Accepted (37):
- UnspokenHistory
A Forgotten History: How Chinese Mathematics have Contributed to Modern Methods of Problem Solving — Kari Mays <kariormsby@gmail.com>
This paper explores the historical roots of modern mathematics. It compares ancient Chinese problem solving with contemporary methods. The paper compares multiplication visuals to area models used today. This paper also compares the Fengcheng rule for solving systems of equations to the Gaussian Elimination method. It emphasizes the contribution of Chinese mathematics to the solving of systems of equations long before the Gaussian Elimination method was used in Europe. Through analyzing the introduction to the commentary on Nine Chapters on Mathematical Art, this paper highlights the contributions of mathematician Liu Hui to the field of mathematics. This paper touches on the importance of studying non-Western contributions to mathematics. Exploring non-Western mathematical techniques furthers our understanding of the discovery of mathematics.
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- UnspokenHistory
A Brief Story of the Chinese Mathematician Liu Hui — Charlie Liu <cliu97@utm.edu>
Liu Hui was one of the most renowned mathematicians in ancient China. He was primarily known for his approximation of $\pi$, the ratio of a circle's circumference to its diameter. In this submission, I will provide a summary of some life stories of him that are in general little known, including his work on $\pi$, one of his books named the "Sea Island Mathematical Manual", his commentary on the classic Chinese mathematics book "the Nine Chapters", his very clever approach of the proof of the Pythagorean Theorem, his work on the bicylinder or the double box-lid model and etc.
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- DataLit
A Data Competency Quality Enhancement Plan — Crista Arangala <ccoles@elon.edu>
With a data focused 2020-2030 Strategic Plan, Elon University committed to a Data Competency QEP that harnesses the data-centric interdisciplinary work done across campus. This talk will highlight this work and a variety of ideas to achieve disciple specific advanced data competency for all.
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- DataLit
A Second Wind of Mathematics Departments due to Data Ubiquity: A Proof of Concept — Ivan Dungan <ivan.dungan@fmarion.edu>
As Mathematics Departments have been adjusting over the last decade due to the ubiquity of data and the demand for data scientists, ML and AI have taken the world by storm. Fortunately, these fields’ reliance on data has made a data-centric shift more strategic and has even given a possible new heading. We have been slowly testing a conservative, curriculum restructuring approach in hopes of a proof-of-concept, at least for Math Departments with similar conditions which continue the data-centric focus but in a new form. The restructuring is based around the principle that mathematics plays a central role in ML and AI, and the mathematics in ML and AI touches every math class in a standard college math curriculum. The restructuring is conservative in the sense that the curriculum needs little formal change since most is a shift in material presentation and a continuation of these presentations externally through research projects. There are a few minor formal changes, but we will show how we have navigated those changes at least during the proof-of-concept period. In our talk, we will discuss the details of our approach to-date including motivation and anecdotes. We believe that the most enduring benefit of this approach (besides reinvigorating math departments a second time) is helping reduce a major limitation of future development of ML and AI: understanding the mathematics of ML and AI.
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- FavoriteProb
AMC Problems from the Co-Editor-in-Chief's Perspective — Carl Yerger <cayerger@davidson.edu>
In this talk, an look inside the problem development process will be presented from one of the current Co-Editor's-in-Chief of the MAA AMC 10/12 Contest. What makes a problem interesting for a broad audience of students participating in the contest will be discussed, and a few favorite problems will be shared.
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- UnspokenHistory
Ancient Algebra and Contemporary Conflict — Jared Kettinger <jkettin@clemson.edu>
While the contention over the forefathers of calculus is well known, many are unaware of a similar conflict over the progenitor of algebra. Some contend this title belongs to Diophantus with his introduction of symbols for unknown quantities; others argue the moniker is more properly suited to al-Khwarizmi who's work better embodies abstraction from specific numbers and a more comprehensive approach to algebraic problems. In this talk, we will explore the merits of both sides of this debate. In doing so, we will see how Eastern mathematicians preserved and improved upon Western results and methods as the latter entered a dark period in its mathematical history.
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- UGRMentors
Balancing Structure and Flexibility: Implementing Course-Based Undergraduate Research — Kelly Buch <buchk@apsu.edu>
Course-based Undergraduate Research Experiences (CURE) provide an opportunity to engage students in undergraduate research, particularly in settings where external research support is limited. However, integrating this high-impact practice into coursework presents several challenges: while courses require structured syllabi and clear assessment criteria, research often demands flexibility to explore unplanned directions. Additionally, research is typically an open-ended and lengthy process, but in a course-based setting, projects must be completed within the constraints of a single semester. In this talk, I’ll share my experience incorporating student research into a mathematical modeling course, highlighting strategies to balance these competing needs and challenges. I will discuss how a scaffolded approach helped students navigate the research process while developing mathematical models using foundational frameworks. This approach to structuring student research is adaptable and can be applied to other courses or areas of mathematics to foster inquiry-driven learning.
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- UGRMentors
Beyond the Classroom: Guiding Student Research and Career Development — Laurie Zack <lmzack@ncat.edu>
As educators, our role extends far beyond simply teaching course content; we are also mentors who help students navigate the complex landscape of research, career development, and personal growth. This talk will explore strategies for mentoring students in mathematics, focusing on undergraduate research projects, internships, and career preparation. Drawing from 20 years of experience, I will share insights on how to support students in various research areas and finding REU's and internship opportunities. By cultivating trust and creating lasting relationships with students, mentors can help students not only excel academically but also prepare for success in their careers.
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- DataLit
Building and Supporting a Data Science Degree Program at a Primarily Undergraduate Institution — Zach Abernathy <abernathyz@winthrop.edu>
Over the past few years, mathematics faculty at Winthrop University have made efforts to infuse data science into the curriculum, culminating in the recent launch of an undergraduate degree program in data science. The program has been built with an applied focus to maximize student employability upon graduation, including features such as the use of real-world data sets throughout the curriculum, partnerships with industry and research groups, and an emphasis on domain knowledge in a student’s chosen field of interest. We will discuss how we built the program around our current curricular structure and challenges we’ve faced along the way. We will also explore several ongoing goals related to supporting the program, including the acquisition of biomedical datasets in collaboration with biology and chemistry faculty, expanding data science instruction across STEM disciplines, and mentoring undergraduate research projects in data science.
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- UnspokenHistory
Celebrating the Achievements of Women in Mathematics — Denise Rangel Tracy <rangel.tracy@fmarion.edu>
The contributions of women to mathematics have often been overlooked, yet their achievements have shaped the field in profound ways. In 2021, the Association for Women in Mathematics (AWM) released the first of four planned card decks, titled EvenQuads, highlighting notable women in mathematics. EvenQuads cards are double sided; one side of the cards shows symbols that appear in varying colors and quantities used to play various pattern seeking games and the other side features a profile of a woman mathematician who has made significant contributions to the field of mathematics. In this talk, we will spotlight some of the remarkable women mathematicians featured in the EvenQuads decks. By uncovering their lesser-known contributions and some of the challenges that they faced we gain a deeper appreciation for their resilience and the roles they played in shaping the field of mathematics. We will also briefly describe the games that can be played with the profile side of the cards and explore how they can be used in a mathematics classroom.
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- RecMath
Characterizing quad-free sets in the card game EvenQuads — Timothy Goldberg <timothy.goldberg@gmail.com>
EvenQuads is a SET-like card game published by the AWM whose goal is to find “quads”, which are sets of four cards satisfying a particular pattern. The cards can be viewed as points in the finite affine geometry AG(6,2), and a quad in the card game corresponds to a plane in AG(6,2). We are most interested in quad-free collections of cards, which turn out to be Sidon Sets. We will describe an analog of the "Cap Set problem" for EvenQuads, and discuss known results. In particular, we will address the question of how many cards you must lay down to guarantee a quad.
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- DataLit
Consumer Statistics Unit for 100-Level Quantitative Literacy Mathematics Courses — Laura Lembeck <lslembeck@wcu.edu>
In this session, I will describe how I teach the concepts of good and bad statistical practices. I will include lecture materials that have been created in collaboration with my students in an open resourced learning environment, as well as in-class and out-of-class exercises to allow for group work and interactive learning. I will describe the process we use for collecting, organizing and analyzing our own data set. Finally, I will describe how we work in groups to create research projects - oral presentations, utilizing our subject librarian’s expertise, and the rubric that promotes excellence, all under the umbrella of incorporating learning-centered inquiry methods to support each individual’s growth in their knowledge base.
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- FavoriteProb
Crafting Challenges: Writing Competition Problems and Tests — Risto Atanasov <ratanasov@wcu.edu>
Drawing from my experience in crafting problems for various mathematical competitions, including the AMC, I will share examples of some of the most beautiful and elegant problems I've encountered. These examples will illustrate the blend of creativity and rigor that goes into problem creation. We will explore the art behind writing competition questions, discussing the key elements that make a problem both challenging and engaging. Additionally, we'll address the broader process of designing contest tests, ensuring a balanced and comprehensive assessment of participants' skills.
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- FavoriteProb
Dandelin Spheres: the Unintended Benefits of Being Stumped — Stephen Davis <stdavis@davidson.edu>
A lack of personal insight regarding a problem from the 2019 College of Charleston Math Meet Level III Written Test (#25: about the area illuminated by a spotlight) led to an encounter with the spheres of the 19th century French mathematician Germinal Dandelin. In this talk, we learn about Dandelin spheres and how they could be used to solve the CofC problem (and maybe also see a sketch of a sphere-less solution).
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- DataLit
Data Literacy Course and Initiatives at Converse University — Amanda Mangum <amanda.mangum@converse.edu>
Converse University recognizes the increasingly important role of data literacy in educating tomorrow's workforce. With this in mind, I have created and taught a new general education course, Data Literacy. Converse has also recently approved a new general education program that includes a data component. This talk will address efforts to promote data literacy across campus and to create new courses that support this focus.
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- UnspokenHistory
Developing an Interdisciplinary Course on the History of Women in Mathematics — Brittany Riggs <briggs@elon.edu>
In this session, I will share my experience designing an interdisciplinary course on the history of women in mathematics, starting with Hypatia in Ancient Alexandria and extending to Maryam Mirzakhani, the first woman to win the Fields Medal. The presentation will include a summary of the women covered in the course, highlights of their contributions within and outside mathematics, as well as examples of math activities used in the course. I will also touch on lessons learned in the design and unexpected insights into the narrative of women in mathematics.
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- UGRMentors
Engaging Students in Math Research Through Games: Quads, Spot It!, and Beyond — Lauren Rose <rose@bard.edu>
Mathematical puzzles and games offer rich opportunities for faculty seeking to develop student research projects. By exploring math in a recreational context, students can naturally notice patterns, ask questions, make hypotheses, and delve deeper into mathematical investigations. We have used card games such as $\textit{Quads}$ and $\textit{Spot It!}$ to generate accessible projects for students at a variety of levels. We discuss the successes and challenges of both virtual and in-person research groups, highlighting the dynamics of collaborative work in different settings.
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- UGRMentors
Finding Projects and Managing Expectations — Zih-Syun FU <bbaker2@citadel.edu>
In this talk, we will consider several projects that undergraduates have worked on in the past several years. We will discuss how the problems were chosen as well as what the students were expected to accomplish in various time frames.
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- DataLit
From small steps to giant leaps toward data literacy — Laurie Heyer <laheyer@davidson.edu>
Small steps -- a single workshop, a single course, a single tutor -- can create a launchpad for giant leaps in a data science program. We describe how data science courses, curricula and programming form a web of support for students across the disciplines at Davidson College.
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- UGRMentors
Guiding High School and Undergraduate Students into the World of Mathematical Research — Rigo Florez <rflorez1@citadel.edu>
In this talk, we explore strategies for engaging students with basic mathematical knowledge in research projects. This approach leverages open problems from respected academic journals. We will discuss methods for guiding students through problem--solving, publishing their results, and ultimately presenting their findings publicly. This technique can also benefit educators without prior research experience who wish to begin exploring research themselves. We discuss how to stimulate students' curiosity through visual tools, including classic experiments involving the Mo\"bius strip and the Klein bottle. These experiments involve constructing the objects, observing their properties, and using hands-on activities to show how altering the objects by cutting disrupts their inherent properties. At the end of the presentation, we will discuss problems our students have solved from journals as well as original problems related to our own research topics. Additionally, we will provide a list of current problems along with recommended books and articles to help students prepare for future projects. Join work with Drs. Chen, Mukerjee, and Swart.
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- RecMath
How Many Dice Do You Need for a Bell Curve? — Jeffrey Clark <clarkj@elon.edu>
The Central Limit Theorem is one of the most fundamental principles in probability, stating that the probability distribution of the average of independent measurements of the same random variable has the ubiquitous bell curve as a limit as the sample size increases. This talk will use different numbers of fair dice to explore this convergence as one of the easiest examples of that convergence if not the quickest.
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- UGRMentors
Lessons learned from 30+ years of undergraduate research direction — Anant Godbole <godbolea@etsu.edu>
This is a personal tale of how I have directed undergraduate research at MTU and ETSU via NSF-REU awards. I was the sole advisor from 1991 to 2018, and have worked with Fernando Piñero and Pamela Harris since then. I retired in 2024. Some aspects of my talk are *How I used undergraduate research as a springboard to solidify and define my own research; *How I learned so much from my students while teaching them sophisticated and bread-and-butter techniques; and *The illustrious careers of my students.
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- DataLit
MAA’s StatPREP Project: Using Data-Centric Methods to Teach Introductory Statistics — Jenna Carpenter <carpenter@campbell.edu>
The MAA’s NSF-funded StatPREP Project had, as its mission to empower statistics instructors to create data-driven learning opportunities so that students can gain the skills and knowledge needed to work and live in a data-centric world. The forthcoming MAA Notes volume on the StatPREP Project showcases the tools and resources developed by the project, dives into examples of how to transform the introductory stats classroom (including lessons on common intro stat topics that use tools like the Little Apps to explain and explore topics using R online via a web browser), as well as other topics and considerations for improving and expanding data science education. We will explore these tools and ways they can be used in your classroom.
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- RecMath
Math Engagement: Math is Fun! — Laura Steil <lsteil@mhu.edu>
This talk will focus on an initiative at Mars Hill University for co-curricular math exploration. Math faculty members use problems, activities, and puzzles from Math Circles to engage with students outside of the lecture classroom. The ideas used in the activities are applications that students would not necessarily encounter in the classroom but allow for exploration with patterns, strategies for games, and recognition of mathematics in everyday life. A large emphasis of the initiative is for students to realize that math can be fun!
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- UGRMentors
Modeling Bromeliads: An Ongoing Interdisciplinary Collaboration with Multiple Undergraduate Research Projects — Erin Bodine <bodinee@rhodes.edu>
Team Bromeliad is an ongoing seven-year interdisciplinary collaboration Dr.~Erin N.~Bodine (biomathematician) and Drs.~Rachel Jabaily, Brad Oberle, and Brian Sidoti (botanists) to study the growth, reproduction, and population dynamics of bromeliads (a plant family of rosette-structured flowering plants that includes the pineapple and Spanish moss) using greenhouse and field experiments in conjunction with mathematical modeling. The long lifespan of many bromeliads (up to 100 years in some species) can make it difficult to study individual rosettes \textit{in situ} over their lifetime. However, this provides fertile ground for developing mathematical and computational models that can simulate and predict growth, reproduction, and population dynamics over many decades. These models have the additional benefit of allowing for simulations that consider the impact of changing environmental conditions, such as climate change or the introduction of invasive species. In this talk, we will tour a selection of mathematical models of bromeliad growth, reproduction, and population dynamics that have been developed and analyzed in collaboration with undergraduate students from a variety of institutions. From simple single equation continuous functions and discrete difference equations to more intricate models of systems of differential equations and agents-based models, each model provides a different lens from which to view and understand bromeliad growth and reproduction. Additionally, this talk will reflect on the elements of this collaboration that have enabled it to persist and evolve over time, and to provide research opportunities for over 20 undergraduate students.
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- DataLit
New Courses and Programs to Promote Data Literacy — Ellen Breazel <ehepfer@clemson.edu>
In an increasingly data-driven world, fostering data literacy has become essential for students across disciplines. This presentation describes the steps the School of Mathematical and Statistical Sciences has taken to promoting data literacy through the development of an undergraduate major, specialized courses, and an online Master’s program. By integrating data literacy into the curriculum, students will not only gain essential analytical skills but will also learn to apply data-driven decision-making in diverse fields. The general education undergraduate course focuses on foundational data concepts, while the major offers an in-depth exploration of data analysis, programming, and ethical implications in a wide variety of disciplines. The online Master's program was designed for working professionals, providing flexible access to advanced data literacy training. This session will explore the rationale behind these initiatives, the curriculum design, and the impact on both academic and professional communities.
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- RecMath
Phun with “Phractals” and Phi for 100-Level Quantitative Literacy Mathematics Courses — Laura Lembeck <lslembeck@wcu.edu>
In this session, I will describe how I introduce fractal mathematics with iterative processes and focus on key aspects of the golden ratio and transcendental number Phi. I will include some of the video clips I use to get students engaged with the concepts, examples they practice in the classroom to further their understanding, and assignments that align with the learning objectives of this course - “Students will craft written and/or oral communication demonstrating organization, clarity, logic and skill for various audiences.”
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- RecMath
Playing with Proof: Combinatorial Game Theory in Liberal Arts Mathematics — Bill Shillito <bshillito@oglethorpe.edu>
Proof lies at the heart of mathematical reasoning, yet teaching proof in a liberal arts mathematics course poses a unique challenge. How can we showcase the power and utility of axiomatic reasoning while keeping the content accessible to students from diverse majors and backgrounds? A simple game involving blue and red poker chips can offer the perfect balance of accessibility and depth, inviting students to explore axiomatic reasoning in an engaging yet rigorous way. With just three axioms, students can discover hidden structures within the game and even determine their optimal next moves. We will introduce the game and its axioms, and then we will discuss how it can be used as a classroom activity to demonstrate the elegance of mathematical proof through play.
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- UnspokenHistory
Primes and Pyramids — Satish C. Bhatnagar <satish.bhatnagar@unlv.edu>
This article was written is a reflective mode after visiting the Grand Pyramid of Giza on January 02, 2025. Prime numbers and pyramid constructions are poles apart, yet an effort is made to build a bridge over them. In life, a bridge is only known for its one of the longest spans.
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- RecMath
Quad-free sets in the card game Quad-128 — Lauren Rose <rose@bard.edu>
Quad-128 is a game played with two distinguishable Quad-64 decks; for example, each deck has a different background color. The game play is similar, but the combined deck is now a model for the affine geometry $AG(7,2)$ rather than $AG(6,2)$. We define a $\textit{cap}$ to be a quad-free set of cards. We determine the maximum size of a cap, which tells us how many cards we must lay out to guarantee a quad. More generally, we classify all caps in $AG(7,2)$ up to affine equivalence.
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- RecMath
Some aspects of combinatorial game theory — Tolulope Oke <oket@wfu.edu>
Combinatorial game theory is a branch of mathematics and theoretical computer science that typically studies sequential games with perfect information. Study has been largely confined to two-player games that have a position that the players take turns changing in defined ways or moves to achieve a defined winning condition. In this talk, I will present some ideas about the structural properties of a combinatorial game - in particular, the subtraction game.
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- DataLit
Statistics Start-Up — Nicole Panza <npanza@fmarion.edu>
Employers are demanding more statistical and data analysis skills from our graduates. In an effort to meet that demand, our Mathematics Department at Francis Marion University implemented a minor in statistics. This talk will discuss how we came to that decision, how we implemented the minor and how it has worked out so far.
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- RecMath
Temari Projections on Assorted Surfaces — Shemsi Alhaddad <alhaddad@email.sc.edu>
Temari is a traditional Japanese fiber art in which designs are stitched to the surface of a ball. Many Temari designs begin with a geometric partition of the sphere. Temari designs can be viewed through the lens of recreational math as it is a leisure art with mathematical properties. In this presentation, I will first describe a standard procedure for partitioning Temari balls. I will then demonstrate application of this procedure to difference surfaces. Finally, I will compare the results to standard mathematical projections, such as stereographic and cylindrical projections.
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- RecMath
The Gauss-Bonnet theorem and triangular Tangles — Doug Torrance <dtorrance@piedmont.edu>
A Tangle is a smooth closed curve formed by the union of arcs of congruent circles, known as links. We use the Gauss-Bonnet theorem to prove an interesting result about the number of concave v. convex links in a Tangle. This in turn allows us to show that all "triangular Tangles" (planar Tangles formed from sixths of circles) may be constructed by a sequence of fundamental operations starting from a circle.
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- UnspokenHistory
The Life and Work of Shing-Tung Yau — Zachery Keisler <zkeisler@saludaschools.org>
Shing-Tung Yau is one of the most prolific geometers alive today, from being awarded the Fields Metal in 1984 for his contributions to partial differential equations and his proof of the Calabi Conjecture in algebraic geometry to publishing his book titled The Shape of Inner Space: String Theory and the Geometry of the Universe’s Hidden Dimensions with Steve Nadis in 2010. Today's talk will examine the major life events that molded Shing-Tung Yau into the geometer he is today while also examining the many contributions he made in the field of mathematics as a whole.
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- UGRMentors
Undergraduate Research: Recruitment, Retention, Mentoring — Shalmali Bandyopadhyay <sbandyo5@utm.edu>
This presentation shares my experiences and insights from undergraduate research mentoring at my current institution, UT Martin. I discuss the challenges and successes of integrating multiple disciplines, navigating the mentor-mentee relationship and promoting student autonomy in team-based research. This reflective analysis aims to contribute to best practices in undergraduate research mentorship, highlighting the benefits and complexities involved and challenges faced as an entry-level faculty member.
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- FavoriteProb
Using High School Competition Problems to Create Rich Mathematical Tasks for Undergraduate Mathematics Students — Doug Ensley <dougensley@gmail.com>
In this talk we will share some specific problems from MAA competitions (pitched at middle- and high-school students), and we will show how these problems can be deconstructed and adapted to create engaging content for undergraduate students that promote active learning by intentionally addressing communication and problem-solving standards. Topics will include elementary number theory, combinatorics and probability in the context of an introductory course in discrete mathematics.
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