UWEC CERCA 2025: Full Schedule

7:59am CDT

The 33rd Annual UWEC Mathematics Retreat

Monday April 21, 2025 7:59am - 3:00pm CDT

The UWEC Mathematics retreat is a celebration of the research done in the Math department at UWEC. The event features talks given by students and faculty members on topics that they have been researching independently, in the context of student-faculty research, and during their classes. During the afternoon it concludes with a keynote speaker and a fun team-based mathematics competition.

Monday April 21, 2025 7:59am - 3:00pm CDT
Hibbard Hall

Mathematics Retreat

Department Mathematics
College CAS

8:30am CDT

Analytic Continuation

Monday April 21, 2025 8:30am - 8:50am CDT

Hibbard Hall 311

A complex-valued function f is considered analytic on a domain D when its derivative f’ is defined for all points z in D. Many complex functions can be extended to larger domains while still being analytic. Such a function F is considered an analytic continuation of f. These functions have a variety of uses, including extending functions beyond their traditional contexts, as in the case of the geometric sum formula. This presentation will discuss relevant notions within complex analysis, formally define analytic continuation, provide some examples of analytic continuation's use, and present some theorems of interest.

Presenters

Isaac Ackerman

University of Wisconsin - Eau Claire

Matthew Kreiger

University of Wisconsin - Eau Claire

Jack Paulsen

University of Wisconsin - Eau Claire

Faculty Mentor

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 8:30am - 8:50am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

8:30am CDT

Investigating possible relationships between teacher or student motivations related to mathematics

Monday April 21, 2025 8:30am - 8:50am CDT

Hibbard Hall 320

Motivation in mathematics classrooms has been researched in various ways, from teacher burnout to Wigfield and Eccles' theory of student expectancy-value. After examining the existing literature on student and teacher motivations, the results showed a need to focus on teacher and student connections within the mathematics classroom to improve learning environments. The purpose of this research is to use survey instruments to extend previous research by examining potential relationships between teachers’ motivations when teaching mathematics and students’ motivations when learning mathematics. The study consists of completing one of two survey instruments, one for teachers and one for middle and high school students. Both have a set of Likert scale questions and open-ended questions about mathematics teaching or learning along with relevant demographic questions. The data collected from both surveys will be used to examine potential relationships between mathematics teacher and student motivations. These results and implications will be discussed.

Presenters

Maddie Sasse

University of Wisconsin - Eau Claire

Faculty Mentor

Christopher Hlas

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 8:30am - 8:50am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

8:30am CDT

Reconstructing Signals from Erasures

Monday April 21, 2025 8:30am - 8:50am CDT

Hibbard Hall 322

The Shannon-Whittaker Sampling Theorem states that a band-limited signal can be reconstructed from its sample values on a uniformly spaced lattice. Erasures can occur when some of the sample values are lost or corrupted. We aim to recover the signal despite these erased samples. One such algorithm to accomplish this is called Reduced Direct Inversion. We provide error bounds and supporting experiments for this algorithm.

Presenters

Rebecca Yoshino

University of Wisconsin - Eau Claire

Faculty Mentor

Sam Scholze

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 8:30am - 8:50am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

8:30am CDT

The Boy Girl Paradox: Why Probability Makes No Sense.

Monday April 21, 2025 8:30am - 8:50am CDT

Hibbard Hall 312

I will be presenting on the Boy-Girl Paradox, an intriguing concept in probability theory that explores the surprising outcomes when trying to determine the gender of children in a family based on limited information. The paradox challenges our intuitive understanding of statistics and probability, highlighting how seemingly irrelevant information can drastically change probability.

Presenters

John Holmberg

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 8:30am - 8:50am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:00am CDT

Bike Lock Conundrum!

Monday April 21, 2025 9:00am - 9:20am CDT

Hibbard Hall 312

Oh no! You've forgotten your four-digit pin to unlock your bike, and you are running late for a class! However, six incorrect attempts locks your bike for good, and you REALLY don't want to have to run to your class! You've already used FIVE attempts- given some hints, and seeing the first five attempts, will you be able to plug in the correct pin on the last possible attempt? In this presentation, we will discuss the logic, problem solving, and reasoning it takes to get through this problem, all while audience members get to try it themselves!

Presenters

Kahlyn Geiger

University of Wisconsin - Eau Claire

Finnley McGowan

University of Wisconsin - Eau Claire

Ellah Olson

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:00am - 9:20am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:00am CDT

Exploring the set of constructible numbers

Monday April 21, 2025 9:00am - 9:20am CDT

Hibbard Hall 320

Proven impossible by Pierre Wantzel in 1837 and Ferdinand von Lindemann in 1882, the classical problems of squaring the circle, doubling the cube, and trisecting an arbitrary angle using only a compass and straightedge have been of mathematical interest since Greek antiquity. Through advances in mathematics in the 17th-19th centuries, we discovered the set of constructible numbers in abstract algebra, which showed deep connections to our classic problems. We explore the constructible numbers, a field extension of the rational numbers, and the set of numbers discoverable using a straightedge and compass. In this talk we will present these classic geometric problems from ancient Greece, their history, and discuss how the set of constructible numbers relates back to the problems’ impossibility.

Presenters

Harlea Monson

University of Wisconsin - Eau Claire

Dylan Simanski

University of Wisconsin - Eau Claire

Faculty Mentor

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:00am - 9:20am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:00am CDT

Longitudinal Comparison of Models to Predict Match Outcomes in the WTA

Monday April 21, 2025 9:00am - 9:20am CDT

Hibbard Hall 322

Analytics have been less utilized in women’s professional tennis (WTA), compared to other professional sports. Despite unique difficulties in predicting match outcomes, there has been a spate of recent articles that utilize prediction tools applied to men’s professional tennis (ATP) data. Our research adds efficiencies and new features to previously-created probabilistic models for longitudinal predictions of WTA matches. We compute, update, and analyze a set of related summary statistics along with specific match details for individual players and integrate these with Bradley-Terry algorithmic modeling of match probabilities to incorporate strength of schedule. Data for player statistics and results of WTA tournaments was obtained from a GitHub repository under a Creative Commons license. We edited and created original functions in R: wrangling the data across an appropriate time window, court surface, and player rank; and implementing an existing algorithm for prediction and assessment. We also apply Elo ratings for comparative prediction, utilizing a longitudinal update and weighting by strength of win. We discuss the methods, data cleaning, and coding, and apply elevated error analysis of match predictions compared to observed match outcomes to determine the overall accuracy of our model; accurate predictions could further inform the ranking of WTA players. Additional collaborator: Brynn Bergeson.

Presenters

Morgan Dekan

University of Wisconsin - Eau Claire

Anna Lee

University of Wisconsin - Eau Claire

Faculty Mentor

Jessica Kraker

Professor, Department of Mathematics, University of Wisconsin - Eau Claire

I have been teaching at UW - Eau Claire since 2006, covering courses in undergraduate statistics (introductory and upper-level) and Master’s-level data mining and programming. My research is in data-mining techniques, with a focus on penalized regression. My recent (last ~ 6 years... Read More →

Monday April 21, 2025 9:00am - 9:20am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:00am CDT

Staying Within the Bounds: Liouville’s Theorem

Monday April 21, 2025 9:00am - 9:20am CDT

Hibbard Hall 311

Liouville’s theorem is a fundamental result in complex analysis which has profound implications across various fields. The theorem states that if a function is both bounded and entire, then it must be constant. These seemingly simple constraints on a function lead to powerful conclusions, as Liouville’s theorem demonstrates its importance in proofs such as that of the Fundamental Theorem of Algebra. This presentation will explore the proof of Liouville’s theorem, highlighting its reliance on Cauchy's integral formula.

Presenters

Brianna Evans

University of Wisconsin - Eau Claire

Carter Klug

University of Wisconsin - Eau Claire

McKenzie Mack

University of Wisconsin - Eau Claire

Faculty Mentor

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:00am - 9:20am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:30am CDT

Fractional Linear Transformations: Properties and Applications

Monday April 21, 2025 9:30am - 9:50am CDT

Hibbard Hall 311

Fractional Linear Transformations, also known as Mōbius Transformations, play a fundamental role in complex analysis and have significant applications in geometry, physics, and engineering. This presentation explores the mathematical structure of these transformations, defined as functions of the form f(z) = (cz+d)/(az+b), where a, b, c, and d are complex numbers satisfying ad – bc ≠ 0. We will examine their geometric properties, including how they map lines and circles to other lines and circles, and their role in conformal mappings. Additionally, we will discuss applications in computer graphics, control theory, and relativity. Through visual demonstrations and problem-solving exercises, this presentation aims to provide an intuitive understanding of Fractional Linear Transformations and their relevance in various fields.

Presenters

Angelo Brantner

University of Wisconsin - Eau Claire

Isaac Geffers

University of Wisconsin - Eau Claire

Damian Nguyen

University of Wisconsin - Eau Claire

Faculty Mentor

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:30am - 9:50am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:30am CDT

Math Department Scheduling Using Number of Preps and Back-to-Back Courses

Monday April 21, 2025 9:30am - 9:50am CDT

Hibbard Hall 322

Scheduling classes is a challenging and time-consuming task. The mathematical technique of linear programming has the potential to simplify this challenge by building a model of linear constraints to find the most optimal solution that satisfies all the constraints. In this project, we are implementing a linear programming model using the DOCplex library in Python. The objective function represents instructor satisfaction with different courses and the constraints represent limitations such as the fact that one instructor cannot teach two courses at the same time. These constraints allow many ways to build a schedule. The goal of our program is to identify the most optimal solution, that maximizes the professor's satisfaction and class availability. We will present a system for encoding the preferences about number of preps and back-to-back courses, as well as discussing the advantages of using binary variables to represent combinations of courses, professors, and meeting patterns (such as MWF 9-9:50) instead of individual day-time pairs. We will also present results from adding constraints and preferences about course distribution throughout the day, depending on whether the number of sections is above or below a threshold. Additional Collaborators: Theodore Schwantes and Annabelle Piotrowski.

Presenters

Brynn Bergeson

University of Wisconsin - Eau Claire

Faculty Mentor

Abra Brisbin

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:30am - 9:50am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:30am CDT

Tower of Hanoi

Monday April 21, 2025 9:30am - 9:50am CDT

Hibbard Hall 312

The project that we will be presenting today is on the importance of restrictions or rules in a problem in order to make any problem easier to solve. We will be discussing this using a problem called the Tower of Hanoi, which is a puzzle problem of moving a tower of disks from one side of the board to the other in the least amount of moves possible. We will explain the original restrictions of the problem and then change or remove them to see what effects that has on the problem's pattern, and the ability to solve it. As a problem that has a lot of rules in place in order to keep its structure, the changes we make to this problem might greatly affect the puzzle this problem is considered to be.

Presenters

Elaynah Jaschob

University of Wisconsin - Eau Claire

Adelynn Stanley

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:30am - 9:50am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

9:30am CDT

What's yellow and is equivalent to the Axiom of Choice? Zorn's Lemon!

Monday April 21, 2025 9:30am - 9:50am CDT

Hibbard Hall 320

Zorn's Lemma was proven under the assumption of the Axiom of Choice in 1922 by Kazimierz Kuratowksi, but was proven without well-ordering in 1935 by Max August Zorn. The Axiom of Choice states that for any collection of sets, a choice function exists. Zorn's Lemma states that in every nonempty partially ordered set with upper bounds for each chain, there exists a maximal element. These claims are in fact equivalent. In this presentation, we will introduce basic set theory notions, prove the equivalence of the Axiom of Choice and Zorn's Lemma, and show its applications in other disciplines of mathematics.

Presenters

Matthew Kreiger

University of Wisconsin - Eau Claire

Noah Woodruff

University of Wisconsin - Eau Claire

Faculty Mentor

aBa Mbirika

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 9:30am - 9:50am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:00am CDT

Color me Confused!!!

Monday April 21, 2025 10:00am - 10:20am CDT

Hibbard Hall 312

This problem is suited for individual and/or group work. Together we will explore the color theorem by having you explore a map of the United States and try coloring each state with different colors. In doing so in such a way where there are no two states touching each other that are the same color. What is the least number of colors in which this is possible to do? This presentation will include presenting the problem, providing work and discussion time, as well as a detailed solution and explanation of why the color theorem works.

Presenters

Jakob Leonard

Jacob Lynch

University of Wisconsin - Eau Claire

Ainsley Nutt

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:00am - 10:20am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:00am CDT

Deterministic and Heuristic Analysis of Two-Dimensional Iterated Function Systems

Monday April 21, 2025 10:00am - 10:20am CDT

Hibbard Hall 322

Iterated function systems offer a framework for generating complex, self-similar patterns through the iterative plotting of points. An iterated function system is a family of functions that map ℝ² to ℝ². For each iteration of the system, a variation is chosen with a certain probability. The asymptotic points make up the final fractal image. In this work, we examine specific variations using various heuristics that measure behavior between iterations and reveal the system's deeper patterns that improve our understanding of the system's intrinsic behavior. Our research focuses on developing and applying a multitude of heuristics designed to analyze the dynamic behavior of individual variations within these systems. Through visualizations produced by each heuristic, we illustrate the distinct characteristics of each heuristic across multiple variations.

Presenters

Clara Bartlett

University of Wisconsin - Eau Claire

Finn Walker

University of Wisconsin - Eau Claire

Faculty Mentor

Chris Ahrendt

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:00am - 10:20am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:00am CDT

Rouché's Theorem

Monday April 21, 2025 10:00am - 10:20am CDT

Hibbard Hall 311

Have you ever been walking your dog and the leash got tangled around a lamp post? Are you wondering what this has to do with Complex Analysis? Don’t worry, we are here to tell you! Our goal is to explore and explain Rouché’s Theorem through an accessible analogy and mathematical proof. The theorem states: If f and h are each functions that are analytic inside and on a simple closed contour C and if the strict inequality h(z) < f(z) holds at each point on C, then f and f + h must have the same total number of zeros (counting multiplicities) inside C. Therefore, this theorem is typically used to find the location of zeros of a complicated analytic function. In our presentation, we will explain Rouché's Theorem using this dog-walking analogy, discuss why this theorem is valuable, and prove the theorem.

Presenters

Grace Cole

University of Wisconsin - Eau Claire

Paige Cole

University of Wisconsin - Eau Claire

Katherine Conklin

University of Wisconsin - Eau Claire

Faculty Mentor

Aiham Hassan

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:00am - 10:20am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:00am CDT

You Can’t Run From Community: Quantifying Connectedness

Monday April 21, 2025 10:00am - 10:20am CDT

Hibbard Hall 320

Community Detection of Indigenous Beaders on Instagram involves roots in coding theory and graph theory. Given a data set, the objective is to detect underlying communities within a population. We view the given data set as the output of a noisy communication channel and use decoding techniques to reveal the underlying communities. Essentially, any population of a particular size has a set of allowed possibilities for clusters. Using techniques from coding theory, we hope to unveil a “best fit” community cluster formation from our gathered data. Through a sampling of 50 Indigenous beaders on Instagram, we gather data about Instagram follows to eventually decode to smaller community clusters. We imagine the community clusters could reveal tribal affiliation, stitching techniques, or geographic location.

Presenters

Maddie Blong

University of Wisconsin - Eau Claire

Faculty Mentor

Allison Beemer

MATHEMATICS, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:00am - 10:20am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:30am CDT

Chance of Victory - Probability Unveiled

Monday April 21, 2025 10:30am - 10:50am CDT

Hibbard Hall 312

In this presentation the classic game of rock, paper, scissors as well as rock, paper, scissors minus one will be used to understand the basic concepts of probability. This presentation will give students the chance to engage in the concepts of probability by playing several rounds of each game. Before students participate in their own game against others, a demonstration will be provided to allow for a thorough understanding of the topic being presented. These games will be followed up with a discussion to allow students to analyze the difference between each version which allows them the best chances at victory.

Presenters

Dakota Borths

University of Wisconsin - Eau Claire

Kole Sonnenberg

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:30am - 10:50am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:30am CDT

Communication in the Claw Network

Monday April 21, 2025 10:30am - 10:50am CDT

Hibbard Hall 320

Adversarial networks model communication through a graph of edges where information is sent from sender to receiver using a code. This presentation discusses the scenario in which a hostile adversary can corrupt along a restricted subset of edges within a “claw” network structure. In particular, we examine claw networks in which the sender sends a symbol along 2n edges, with n edges in each claw. We examine the families of claws with varying n, and give results on communication capacity as the influence of an adversary grows.

Presenters

Elise Bormann

Undergraduate Presenter, University of Wisconsin - Eau Claire

Faculty Mentor

Allison Beemer

MATHEMATICS, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:30am - 10:50am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:30am CDT

Mathematics Students’ Perceptions of Learning Opportunities and Barriers in Developmental Mathematics

Monday April 21, 2025 10:30am - 10:50am CDT

Hibbard Hall 311

This Scholarship of Teaching and Learning project aims to learn more about students’ perceptions of their learning opportunities and barriers in a developmental mathematics classroom through a mixed methods analysis of data gained from surveys of current and former students. Often with high DFW rates, developmental mathematics courses can reinforce negative feelings about mathematics and keep some students from moving forward with their degree path, often disproportionately impacting first generation and other minoritized populations. Many supports and interaction opportunities have been added to the course over previous semesters, and yet there continues to be an achievement gap between students who make use of resources and succeed, and those who do not. Additionally, we will examine factors related to college readiness such as attitudes toward the content being presented and ownership of learning and factors related to classroom engagement such as motivation to learn and sense of belongingness.

Presenters

Kenzi Schneider

University of Wisconsin - Eau Claire

Bree Stanford

University of Wisconsin - Eau Claire

Faculty Mentor

Katrina Rothrock

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:30am - 10:50am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

10:30am CDT

Part 1: Transfer Systems for Non-abelian Groups

Monday April 21, 2025 10:30am - 10:50am CDT

Hibbard Hall 322

Homotopical combinatorics uses tools from combinatorics to explore and understand structures in equivariant homotopy theory. One object of study in homotopical combinatorics is a G-transfer system, which is defined by five axioms. In this talk, we define transfer systems, and we present the difference between abelian transfer systems, where the order of operation on group elements doesn't matter, and nonabelian transfer systems, where order does matter. We describe how to find transfer system for cyclic groups, and contrast this with transfer systems for dihedral groups, which are nonabelian.

Presenters

Koki Shibata

University of Wisconsin - Eau Claire

Faculty Mentor

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 10:30am - 10:50am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:00am CDT

Gambler’s Fallacy: How Probabilities Lie to Us

Monday April 21, 2025 11:00am - 11:20am CDT

Hibbard Hall 312

The Gambler's Fallacy is the idea that if an event occurs less than expected, it is due to happen sometime soon. In other words, if you flip a coin and it lands on heads three times in a row a tail is bound to land on the next flip. Right? In this session we will discuss and evaluate our flawed perception of chance and how to properly view probability through our own rigorous testing, in-room experiments, and logical evaluation of scenarios.

Presenters

Katherine Conklin

University of Wisconsin - Eau Claire

Jakob DeFosset

University of Wisconsin - Eau Claire

Michael Holtz

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:00am - 11:20am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:00am CDT

Part 2: The Width of Non-Abelian Transfer Systems

Monday April 21, 2025 11:00am - 11:20am CDT

Hibbard Hall 322

In continuation of the previous talk on transfer systems by Koki Shibata, we explore the width of non-abelian transfer systems. A transfer system of G is said to be complete if it contains all possible arrows. The width of a G-Transfer System, defined in 2025 by Adamyk, Balchin, Barrero, Scheirer, Wisdom, and Zapata Castro is the number of relations needed to force a G-transfer system to be complete. We explore how the width is related to the prime factorization of the order of the group. In this talk, we present a proof that the width of is C_pn_qm is n + m. Further, we show the width of D₂n is 5 and the width of D_P1ɑ1_P2ɑ2_...Pnɑn is equal to the number of maximal subgroups.

Presenters

Harlea Monson

University of Wisconsin - Eau Claire

Faculty Mentor

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:00am - 11:20am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:00am CDT

Rate My Communication Channel!

Monday April 21, 2025 11:00am - 11:20am CDT

Hibbard Hall 320

An n-user arbitrarily varying multiple-access channel (AV-MAC) is an information channel that, given n codewords and an adversarial input, outputs a separate word. A channel's capacity is the maximum amount of information that can be sent per bit used over all possible codes. One of the main challenges in information theory is determining what criteria a given channel must have to guarantee that there exists a code such that, with high probability, a given output can be decoded to obtain the original inputs. Any channel that satisfies that criteria is said to have nonzero capacity. A similar, but less restrictive notion is that of partial correction. For a multiple user channel W and real number γ between 0 and 1, we say W is γ partially correctable if it is possible to recover at least a γ fraction of the users' inputs when the adversary acts and recover all users' messages when the adversary does not act. A necessary condition for an AV-MAC to be partially correctable has been found, although the sufficiency of this condition is still an open question. This presentation will focus on sufficiency of this condition after discussing some relevant basic notions in information theory.

Presenters

Matthew Kreiger

University of Wisconsin - Eau Claire

Faculty Mentor

Allison Beemer

MATHEMATICS, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:00am - 11:20am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:00am CDT

Area Proofs of the Pythagorean Theorem

Monday April 21, 2025 11:00am - 11:50am CDT

Hibbard Hall 311

Area proofs of the Pythagorean theorem provide a geometric approach to understanding the relationship between the sides of a right triangle. These visual proofs use the additivity and moving principles to demonstrate equality of area and convey the theorem clearly without relying on algebraic manipulation. Students enrolled in the Spring 2025 Math 304 course will engage attendees in a variety of area proofs in this informal presentation.

Presenters

The Students of Math 304

Faculty Mentor

Katrina Rothrock

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:00am - 11:50am CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:30am CDT

An Analysis of AI-generated Proof and Student Proof Validation

Monday April 21, 2025 11:30am - 11:50am CDT

Hibbard Hall 322

Within the last two years, rapid advancements have made AI chatbot tools such as ChatGPT widely accessible to students. The novelty of these generative AI tools means that research on how students regard and use them is still emerging. Throughout our research, we have applied the theories of mathematical proof as a genre (Selden and Selden, 2013) to study AI generated proofs and how they adhere to these genre conventions. In this talk, we discuss how the knowledge that a mathematical argument was generated by ChatGPT impacts student perceptions of proof validity. We will share initial findings from a survey developed to explore this question and will discuss the pedagogical implications of these AI tools for students’ ability to validate mathematical proofs. We will also discuss how generative AI can be used to assist teachers and students within their classroom and how it can be incorporated into mathematics curriculums.

Presenters

Ellah Olson

University of Wisconsin - Eau Claire

Madison Schwartz

University of Wisconsin - Eau Claire

Faculty Mentor

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire

Jihye Hwang

Monday April 21, 2025 11:30am - 11:50am CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:30am CDT

One + Two + Two + Three + Three = Eleven

Monday April 21, 2025 11:30am - 11:50am CDT

Hibbard Hall 312

We will discuss cryptarithms, what they are and some strategies for solving. Specifically, our presentation will tell a brief history and origin of cryptarithms, present a problem, offer some time for solving, and explain the solution. A small sheet of various cryptarithms will be provided for further exploration at the end of the presentation.

Presenters

Allison Beilke

University of Wisconsin - Eau Claire

Annyka Schnettler

University of Wisconsin - Eau Claire

Faculty Mentor

Jennifer Harrison

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:30am - 11:50am CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

11:30am CDT

Stop! In the Name of Error Correction with Tanner Graphs

Monday April 21, 2025 11:30am - 11:50am CDT

Hibbard Hall 320

Graph based codes allow us to visualize codes and can construct systems of decoding. In graph-based decoding of error correcting codes, it is possible to run into roadblocks called stopping sets which prevent further error correction. How could we construct encoding methods which avoid these roadblocks? We investigate a setting where we must look at partitions of variable nodes with the goal of avoiding stopping sets in at least one part. We examine a particular example with 6 vertices represented by a Tanner graph and corresponding parity check matrix.

Presenters

Grace Cole

University of Wisconsin - Eau Claire

Faculty Mentor

Allison Beemer

MATHEMATICS, University of Wisconsin - Eau Claire

Monday April 21, 2025 11:30am - 11:50am CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

12:00pm CDT

Classifying Enzyme Substrates Using Machine Learning

Monday April 21, 2025 12:00pm - 12:20pm CDT

Hibbard Hall 322

Knowing what types of enzymes a molecule will interact with can aid drug development by minimizing side effects due to unwanted interactions. In this project, we built and interpreted models for classifying enzyme substrates. We utilized the machine learning technique XGBoost in Python to build a predictive model for each enzyme class using the original molecular data as well as top linear combinations of the data obtained using Principal Components Analysis. We will discuss the process of developing code to automatically tune the parameters of XGBoost to optimize the model. We will also present examples of how to interpret these models by writing code to visualize the impact of variables in each model and identifying common factors in the top contributing variables of significant principal components to characterize each enzyme class. For example, we found that the probability of a molecule interacting with oxidoreductase enzymes is positively associated with the number of nonpolar regions. A particular descriptor is NOCount, the number of (polar) NO groups in the molecule, which was negatively associated with the probability of interacting with oxidoreductases.

Presenters

Kyle He

University of Wisconsin - Eau Claire

Faculty Mentor

Abra Brisbin

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 12:00pm - 12:20pm CDT
Hibbard Hall 322 154 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

12:00pm CDT

Knot Theory, Link Homotopy, and Quandles

Monday April 21, 2025 12:00pm - 12:20pm CDT

Hibbard Hall 311

In the 1950s Milnor defined the notion of link homotopy. Since then, its study has been central to the field of knot theory. In the 1980s, Joyce, building on the work of Takasaki, defined a mathematical object called a quandle which is well adapted to the transformation of knot theoretic questions into algebraic questions. Trivial orbit quandles, defined in 2007 by Harrell and Nelson, are a type of quandle useful for studying link homotopy. In this presentation, we define a new trivial orbit quandle called the reduced free quandle, and we go about classifying it for 2 and 3 generators. This gives a classification of 2 and 3 component links up to link homotopy.

Presenters

Keira Darnall

University of Wisconsin - Eau Claire

Nathan Phillips

University of Wisconsin - Eau Claire

Briar Weston

University of Wisconsin - Eau Claire

Faculty Mentor

Christopher Davis

Mathematics, University of Wisconsin - Eau Claire

Monday April 21, 2025 12:00pm - 12:20pm CDT
Hibbard Hall 311 130 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

12:00pm CDT

Putting Respect on the Name of Complex Differentiability

Monday April 21, 2025 12:00pm - 12:20pm CDT

Hibbard Hall 312

The limit definition of a derivative is as rigorous as it is tedious. Thankfully there are a handful of rules which act as short-hand for the difference quotient’s evaluation. Once we learn these, the limit definition becomes an antiquated theorem seemingly used only for exam questions. Rather than a line, the complex numbers form a plane with one variable. Instead of left and right, a limit there must account for the infinitely many paths one could take to the point in question. We will explore this restriction and show how it leads to the Cauchy-Reimann Equations and how a power series follows from a complex derivative.

Presenters

Duncan Koepke

Monday April 21, 2025 12:00pm - 12:20pm CDT
Hibbard Hall 312 138 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

12:00pm CDT

Simulating an Adversarial Presence in a Decentralized Machine Learning Scheme

Monday April 21, 2025 12:00pm - 12:20pm CDT

Hibbard Hall 320

While decentralized machine learning offers several advantages, this process introduces the potential danger of adversarial agents. Rather than changing the learning protocol to accommodate possible adversaries, our work seeks to develop a short, low-overhead validation procedure that allows each honest agent to determine if there is adversarial presence in the network’s learned models. The validation procedure essentially checks whether the local models of neighboring agents differ by too much to reasonably belong to honest nodes. To test the robustness of the algorithm, we simulated a “worst-case” adversarial attack operating in our learning scheme that makes no specific assumptions about how the adversary is able to act on the network. The simulation seeks to quantify how much noise the adversary can inject into the trained non adversarial model trained on MNIST such that our algorithm still accepts it at the validation step. However, results of the simulations revealed a major flaw in our approach and raised subsequent questions which will be discussed in the talk.

Presenters

Morgan Fiebig

University of Wisconsin - Eau Claire

Faculty Mentor

Allison Beemer

MATHEMATICS, University of Wisconsin - Eau Claire

Monday April 21, 2025 12:00pm - 12:20pm CDT
Hibbard Hall 320 146 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

2:00pm CDT

Quantitative Finance: What is it and is it right for me?

Monday April 21, 2025 2:00pm - 2:50pm CDT

Hibbard Hall 102

In this talk, I will describe the discipline of quantitative finance, why it may be a great choice for people with strong STEM skills, and different paths to enter the field. Along the way, I will describe my journey and share some lessons learned.

Presenters

Dr. Gary Hatfield

Monday April 21, 2025 2:00pm - 2:50pm CDT
Hibbard Hall 102 155 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

3:30pm CDT

Mathematics Competition

Monday April 21, 2025 3:30pm - 4:30pm CDT

Hibbard Hall 102

The 33^rd Annual Math Retreat will conclude with the Mathematics Competition. Join our students as they compete to solve a series of challenging Mathematics problems.

Monday April 21, 2025 3:30pm - 4:30pm CDT
Hibbard Hall 102 155 Garfield Ave, Eau Claire, WI 54701, USA

Mathematics Retreat

Department Mathematics
College CAS

2:00pm CDT

Knot Theory, Link Homotopy, and Quandles

Tuesday April 22, 2025 2:00pm - 3:30pm CDT

Davies Center: Ojibwe Ballroom (330)

Knot Theory, Link Homotopy, and QuandlesIn the 1950s Milnor defined the notion of link homotopy. Since then, its study has been central to the field of knot theory. In the 1980s, Joyce, building on the work of Takasaki, defined a mathematical object called a quandle which is well adapted to the transformation of knot theoretic questions into algebraic questions. Trivial orbit quandles, defined in 2007 by Harrell and Nelson, are a type of quandle useful for studying link homotopy. In this poster, we define a new trivial orbit quandle called the reduced free quandle, and we go about classifying it for 2 and 3 generators. This gives classification of 2 and 3 component links up to link homotopy.

Presenters

Keira Darnall

University of Wisconsin - Eau Claire

Nathan Phillips

University of Wisconsin - Eau Claire

Briar Weston

University of Wisconsin - Eau Claire

Faculty Mentor

Christopher Davis

Mathematics, University of Wisconsin - Eau Claire

Tuesday April 22, 2025 2:00pm - 3:30pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

Spotlight on First-Year Research, Mathematics

Department Mathematics
College CAS

11:00am CDT

Poster 075: Generating Symmetric Crossword Grids for the New York Times Mini Puzzle

Wednesday April 23, 2025 11:00am - 1:00pm CDT

Davies Center: Ojibwe Ballroom (330)

A standard crossword puzzle grid contains words of at least three letters, has no completely black rows or columns, and is symmetric. These grids are combinatorial in nature, making them an interesting object of mathematical study. We present code that generates all possible 5×5 crossword grids under specific symmetry constraints, inspired by the format of The New York Times Mini crosswords. Our work builds on existing research by Cote and Merrill (2021) which gave a representation of crossword grids as bipartite graphs with a node for each word and an edge connecting any intersecting words. We construct crossword graphs for all 5x5 grids with various symmetries and study their graph theoretic features. This project contributes new results to the mathematical study of crossword puzzles by exploring non-traditional symmetries in puzzle grids (diagonal, horizontal, vertical) which have not previously been studied.

Presenters

Kirsten Balgord

University of Wisconsin - Eau Claire

Faculty Mentor

Chloe Lewis

Mathematics, University of Wisconsin - Eau Claire

Wednesday April 23, 2025 11:00am - 1:00pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Posters, 1 Wednesday

Department Mathematics
College CAS

12:30pm CDT

Investigating possible relationships between teacher or student motivations related to mathematics

Wednesday April 23, 2025 12:30pm - 12:45pm CDT

Davies Center: Ho-Chunk Room (320E)

Motivation in mathematics classrooms has been researched in various ways, from teacher burnout to to Wigfield and Eccles' theory of student expectancy-value. After examining the existing literature on student and teacher motivations, the results showed a need to focus on teacher and student connections within the mathematics classroom to improve learning environments. The purpose of this research is to use survey instruments to extend previous research by examining potential relationships between teachers’ motivations when teaching mathematics and students’ motivations when learning mathematics. The study consists of completing one of two survey instruments, one for teachers and one for middle and high school students. Both have a set of Likert scale questions and open-ended questions about mathematics teaching or learning along with relevant demographic questions. The data collected from both surveys will be used to examine potential relationships between mathematics teacher and student motivations. These results and implications will be discussed.

Presenters

Maddie Sasse

University of Wisconsin - Eau Claire

Faculty Mentor

Christopher Hlas

Mathematics, University of Wisconsin - Eau Claire

Wednesday April 23, 2025 12:30pm - 12:45pm CDT
Davies Center: Ho-Chunk Room (320E) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Open Oral Presentations and Performances, 1 Wednesday Ho-Chunk

Department Mathematics
College CAS

2:00pm CDT

Poster 079: Math Department Scheduling Using Number of Preps and Back-to-Back Courses

Thursday April 24, 2025 2:00pm - 4:00pm CDT

Davies Center: Ojibwe Ballroom (330)

Presenters

Brynn Bergeson

University of Wisconsin - Eau Claire

Annabelle Piotrowski

University of Wisconsin - Eau Claire

Theodore Schwantes

University of Wisconsin - Eau Claire

Faculty Mentor

Abra Brisbin

Mathematics, University of Wisconsin - Eau Claire

Thursday April 24, 2025 2:00pm - 4:00pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Posters, 2 Thursday

Department Mathematics
Special Categories WI Focus
College CAS

2:00pm CDT

Poster 080: Classifying Enzyme Substrates Using Machine Learning

Thursday April 24, 2025 2:00pm - 4:00pm CDT

Davies Center: Ojibwe Ballroom (330)

Presenters

Kyle He

University of Wisconsin - Eau Claire

Faculty Mentor

Abra Brisbin

Mathematics, University of Wisconsin - Eau Claire

Thursday April 24, 2025 2:00pm - 4:00pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Posters, 2 Thursday

Department Mathematics
College CAS

2:00pm CDT

Poster 089: Longitudinal Comparison of Models to Predict Match Outcomes in the WTA

Thursday April 24, 2025 2:00pm - 4:00pm CDT

Davies Center: Ojibwe Ballroom (330)

Analytics have been less utilized in women’s professional tennis (WTA), compared to other professional sports. Despite unique difficulties in predicting match outcomes, there has been a spate of recent articles that utilize prediction tools applied to men’s profession tennis (ATP) data. Our research adds efficiencies and new features to previously-created probabilistic models for longitudinal predictions of WTA matches. We compute, update, and analyze a set of related summary statistics along with specific match details for individual players and integrate these with Bradley-Terry algorithmic modeling of match probabilities to incorporate strength of schedule. Data for player statistics and results of WTA tournaments was obtained from a GitHub repository under a Creative Commons license. We edited and created original functions in R: wrangling the data across an appropriate time window, court surface, and player rank; and implementing an existing algorithm for prediction and assessment. We also apply Elo ratings for comparative prediction, utilizing a longitudinal update and weighting by strength of win. We discuss the methods and coding, and apply elevated error analysis of match predictions compared to observed match outcomes to determine the overall accuracy of our model; accurate predictions could further inform the ranking of WTA players.

Presenters

Brynn Bergeson

University of Wisconsin - Eau Claire

Morgan Dekan

University of Wisconsin - Eau Claire

Anna Lee

University of Wisconsin - Eau Claire

Faculty Mentor

Jessica Kraker

Professor, Department of Mathematics, University of Wisconsin - Eau Claire

Thursday April 24, 2025 2:00pm - 4:00pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Posters, 2 Thursday

Department Mathematics
College CAS

2:00pm CDT

Poster 106: Knot Theory, Link Homotopy, and Quandles

Thursday April 24, 2025 2:00pm - 4:00pm CDT

Davies Center: Ojibwe Ballroom (330)

Presenters

Keira Darnall

University of Wisconsin - Eau Claire

Nathan Phillips

University of Wisconsin - Eau Claire

Briar Weston

University of Wisconsin - Eau Claire

Faculty Mentor

Christopher Davis

Mathematics, University of Wisconsin - Eau Claire

Thursday April 24, 2025 2:00pm - 4:00pm CDT
Davies Center: Ojibwe Ballroom (330) 77 Roosevelt Ave, Eau Claire, WI 54701, USA

CERCA Posters, 2 Thursday

Department Mathematics
College CAS

2:00pm CDT

Poster 107: Deterministic and Heuristic Analysis of Two-Dimensional Iterated Function Systems

Thursday April 24, 2025 2:00pm - 4:00pm CDT

Davies Center: Ojibwe Ballroom (330)

Iterated function systems offer a framework for generating complex, self-similar patterns through the iterative plotting of points. An iterated function system is a family of functions that map R^2 to R^2. For each iteration of the system, a variation is chosen with a certain probability. The asymptotic points make up the final fractal image. In this work, we examine specific variations using various heuristics that measure behavior between iterations and reveal the system's deeper patterns that improve our understanding of the system's intrinsic behavior. Our research focuses on developing and applying a multitude of heuristics designed to analyze the dynamic behavior of individual variations within these systems. Through visualizations produced by each heuristic, we illustrate the distinct characteristics of each heuristic across multiple variations.

Presenters

CERCA Posters, 2 Thursday

Department Mathematics
College CAS