Subject Area: Ordinary Differential Equations and Dynamical Systems

McKenzie Garlock*, Eastern Oregon University
Jeremy Bard*, Eastern Oregon University
Zach Nilsson*, Eastern Oregon University
Mathematical Modeling of Heat Through a Hot Bath
No one likes a cold bath. When the bath water starts to get cold a person might turn on a constant trickle of water to keep the water tepid. We attempted to model, and optimize, this behavior with differential equations. To do this we simplified the situation and started with a bathtub that had...

Aubrey Ibele*, Gonzaga university
Audrey Gomez*, Gonzaga University
Dynamic of Love
Dynamical systems both linear and nonlinear have the power to describe intricate behavior and provide analysis. In this paper, linear and nonlinear models are employed to replicate the interaction between individuals with varying romantic styles. Using traditional analysis methods the goal was...

Thomas Burns*, Southern Oregon University
Jacob Schultz*, Southern Oregon University
How to Take a Hot Bath, if You Can Spare the CPU Cycles
We discuss multiple methods for modelling the temperature of a bathtub taking into account conductance, evaporation, and turbulence. One model uses a system of ordinary differential equations to represent the temperature with respect to time of multiple materials in the system, while another...

Steven Beres*, Gonzaga University
Caleb Tjelle*, Gonzaga University
An Elementary Analysis of Chua's Circuit
Prior to the invention of Chua's circuit by Leon Chua in 1983, it was generally believed that it was not possible to design an electronic oscillator which exhibited chaos. In this talk, we provide an overview and analysis of Chua’s chaotic circuit. Principally, we will show the...

Svetlana Dyachenko*, Western Oregon University
Equations for Bacteria Growth
Bacteria growth is really important in our life. Some bacteria cells help us overcome different diseases, while others bring those diseases to us. We have learned to produce medicine with help of bacteria growth, like insulin, to help those who are ill. Modeling bacteria growth is an important part...
Subject Area: Algebra

Bryce Boyle*, George Fox University
Matt DeBiaso*, George Fox University
Analyzing Transition Matrices of Chutes and Ladders Game Variant
Imagine each directional chute and ladder in the classic board game replaced with bidirectional portals. How does the game change? Expected game play and probabilities of each position are determined by the location and type of eigenvalues. We analyzed the transition matrix and discovered...

Nhan Nguyen*, University of Montana
Kummer subspaces of Central Simple Algebras
Let $F$ be a field containing a primitive $d^{th}$ root of unity $\rho$ and char$(F)\notd$. Let $A$ be the tensor product of $n$ cyclic $F$algebras. An element $v\in A$ is Kummer if $v^{d}\in F$. A subspace of $A$ is Kummer if every element is Kummer. Kummer spaces have been used to bound the...

Tyler McAfee*, Western Oregon University
Commuting Pairs in Finite Nonabelian Groups
The study of the probability that two group elements commute dates back to 1968 with the work of Paul Erdos and Paul Turan. Since then, much has been deduced about these probabilities, including its bound of $5/8$ for nonabelian groups. During this talk, we will look at the associated probabilities...
Subject Area: Topology

Hayley Olson*, Gonzaga University
Bryan Strub*, Gonzaga University
Ryan Lattanzi, Gonzaga University
Klein links versus torus links, part II
We will examine the relationship between Klein links and torus links, using both diagrammatic techniques and link invariants. We determine the types of components in a Klein link, and use this result to look at which Klein links are torus links and which are not.

Allison Stacey*, Oregon State University
A Basis for the Space if Order 5 Chord Diagrams
In the study of Vassiliev Knot Invariants, the algebra of chord diagrams plays a key role. A chord diagram of order n is a circle with 2n vertices around it with chords through the circle connecting the vertices pairwise. The algebra of such diagrams is isomorphic to closed Jacobi diagrams which...

Ryan Lattanzi*, Gonzaga University
Bryan Strub*, Gonzaga University
Hayley Olson, Gonzaga University
Klein links versus torus links, part I
We will examine the relationship between Klein links and torus links, using both diagrammatic techniques and link invariants. We begin with definitions of these links and some basic results about Klein links.

Brett Hegge*, Western Oregon University
From Manipulatives to Theory in Knot Theory
Knot Theory is the study of simple closed curves in three dimensions. Complicated structures can be analyzed using three basic moves and knots can be shown to be equivalent. We discuss ways of using physical manipulation to get middle school students interested in mathematics. We also, explore the...

Anthony Dominquez*, Western Oregon University
Separability and the Cantor Set
The Cantor Set is a famous set in pointset topology. There are a wide variety of types of Cantor Sets. However, we will only cover the ternary, or standard Cantor Set. In this talk, we will define and discuss what it means for a set to be separable and prove that the Cantor Set satisfies this...
Subject Area: Combinatorics

Kyle Oddson*, Portland State University
Math and Sudoku: Exploring Sudoku boards through graph theory, group theory, and combinatorics
Encoding Sudoku puzzles as partially colored graphs, we state and prove Akman’s theorem regarding the associated partial chromatic polynomial; we count the 4x4 sudoku boards, in total and fundamentally distinct; we count the diagonally distinct 4x4 sudoku boards; and we classify and enumerate the...

Amanda Evola*, Western Oregon University
Examining Ramsey Numbers
This paper explores the work of Frank P. Ramsey who founded Ramsey’s Theorem and is centered on the fact that complete disorder is impossible. The goal is to dig into Ramsey’s Theory by examining various Ramsey Numbers and bounds. Through this examination of Ramsey Numbers we will begin to see...

Emily Hiscox*, George Fox University
Ellen Pearson, George Fox University
Adding Color to Combinatorics
Taking the conclusions found in Candy Crush Combinatorics by Dana Rowland, and expanding them by one color to see how many possible combinations can be found using two rows of candy's and 3 colors.

Omid Khormali*, University of Montana
On the Turan number of forests (Canelled)
A wellknown conjecture of Erd\H os and S\'{o}s states that the Tur\'{a}n number for paths is enough for any tree i.e. a graph $G$ on $n$ vertices and more than $\frac{k2}{2}n$ edges contains any tree on $k$ vertices.
A natural extension of the problem is the determination of the Tur\...
Subject Area: Other

Crystal Susbauer*, Pacific University
Graph Products and Colorings in Relation to the Hedetniemi Conjecture
There are many types of product operations defined in graph theory. These products use the vertices and edges of two (not necessarily distinct) graphs to create a new graph. We focus on four important types of graph products: the Cartesian product, the direct product, the strong product, and the...

Jillian Welk*, George Fox University
A Mad Math Tea Party
This poster presentation will focus on the research done in an article on cyclic partitions involving an Alice in Wonderland theme.

Carter Bedsole*, George Fox University
Gary Buckley*, George Fox University
Understanding the Traveler's Dilemma
In the game theory problem The Traveler's Dilemma, the theoretical and experimental results differ greatly. This discrepancy is explained through evolutionary game theory.
Subject Area: History of Mathematics

Eric Rogers*, Gonzaga University
Ethan Snyder*, Gonzaga University
InfinitesimalBased Calculus
When Newton and Leibniz first developed calculus, they did so by using infinitesimals (really really small numbers). Infinitesimals were used until calculus was made more rigorous by Weierstass. The calculus that we are taught today is based on Weierstass’s ϵδ definition of the limit. However,...

Garrison Iams*, Klamath Community College
The Math Behind The Rubik’s Cube
Come hear about the intricacies of the Rubik's Cube! I will discuss the history of God's number, which is the least amount of moves it takes to solve a scrambled Rubik’s Cube. There are many techniques to solve a scrambled Rubik's Cube. One solution technique which can be modeled by...

Lane Thomason*, Southern Oregon University
Rearrangement in an Infinite Series
Typically we are free to use associative and commutative properties without problems with real numbers. However, under certain conditions, these can break in infinite series. This talk will look into what happens when these conditions are met.
Subject Area: Mathematics Applications in the Sciences

Luke Campbell*, Central Washington University
Mathematical Modeling of Competition and Coexistence of Phytoplankton Species
Microscopic phytoplankton form the basis of the food chain in the earth’s oceans. A system of differential equations relates phytoplankton population and nutrient concentration in an isolated environment. The equations were modeled with MATLAB. I conducted sensitivity analyses to determine the...

TJ Norton, Klamath Community College
Starved? Let's Solve That Math Hunger!
We all enjoy that time of day when we get to sit down and enjoy our favorite meal. We typically eat three or more times per day. However, being a hardworking college student and living on a college budget often severely restricts the amount of money we can spend. Essentials like lunch, dinner, and...

Thad Joachim*, Klamath Community College
Theatrical! Practical! Mathematical!
My talk will focus on how mathematics can be used in the real world relating to theatre arts, and I will support my discussion by giving realworld examples. Actors and other theatre individuals should be able to take math seriously when the math is involved with a theatrical performance. I will...

Nikki Carter*, University of Portland
Eigensystems of Electrical Networks
The eigenvectors of an electrical network are voltages that, when placed at the boundary vertices, produce boundary currents that are a scalar multiple of the boundary voltage. The objective of this research is to gain information about a given electrical network using eigensystems. In particular,...

Will Kugler*, Klamath Community College
Fractals in Geology: Measuring Intricate Forms (Cancelled)
First I will give an introduction to fractals, a naturally occurring mathematical set that repeats a detailed pattern visible at any scale. Then I will connect fractals to realworld applications in Geology and Earth Science. I will discuss how fractals are used by geologists with the use of...

Kayla Vincent*, Western Oregon University
The process of representing food webs as interval competition graphs
A food web is defined as an acyclic graph where vertices represent different species and there is a directed edge from species x to species y if species x preys on species y. Food webs are important in Biology because they model the flow of energy in an ecosystem. A competition graph has the same...

Kaylee Church*, Western Oregon University
Insects and Spirals
The logarithmic spiral, also known as the growth spiral, is an interesting form in mathematics that happens to be very applicable to the natural world. We explore the structure of this curve, and how this spiral can be used to model the flight pattern of a moth. Specifically, we investigate...
Subject Area: Logic and Foundations
Subject Area: Numerical Analysis and Scientific Computing

David Calkins*, George Fox University
Rat Game Expanded
Mathematician Aviezri S. Fraenkel wrote a paper on a game called The Rat Game, which involves mathematical moves and strategies. I plan to inform and expand on some of these moves and add to the game.

Sally Peck*, Western Oregon University
Algorithmic Variants of QR
One of the fundamental computations in numerical linear algebra is the QR factorization. A QR factorization decomposes a matrix into the product of an orthogonal matrix and an upper triangular matrix. The algorithms that compute these decompositions can often be costly, and at times, do not...

Joseph Stauss*, Gonzaga University
Perturbing Equilibria of the ThreeBody Problem
The LagrangeRelative Equilibrium and the Figure8 Equilibrium are the only known periodic solutions of the ThreeBody problem in the case of equal masses. These equilibria were analyzed by using a finitedifference method to approximate their perturbationresponse for various quantities. The...

Alleta Maier*, Linfield College
Looking for a (Super)resolution to an Image Processing Problem.
In recent years sparse coding has been employed to efficiently process images. Since recovering sharp images from images corrupted with noise is a wellknown illposed problem, small perturbations in the image lead to large deviations in the reconstructed image. We look to combine research in...
Subject Area: Geometry

Mackenzie Koll*, Western Oregon University
Regular Stars, Polygons, and Musical Scales
Edge scales are musical scales constructed from the edges and vertices of a regular polygon. Regular polygons are polygons that have specific structure and they can be constructed from regular stars.
We will discuss this structure using elements of rational trigonometry and discuss regular stars...

Viv Diebel*, George Fox University
Ian Johnson, George Fox University
A Visual Expansion of the Pythagorean Theorem
The poster is a visual expansion of the Pythagorean Theorem.

Jonathan David Evenboer*, Oregon State University
Laplacians & Laplace Transforms with Respect to Geometric Analysis of 1Manifolds of Constant Curvature
This presentation continues on the course begun in past NUMS presentations. Properties of the Laplacian values of the Circle and Aster, and the Laplacian's role in construction of the heat kernel on both manifolds, are covered. Also covered will be properties of the Laplace Transform values of...
Subject Area: Number Theory
Subject Area: Probability and Statistics

Travis Lowe*, Eastern Oregon University
Sydney Nelson*, Eastern Oregon University
Amy Yielding, Eastern Oregon University
Applying a Multilinear Regression Model to Predict Air Quality in Burns, Oregon
The City of Burns, Oregon has a serious air quality issue. The city frequently experiences very high levels of PM2.5. PM2.5 consists of a variety of particulates whose size is less than 2.5 micrometers. Such particulates can be inhaled and generally accumulate in the lungs of humans, displaying a...

Charles Haneberg*, George Fox University
Predicting Wins and Losses in Division III Women's Basketball
A method is presented for predicting future wins and losses in tournamentstyle games based on previous game outcomes. This method is applied to the recent Division III women's basketball season.

Bridget Daly*, Pacific University
Use and Misuse of Regression for Chemical Analysis
It is standard practice in analytical chemistry to use linear regression, particularly to calibrate analytical instruments. If a regression line were used to estimate the output of the instrument for a known concentration of analyte, all would be well. However, chemists use this line in reverse,...

Dora Bixby*, Southern Oregon University
Logging with Markov chains
Oregon is the U.S.'s top lumber producer and the industry makes up a large portion of the jobs in the Oregon workforce. I will be discussing the use of absorbing Markov chains to model the growth of trees in a stand, then analyzing the model to develop a reliable and steady harvesting schedule.
Subject Area: Mathematics Education

Emma Winkel*, Pacific University
Reading $\pi$: Helping children move from symbol to meaning
Students currently learn of $\pi$ in a formulaic context; as a value needed for the effective calculation of the circumference or area of a circle. In this talk, we present an activity that uses manipulatives to help middle grade students develop an understanding of the geometrical meaning of $\pi$.

Tiffany Klink*, Klamath Community College
Math Anxiety: The Common Plight
There are multiple causes to Math Anxiety ranging from actual facts to myths about math. Mathematics is a subject that many people struggle with daily. Not just mathematics involved in engineering, but the basic math skills needed for leaving a tip. Some topics discussed will be: how to think about...