Error analysis is an instructional strategy in which students are asked to identify, analyze, and correct errors in problems that contain intentional mistakes. Error analysis has many potential benefits, including enhancing critical thinking skills, promoting a deeper understanding of concepts, cultivating a growth mindset, and fostering collaboration and communication. This presentation will discuss how error analysis activities were implemented in a Precalculus course.
View Submission
A flipped learning approach was implemented in my college trigonometry course. Before the start of the semester, the Canvas course site was redesigned to include video(s), PowerPoint, and other materials for each class meeting. Students were expected to watch the video(s) and/or study the PowerPoint prior to class, write down their study notes and questions, and submit their notes to the instructor at the beginning of class. During the first 15 minutes or so of class, the main points of the topics were addressed, and the students’ questions were answered. Then students worked on a worksheet in groups. While the students worked in groups, the instructor walked around to check for and answer any question they might have. At the end of class, worksheets were collected for grading. The previously graded worksheets were also returned to students at the end of class so that if there were any problems on the graded worksheets, The instructor could discuss them with students individually. The flipped learning approach showed very promising results: 1. Class attendance was improved. A traditional face-to-face class the instructor had taught has about 50% attendance rate. This is especially the case after midterm. But the flipped class had a higher attendance rate – almost 100% before midterm and 87.5% or better after midterm. The high attendance rate was mainly due to the requirements that students must work on a worksheet as groups and submit it at the end of class. 2. Students’ participation was increased, and thus active learning was achieved. While working on their worksheets in groups, students have more opportunities to communicate their ideas with each other. This helped students not only to understand the subject matters better, but also improve their communication skills, stimulate their interest in the subject, and sort the concepts involved straight and clear. 3. The flipped approach resulted in better learning outcomes and a lower DWF rate. 50% of the class received an A grade, 25% of students received a B, and another 25% students received a C, and thus a 100% passing rate was achieved.
View Submission
Fraud detection is a critical application of machine learning in the financial sector. It aims to find out fraud transactions with minimal impact on legitimate transactions. This project uses logistic regression, one of the most popular classification algorithms, to detect fraudulent transactions in a highly imbalanced credit card transaction dataset. This data contains 284,807 transactions, of which only 492 are fraudulent (Class 1), which accounts for less than 0.2% of the total data. This dataset had a highly imbalanced distribution between the classes, with only a tiny fraud class, which usually creates issues in developing an effective predictive model. This project will utilize various techniques, including SMOTE and threshold tuning of the decision, for better model performance and a balanced trade-off between precision and recall for the minority class.
View Submission
This paper examines the potential risks and advantages of Microsoft's strategic shift away from console development towards software development and the growth of Xbox Game Pass. Microsoft's recent announcement of releasing Xbox exclusives on rival consoles has sparked speculation about their future direction in the gaming industry. The study utilizes a multidimensional approach, combining data from sources such as Kaggle, news outlets, and legal proceedings to analyze the landscape of the video game and video streaming industries. The risks identified include potential losses in console and software sales, customer reluctance to subscribe to the platform on rival consoles, and the possibility of cloud gaming platforms failing all in relation to their potential losses. While the risk of console sales is considered low due to historical trends and Microsoft's console pricing strategy, the risk associated with software sales is more uncertain due to the fact that Microsoft makes money from third-party sales on their hardware. The risk of crossover appeal is considered low, as Microsoft already supports games on other consoles through acquisitions and now holds some of the most successful franchises in history. The risk of cloud gaming failing is also deemed low, given the industry's transition to digital and cloud-based gaming and Microsoft’s unique advantage in the industry. Considering these risks and opportunities, it is recommended that Microsoft seriously consider focusing on Game Pass and leaving the console space to leverage cross-platform availability and tap into a wider customer base.
View Submission
The family of cycloid curves are generated in two different ways in the Euclidean plane: following a tack in a wheel rolling around a circular track and following a tack in a bungee cord whose ends are held by two runners on a circular track. What happens in hyperbolic space? Do the two approaches yield the same curve? Come and find out!
View Submission
Collaborative work is an essential part of learning and for the past couple of years I have tried to make it essential for all my classes. I want my students to feel that benefit not just when they work on some problems during class time or outside of the class for a group assignment, but also to experience the benefit of group collaboration during assessment time. In all my applications classes I have unit assessments during semester and each such assessment has an individual and a group component. This presentation will look into how I use group corrections and review for my unit tests and how I use that to strengthen the group relations, making my students feel more confident while learning to trust themselves and their group mates. I will also talk about how I determined a way of seeing if there is an improvement in my students’ work and how I used their results to motivate them to challenge themselves and their teammates
View Submission
A ropes course consists of a sequence of physical challenges that require participants to maneuver through obstacles constructed of ropes, cables, and wood. Successfully navigating these courses necessitates careful consideration of the route taken through each challenge. The objective is to participate in every obstacle without retracing your steps; thus, an effectively designed ropes course can be likened to an Euler path or circuit. Regrettably, course designers often lack an understanding of the mathematical principles that underpin these structures. In this presentation, I will elaborate on a class activity where my students, who are pursuing degrees in art and design, acquire fundamental concepts of graph theory by creating their own ropes course.
View Submission
The MPAACT project is a collaborative effort across several universities in the UNC system to increase the success of African American males in introductory math courses. This talk will discuss the design of the project, including advising, mentoring, and corequisite support courses for introductory math classes. We will also discuss preliminary findings from data collected from the students and instructors of the support courses. Finally, we will share some challenges faced and lessons learned during the implementation.
View Submission
During the 2024 calendar year, I transitioned my calculus classes from a traditional points-based grading system to a mastery grading system. In this talk, I describe my implementation of mastery grading in these classes, including how mastery of learning objectives was measured, the process for reattempting learning objectives, and the determination of final grades. I will also examine how students’ final grades under the new system compare to data from several previous years of teaching the same classes at the same institution with a points-based system.
View Submission
Experiments in the field of Electrochemistry demonstrate that sound waves act as a catalyst for chemical reactions. A model is developed using conservation of momentum and mass, a boundary motion equation, and a surface tension equation. Chemically, it is clear that the catalytic phenomenon is derived from the sound waves and how they are affected by the top boundary in the cell. When combining all four equations we arrive at a boundary condition that strictly involves the top boundary. Throughout the problem a self-adjoint invertible operator derived in the top (Neumann) boundary condition is established. Then a discussion ensues regarding regularity and formalizing all other boundary and initial conditions. These conditions are then applied to the wave equation. The specific chemical reactions where this phenomenon is observed can be found in batteries, capacitors, and solar cells. The reaction takes place at an interface or boundary in each device. Making these devices more efficient can help decrease our negative impact on the environment.
View Submission
Over-dispersion has been well-known often besetting counting data analysis. In this talk, we assume that data follow the quasi-likelihood distribution that the variance is proportional to a known function of the mean, such that the scale parameter captures over-dispersion. When data fit the generalized linear models, we propose the generalized Huber’s condition, under which the root for inference based on quasi-likelihood estimation converges weakly, along with the other regularity conditions. Based on the large-sample approximation, we apply the simultaneous confidence interval method to the Salmonella data obtained from a mutagenicity test, using the proposed theory.
View Submission
We begin our discussion with a brief summary of methods for determining the Galois groups of cubics & quartics. This discussion will lead us to the notion of resolvents which is a central tool in the computation of Galois groups. We then apply these tools to the family of irreducible
View Submission
This study employs a numerical method for pricing Asian options using the finite difference methods. It approximates the partial differential equation. The price of the option price is obtained by discretizing the underlying asset price and time dimensions into a grid, allowing for the calculation of the option value based on the average price of the underlying asset over a specified period. This provides a robust and flexible tool for evaluating complex Asian option structures.
View Submission
Transcatheter aortic valve replacement (TAVR) is the implantation of an artificial aortic heart valve without an open-heart surgery. Computer modeling and simulation is an important tool in the process of transcatheter aortic valve (TAV) device design, regulatory approval, and indication in the care of specific patients, since there are still many open questions surrounding post-implantation complications. Improved computational models beyond those in the existing literature have the ability to provide more accurate performance predictions for individual patients. We present computational fluid-structure interaction models of TAVs using the immersed finite element-difference method. We perform dynamic simulations of crimping and deployment of the devices as well as their behavior across the cardiac cycle in a patient-specific aortic root anatomy reconstructed from CT image data. These IFED simulations incorporate biomechanics models fit to experimental tensile test data and automatically capture the contact within the devices and between the stents and native anatomies. We apply realistic driving and loading conditions based on clinical measurements of human ventricular and aortic pressures and flow rates, and our models provide informative clinical performance predictions, such as pre- and post-procedure transvalvular pressure differences, detailed flow patterns, leaflet dynamics, and valve orifice areas.
View Submission
Pythagorean Triples such as (3,4,5) and (5,12,13) are a familiar topic in college mathematics. They represent integer sided right triangles, as well as rational points on the unit circle (eg (3/5,4/5), (5/13, 12/13)) and integer vectors with integer lengths (eg (3,4), (5,12)). This talk discusses extensions of these ideas to higher dimensions: Pythagorean 4-ples, 5-ples, n-ples. Though these extensions are not new (for example they can be found in wikipedia), they are not nearly as well known as they deserve to be.
View Submission
COVID-19 is a viral disease that began impacting the world in the latter part of 2019. In early 2020, the world would be in a state of pandemic due to the rapid spread of the disease. Statistical analysis has been an extremely useful tool in determining the impact of COVID-19. Some discussion about the COVID-19 pandemic is how medical and non-medical factors can influence i the severity of the infection of a person. A case study was conducted regarding cases that occurred in Wake County, North Carolina. The relationship between demographic factors (age, sex, and race) and both ICU admittance and death were investigated using the chi-square test of association and binary logistic regression. Age and race were determined to have some significant relationship with severe cases of COVID-19 while sex did not. Binary logistic regression also produced model equations that can be utilized to predict the likelihood of ICU admittance or death of an individual as the result of COVID-19 based on these factors.
View Submission
Machine learning algorithms, such as neural networks, are rapidly gaining popularity as tools for research in pure mathematics. In one application, a classifier is trained on a set of multiplication tables with the goal of detecting property P, where P may be an algebraic property such as commutativity or associativity. We present evidence that relatively small neural networks can solve these problems with high accuracy. We also analyze these models by varying the structure of the training data and show that they likely achieve this accuracy by detecting consequences of property P, rather than property P itself.
View Submission
In this talk, I will describe the Preceptor Program in Mathematics at Mercer University. Topics will include the motivation for the program, the structure of the program, and the benefits of the program. In addition, plans for the improving the program will be discussed.
View Submission
Adopting a new mode of instruction or a new mode of assessment can feel intimidating and isolating as a faculty member. Given the chance to do this with a colleague, I embraced co-teaching as a chance to innovate. Our partnership combined my active learning strategies with my colleague’s expertise in standards-based learning, allowing us to explore how these approaches complemented one another. In this talk, I will share how co-teaching benefited my students and me. Some benefits of co-teaching were expected, but some were only realized in retrospect.
View Submission
Statistical network models are used across the sciences and social sciences in settings such as modeling microbiomes and understanding protein interactions in biology and understanding friendships and strategic alliances in the social sciences. The
View Submission
The Fubini numbers (aka ordered Bell numbers) F_n (A000670) count the number of ways n runners can place in a race, with ties. In this talk, we consider two refinements of F_n: first, by grouping placements by the number of pairs of runners where the runner with the higher bib finishes before a runner with a lower bib; second, by how many runners tie at each place. The former refinement leads to a polynomial refinement of F_n and the latter leads to a symmetric function refinement of F_n. We derive simple generating functions and recurrence relations for both refinements. Moreover, we show that the symmetric function results implies the polynomial results through a general theory on word enumerators. We further view these results in the same sphere of results of Konheim--Weiss (1966) and Haiman (1994) on parking functions by interpretting Fubini words as unit interval parking functions of Harris--Hadaway (2021) and Bradt et al (2024).
View Submission
My presentation introduces an AI model to detect and accurately classify handwritten digits from 0 to 9. The model utilizes a neural network architecture trained on a large dataset of handwritten numerals to achieve high accuracy in digit recognition. The model is optimized to consider handwriting style deviations and noise through preprocessing methods like normalization and data augmentation. The results present great efficiency, with the model performing near-human accuracy on standard datasets such as MNIST. This project displays possibilities for deep learning in practical applications such as digit recognition for forms, checks, and automated data entry systems.
View Submission
This session will showcase the utilization of Polypad, an online collection of virtual manipulatives, to facilitate the instruction of diverse mathematical concepts in mathematics content classes for students pursuing early childhood and elementary teaching certification. The demonstrations will encompass self-assessment activities, the dynamic utilization of pattern construction, and the implementation of drag-and-drop functionality. The subsequent discussion will focus on integrating this tool within the Desmos platform or as a standalone application.
View Submission
While teaching our capstone class in Fall 2024, I realized on an early assignment that many of my students were so used to writing proofs that they assumed writing a math paper meant pasting a bunch of proofs together with little to no exposition between proofs. To help them bridge the gap between proving a homework problem and writing a paper, I developed an activity in teacher.desmos that broke down portions of the writing process into smaller steps. Students responded real-time in class to various prompts and could see each others’ responses anonymously. This generated a class discussion about how best to connect ideas in their papers. The activity generated positive feedback both in the moment and on end of course evaluations. In this talk, I will explain how to use the free resource teacher.desmos to do an activity like this, show details on how I organized it, share samples of what the students wrote, and quote some comments from evaluations. If possible, we will end the talk with a short audience participation demonstration of how it works.
View Submission
Many college courses teach Voting Theory, including topics like Ranked-Choice Voting and voting criteria failure. Students sometimes ask if these voting anomalies have ever occurred in real-world elections, which is hard to answer because the underlying data is often hidden. In this talk, we pull the curtain back and discuss some interesting recent elections in which voting anomalies have occurred. We will also have this data available for any instructors who want to use it in their classes.
View Submission
In 2020 I suffered a traumatic brain injury from a fall. While I have been lucky enough to be able to keep doing and teaching mathematics, the sudden change in my brain’s ability to process information presented an immediate need for accessibility tools and accommodations for myself which gave me a new perspective of accessibility in mathematics in general. In this talk, I will discuss simple ways to support student learning in the classroom and present existing tools and the need for additional tools to help move towards everyone having equal access to learn and do mathematics.
View Submission