Kelson, James;Yamada, Kalynn;Jones, Tyler
A Discrete Model to Aid the Crisis in Puerto Rico
Every year, the Consortium for Mathematics and its Applications (or COMAP) holds the Mathematical Contest in Modeling where participants are tasked to choose one of six types of problems based on a real-world scenario and construct a mathematical model within the four-day contest period. With none of us having ever modeled before, we thought it was the perfect challenge. As a group, we vigorously prepared and learned everything we could about mathematical modeling. When the time of the contest came, we were asked to create a disaster response system to aid Puerto Rico in their time of crisis after the terrible hurricane struck there in 2017. This disaster response system involved various tasks such as selecting a drone fleet, creating a drone schedule, and configuring and placing three cargo containers with necessary medical packages for local hospitals. See how our model successfully supplied the needed hospitals in Puerto Rico with medical relief for over a year.
Mentor(s): Nabity, Matthew
Farnell, Emily
Completing the Square and Squaring the Square
Completing the square is a method that can be used to solve quadratic equations by building a square with rectangular sections from the algebraic components. Using manipulatives with this method provides students a visual way to understand the
mathematics as opposed to just plugging in to a formula. A related puzzle is squaring a
square, in which we take a square and we break it down into multiple squares of distinct areas. In my project, I put together interactive lessons to help students understand the foundations of these concepts.
Mentor(s): Cote, Ben
Hanefeld, Sophia
How Many Seats Can You Fit in a Soccer Stadium?
This presentation focuses on the creation and execution of a four-day lesson plan created for a high school geometry class. These lesson plans exemplify the pedagogy known as Project-Based Learning while incorporating concepts from soccer. I will discuss my experience developing these lesson plans and reflect on my experience teaching one of the lessons in a high school classroom.
Mentor(s): Merrill, Leanne
Piller, Kristen
Jordan Canonical and Isomorphism Relationships
The Jordan Canonical Form of a matrix is a significant theoretical tool in linear algebra but is not as useful in practice because it is difficult to compute. In graph theory, graphs are often represented using adjacency matrices.Isomorphisms between graphs are easy to understand but hard to compute. We explore the connection between the Jordan Form of adjacency matrices and isomorphisms and motivate further study.
Mentor(s): Nabity, Matthew
Roan, Morgan
Kicking It With Geometry
For my mathematics education capstone project, I have created a series of lesson plans that have incorporated certain aspects of my favorite sport, soccer. The main goal of my lesson is to have students work together and make a game plan to solve a complex problem involving geometry. This talk will dive into the importance of Project Based Learning as well as teamwork in a classroom.
Mentor(s): Merrill, Leanne
Miller, Gregory NBA MVP Predictor
The National Basketball Association's (NBA) most valuable player (MVP) award is a regular season award that is decided by a panel of sportswriters and broadcasters which varies from year to year throughout the United States and Canada. Each member of the voting panel casts a vote for first place to fifth place selections. The goal of this work is to create a model of an unbiased NBA MVP Predictor. We present our model and compare to other approaches.
Mentor(s): Nabity, Matthew
Manculich, Aubrey
Newton's Method and Chaotic Behavior
We explore the concept of chaos in mathematics. To do so, we use Newton's method to determine the roots of both real-valued nonlinear functions and complex-valued
nonlinear functions. For complex valued function, we demonstrate chaotic behavior and connect to the idea of Newton Basin's and fractals. We present numerical results that motivate further analytic study.
Mentor(s): Nabity, Matthew
Harmon, Max
Paired Kidney Matchmaking Algorithm and Analysis
In this project, we present work towards an algorithm to assist the finding of cycles of patients and donors that are in need of kidneys and willing to donate respectively. We survey existing approaches, and introduce the tools, primarily graph theory, for
developing and analyzing the algorithm as well as establishing assumptions that the algorithm operates under. We then outline our graph theory approach to developing the algorithm. followed by examining improvements and issues with said algorithm with potential solutions to said issues.
Mentor(s): Nabity, Matthew
Riley, Leslie
Patterns in Wythoff's Game of Nim
Wythoff's Game of Nim is a competitive game where players take turns moving towards a goal through a rectangular grid of points. An optimal play involves a specific set of points, d 믭 "critical points", that – when used properly – result in a win. My project delves into the patterns found in these critical points.
Mentor(s): Beaver, Cheryl
Cervantes Almonte, Yetzaveli
Using Circular Statistics to Investigate Changes in the Day of First Bloom
Climate change is a well-documented phenomenon with many tangible effects. One of the concerning results has been shifting phenological events. We apply circular
statistical methods to investigate the observed day of first bloom of various species found along a mountain trail. We compare the mean day of first bloom between five different elevations and see how these differ through time. Our analysis of the data shows variation in the day of first bloom and motivates further analysis.
Mentor(s): Nabity, Matthew