2024 Mathematics Capstone Symposium

Friday, May 3rd
Join the Mathematics Department in Morken 214 and Morken 216 to hear the senior capstone presentations. If you’re unable to join us in-person, we welcome you to attend via Zoom. You can join the Morken 214 capstone session here. You can join the Morken 216 capstone session here.

Morken 216

1:00pm – The Dynamic Trio
Kirill Perfiliev
In the event of a catastrophe, where help can only be delivered using a helicopter, it is essential to have a distribution plan with the most efficient and least time-consuming routes. Linear Programming (LP), Integer Programming (IP), and Vehicle Routing are the perfect candidates  –  they are all about solving large-scale problems with distributions. LP and IP provide the best optimal distribution of limited resources subject to various constraints, and Vehicles Routing provides the most optimal routes to deliver all of the supplies based on given constraints.

1:30pm – Strategies for Selection: Predicting PLU Student Retention through Multiple Logistic Regression Analysis
Meghan Bonafilia
In this presentation, we will explore a data set with over 4000 observations concerning first year students at PLU and their likelihood of staying at PLU for the next year. Using logistic regression for analysis, we will review different model selection processes and explore several factors like: GPA, race, whether or not a student is first generation, whether or not a student lives on campus, and more.

2:00pm – Statistical Analysis of Bechdel Test Data: How movies are impacted by their representation of women
Eva Reutercrona
The representation of women in movies and media is an important current topic. The entertainment industry has historically  been male dominated and has been slow to change. As a way to analyze a movie’s representation of women, a test was created by Alison Bechdel, an American graphic novelist, to measure representation of female identifying characters in media. In order to pass the test there must be at least two female characters that talk to each other about something other than a man. In this project we will be analyzing movie data from FiveThirtyEight, which contains each movie’s Bechdel  test rating. We will be looking at this rating along with other variables such as genre, budget, and parental ratings. From these variables we will create linear models and perform Chi-Squared Tests to understand the statistical differences in Bechdel passing and non-Bechdel passing movies.

2:30pm – Break

3:00pm – Handling Missing Data in Epidemiology Research: Do Different Approaches Affect How the Federal Income Poverty Ratio Predicts Tap Water Consumption?
Mackenzie Mueller
Missing data in epidemiology and public health research is often poorly handled, poorly analyzed, and sometimes not even reported at all. This can significantly influence the results of these studies, often causing bias towards or against certain populations. The “quick-fix” solution of using only the complete cases in epidemiological research not only diminishes the size of the data by a sometimes unignorable amount, but also takes out a critical component of the narrative behind the data. “Why is this data missing? Why do certain groups have more missing data than others? How can we address this?” These are questions that every researcher should be asking before starting analysis on any dataset, but they are questions that often go overlooked or unanswered. In this presentation, we will explore potential underlying factors for missing data, types of missing data, useful (and not-so-useful) strategies for addressing missing data, and analyze an example dataset from the National Health and Nutrition Examination Survey (NHANES) using R Statistical Software.

3:30pm – Introducing Insurance and Risk: The Fokker-Planck Equation
Quinlan Shick
Mathematical finance is a versatile topic that is connected to our daily life. Insurance companies have been around to help us as citizens pay for damage or uncertainty we encounter in many aspects of our lives. This presentation will give you an introduction to insurance with what risk is, and investigate the uses of the Fokker-Plank equation in mathematical finance. The Fokker-Planck equation is connected to insurance and risk because it helps calculate all the possible outcomes or amounts of money you could receive or have to pay, which would be affected after a certain period based on uncertain events that either have a low or high probability and impact the return you receive.

Morken 214

1:00pm – Exploring Tessellations by Regular Polygons
Lindsey Clark
Have you ever wondered what the math is behind a honeycomb? Or the tiling on your bathroom floor? These, as well as many other structures around us, are often made of tessellations by regular polygons. Tessellations, also known as tilings, have an almost constant presence in our lives, yet the math behind them isn’t always apparent. In this presentation we will explore the ways in which regular polygons tile the plane with a focus on regular and semi-regular tessellations. These ideas will lead us to discover why some regular polygons, on their own or combined with others, can and cannot tile a plane!

1:30pm – Exploring Mathematical Explanation and Induction
Elijah Paez
In the development of mathematics, students and mathematicians often seek explanations for their results: insights that provide reasons why certain statements hold, rather than merely demonstrating that they hold. For philosophers of mathematics, proofs that utilize induction are almost always considered to not be explanations. This project will overview the characteristics associated with mathematical explanations and explore key lines of debate regarding the relationship between explanation and induction, drawn from scientific explanation frameworks and several meta-mathematical proof examples.

2:00pm – Spot It!: A Mathematical Analysis
LeighAnna Zielske
Spot It! is a deceptively simple game wherein players examine a pair of cards, each featuring eight different symbols, and compete to be the first to find a symbol that appears on both. The deck is cleverly constructed so that every pair of cards has exactly one symbol in common. This isn’t by luck or by rote guess-and-check—it’s math! In this presentation we will discuss how the deck can be represented by a geometric structure called a finite projective plane, and thus how a projective plane can be used to create a Spot It! deck. Furthermore, we will discuss how projective planes are generated from affine planes, and demonstrate how the axioms of projective planes guarantee the necessary properties for gameplay.

2:30pm –  Break

3:00pm – Folding a Heptagon
Jacob Roberts
A long-standing problem in mathematics has been the construction of a heptagon. Proven to be impossible to construct with a straightedge and compass in geometry, mathematicians looked for other methods of construction. One of the methods found was origami. We will explore  origami, how it works and how we can use it to fold a heptagon.

3:30pm – Mathematical Assessments of Gerrymandering: Making Your Vote Matter
Clayton Wise
The manipulation of voting district borders is a fact of the American political system that can and has been used, intentionally or not, to repress and bolster certain voting demographics. Despite this known and studied fact, methods for identifying unequal district maps have only recently been developed and used in practice. In this paper, we seek to explain the problems of redistricting, as well as to highlight, explain, and critique mathematical methods for identifying gerrymandered map.