## Session: Plenary Talks

**Karen Saxe*, Macalester College****Measuring Inequality**

Whether a resource -- such as income -- is distributed evenly among members of a population is often an important political or economic question. The Occupy Movement has recently drawn more attention to the fact that income inequality in the United States is increasing. How can we measure this...**Brian Hopkins*, Saint Peter's University****The Symmetric Group and Fair Division: Does Knowledge Matter?**

Sports drafts and divorce settlements are examples of situations where players take turns selecting indivisible goods. Like other topics in fair division, the situation is made more interesting because people may

value the goods in different ways. In this talk, we focus on the case of two...**David Pengelley*, Oregon State University****How efficiently can one untangle a double-twist? Waving is believing!**

Can you do the Philippine candle dance, the Dirac belt trick, or the Feynman plate trick? Whether your answer is yes or no, this event will engage you in this and far beyond in discovering and understanding the most mathematically efficient way to untangle a double-twist in 3-space. Limber up!**Stuart Boersma*, Central Washington University****Cryptologic Tidbits**

Cryptology offers an ideal setting to give students a powerful and successful experience in mathematics. Cryptologic examples allow students to connect new content with prior knowledge, and provide students the opportunity for productive struggle with challenging material. Cryptologic contexts...

## Session: NUMS Student Presentations and Poster Session

### Subject Area: Geometry

**Jonathan David Evenboer*, Oregon State University****Laplacians & Laplace Transforms with Respect to Geometric Analysis of 1-Manifolds 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...**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.

### Subject Area: Combinatorics

**Ian Kit Nicolas*, Pacific University****Proper Graph Colouring via Combinations****(Not Published)**

We develop a new type of proper graph colouring that makes use of a number of colours at most the chromatic number. Proper graph colouring refers to the assignment of labels onto vertices of a graph such that adjacent vertices have distinct labels. This new proper graph colouring, called...**Amanda Evola*, Western Oregon University****Examining Ramsey Numbers**

This paper explores the work of Frank P. Ramsey who founded Ramseyâ€™s Theorem and is centered on the fact that complete disorder is impossible. The goal is to dig into Ramseyâ€™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.**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 Akmanâ€™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...**Omid Khormali*, University of Montana****On the Turan number of forests (Canelled)**

A well-known 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 $\frac{k-2}{2}n$ edges contains any tree on $k$ vertices.

A natural extension of the problem is the determination of the Tur\...

### Subject Area: Topology

**Duot Chol Gak, University of British Columbia****Mathematics of Topology****(Not Published)**

preservation of structures under extreme circumstances. e.g Houses in Tsunami, Bumpers of cars,**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...**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...**Anthony Dominquez*, Western Oregon University****Separability and the Cantor Set**

The Cantor Set is a famous set in point-set 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...**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.**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.

### Subject Area: Mathematics Applications in the Sciences

**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...**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 earthâ€™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...**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,...**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 hard-working 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 real-world examples. Actors and other theatre individuals should be able to take math seriously when the math is involved with a theatrical performance. I will...**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 real-world applications in Geology and Earth Science. I will discuss how fractals are used by geologists with the use of...

### 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...**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,...**Kyle Logan*, Governor's School for Science and Technology****TSER Value Determination of NFL Quarterbacks****(Not Published)**

In American football, an efficient quarterback is key in scoring and winning a game.

This study sought to test whether a higher quarterback TSER value could possibly

determine the chance of a possible team winning record during the regular season

based on the TSER Scale. This study was...**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 tournament-style games based on previous game outcomes. This method is applied to the recent Division III women's basketball season.**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: History of Mathematics

**Eric Rogers*, Gonzaga University****Ethan Snyder*, Gonzaga University****Infinitesimal-Based 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 Weierstassâ€™s Ďµ-Î´ definition of the limit. However,...**Garrison Iams*, Klamath Community College****The Math Behind The Rubikâ€™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 Rubikâ€™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: Ordinary Differential Equations and Dynamical Systems

**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...**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...**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 Chuaâ€™s chaotic circuit. Principally, we will show the...**Aubrey Ibele*, Gonzaga university****Audrey Gomez*, Gonzaga University****Dynamic of Love**

Dynamical systems both linear and non-linear have the power to describe intricate behavior and provide analysis. In this paper, linear and non-linear models are employed to replicate the interaction between individuals with varying romantic styles. Using traditional analysis methods the goal was...**Noah Walton*, Portland State University****Elisa Bellah, University of Oregon****Erin Tannenbaum, Portland State University****Derek Garton, Portland State University****Heuristics for Cycles of Polynomials Over Finite Fields****(Not Published)**

In 2014, Flynn and Garton bounded the average number of components of the functional graphs of polynomials of fixed degree over a finite field. In many cases, their lower bound matched Kruskal's asymptotic for random functional graphs. Their upper bound was far less satisfactory, as it was far...**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...

### Subject Area: Numerical Analysis and Scientific Computing

**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 Three-Body Problem**

The Lagrange-Relative Equilibrium and the Figure-8 Equilibrium are the only known periodic solutions of the Three-Body problem in the case of equal masses. These equilibria were analyzed by using a finite-difference method to approximate their perturbation-response for various quantities. The...**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.**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 well-known ill-posed problem, small perturbations in the image lead to large deviations in the reconstructed image. We look to combine research in...

### 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...

### Subject Area: Algebra

**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...**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$(F)\not|d$. 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...**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...

### Subject Area: Other

**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.**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.**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...

### Subject Area: Logic and Foundations

**Mimi Miller*, George Fox University****7 Variables**

Proving the number of unique fair games that can be played with seven variables and showing that they are isomorphic.

### Subject Area: Number Theory

**Tyler Chin*, George Fox University****Ben Van Vliet*, George Fox University****Triangular Numbers and Squared Numbers**

Visual demonstrations of the relationships between squared numbers and centered squared numbers.

## Session: Junior Faculty Research

**Christian Millichap*, Linfield College****Geometric Invariants of Knots**

Given two arbitrary knots (tangled up strings with their ends tied together), how can we (easily) tell if they are different or not? In general, this problem is extremely difficult to answer, and has led to the development of a variety of knot invariants. In this talk, we will examine geometric...**Yajun An*, Pacific Lutheran University****Dispersion reduction schemes for the wave equations**

Finite Difference (FD) schemes have been used widely in computing approximations for partial differential equations for wave propagation, as they are simple, flexible and robust. However, even for stable and accurate schemes, waves in the numerical schemes can propagate at different wave speeds...**Kyle Riggs*, Eastern Washington University****The Difficulty of Classifying Decomposable Torsion-Free Abelian Groups**

An abelian group is decomposable if it can be written as a direct sum of two (or more) nontrivial subgroups. Otherwise it is indecomposable. The only indecomposable torsion groups are cyclic groups of the form $\mathbb{Z}(p^n)$, where $p$ is prime (as well as Pr\"ufer groups, $\mathbb{Z}(p^\...**Masaki Ikeda*, Western Oregon University****Introduction to permutation patterns**

In enumerative combinatorics, the study of permutation patterns blossomed in the 1980s with the Stanley-Wilf conjecture. In this talk, I will introduce the basic concept of permutation patterns and some approachable examples as well as the final result of my doctoral research.**Kate Kearney*, Gonzaga University****An Obstruction to Knots Bounding Mobius Bands in B^4**

The relationship between embedded surfaces and their knotted boundaries has been one of the main topics of knot theory for much of the last half century. This talk focuses on a particular case, namely whether a given knot in the three-sphere can be the boundary of a Mobius band embedded in the four...

### Subject Area: Numerical Analysis and Scientific Computing

**Corban Harwood*, George Fox University****Using Eigenvalues to Investigate Numerical Oscillations**

In numerically solving linear partial differential equations, carefully formed matrices are powered up as the algorithm iterates the solution through time. Depending upon the eigenvalues, the solution either blows up to non-numerical values, stabilizes with bounded oscillations, or stabilizes free...

## Session: Algebra and Number Theory

**Jeffrey Wand*, Gonzaga University****A Game of 1â€™s and 2â€™s: Constructing level 2 Demazure Filtrations of level 1 Demazure modules**

In this talk we dive into the representation theory of Lie algebras. Representation theory is an area of math that studies algebraic structures and the objects they â€śact on.â€ť In addition, it is also a great tool that takes problems in abstract algebra and turns them into linear algebra problems....**Dibyajyoti Deb*, Oregon Institute of Technology****Visualizing p-adic numbers**

P-adic numbers after its introduction by Kurt Hensel more than a century ago, has been a mainstay in the field of number theory. An abstract concept by itself, in this talk we will look at how we can visualize p-adic numbers with a tree structure and look at some basic questions in p-adic analysis...**Katharine Shultis*, Gonzaga University****Systems of parameters and the Cohen-Macaulay property**

Cohen-Macaulay rings play a central role in commutative algebra and there are many connections between systems of parameters and the Cohen-Macaulay property. In a Cohen-Macaulay ring, every system of parameters is also a regular sequence (roughly speaking it behaves like a set of polynomial...**Shannon Overbay*, Gonzaga University****Hamiltonian Properties of Toroidal Zero Divisor Graphs**

The zero divisor graph of a commutative ring $R$ is formed by taking the nonzero zero divisors of $R$ as the vertices and connecting two vertices exactly when the corresponding product of the two elements is zero. We will show that all 44 planar zero divisor graphs are subgraphs of planar graphs...**Kirk McDermott*, Oregon State University****Decomposable Cyclically Presented Groups and Shift Dynamics**

A group with a cyclically symmetric presentation admits an automorphism of finite order called the shift. In this talk we look at cyclically presented groups which admit a certain decomposition, and relate the shift dynamics for the group to the components of the decomposition. Topological methods...**Tianyuan Xu*, University of Oregon****The subregular part of Lusztig's asymptotic Hecke algebra**

Given an arbitrary Coxeter system (W,S), Lusztig defined its asymptotic Hecke algebra J, an associative algebra closely related to the usual Hecke algebra and the category of Soergel bimodules for (W,S). The algebra J decomposes as a direct sum of subalgebras indexed by the 2-sided Kazhdan-Lusztig...**Robert Ray*, Gonzaga University****G-Sets and Sequences Associated with nth Order Linear Recurrences Modulo Primes}**

We consider nth order linear recurrence relations of the form $S_k=a_{k-1}S_{k-1}+a_{k-2}S_{k-2}+\cdots+a_{k-n}S_{k-n}$ over the finite field $Z_p$, where $p$ is a prime not equal to 2. The results regarding the distribution of elements in the sequence $\{S_0,S_1, \dots \}$ are well known for...**Nicholas Davidson*, University of Oregon****Categories of Representations of the Lie superalgebra q(2)**

I will give an overview of the representation theory of the queer Lie superalgebra q(n), focusing in particular on the representations of q(2) in its BGG category O.**Thomas Morrill*, Oregon State University****Overpartition Statistics**

Many partition results and $q$-series identities are classically derived through analytical techniques, though the results beg for a combinatoric interpretation. -- the standard examples being the Ramanujan congruences. Historically, the combinatorics were filled in by studying integer valued...

## Session: General Papers

### Subject Area: Mathematics Education

**Francisco Savina, University of Texas at Austin****An Active STEM-Prep Curriculum**

The STEM-Prep Pathway is designed as two one-semester courses created by the New Mathways Project that prepare students beginning at the elementary algebra-level to succeed in college-level calculus. All lessons are designed to be contextual and meaningful, with guided student inquiry at the core....

### Subject Area: History of Mathematics

**Nicole Wessman-Enzinger*, George Fox University****An Investigation of Subtraction Algorithms Utilized in the US during the 18th and 19th Centuries**

Over 30 arithmetic texts and 280 cyphering books utilized in the United States during the 18th and 19th centuries were examined for subtraction algorithms. A framework for different types of subtraction algorithms utilized at this time will be presented. The investigation revealed that same...

### Subject Area: Logic and Foundations

**Aaron Montgomery*, Central Washington University****Doug DePrekel, Central Washington University****Infinity (Still) Blows My Mind**

As filler in an undergraduate abstract algebra class, I tossed out a question that I had encountered in a high school math puzzler involving the final state of an infinite process. In the process, chips are added and removed from a bag and the question asks what remains at the end of all additions...

### Subject Area: Ordinary Differential Equations and Dynamical Systems

**David Hammond*, Oregon Institute of Technology - Wilsonville****Propagation of transient behaviour in linear flocking models**

This talk will introduce a set of models for describing the behaviour of linear flocks. One application of these models is to describe groups of autonomous automobiles on a one-lane road, where each automobile controls its acceleration based on the differences of its own position and velocity from...

### Subject Area: Analysis

**Nathan Taylor*, University of Montana, Missoula****Pathological Continuity: A Zoo of Nowhere-Differentiable Functions (CANCELLED)**

Poincare said of pathological functions, "logic sometimes makes monsters." We will investigate some classical examples of the monsters which are continuous but nowhere-differentiable real functions. We will take a historical perspective, with emphasis on visualizing the various examples...

### Subject Area: Mathematics Applications in the Sciences

**Terri Torres*, Oregon Institute of Technology****Hypothesis Testing with Person-Time Data**

In the area of epidemiology person-time data is a common measurement. I will address the inference associated with this measurement.**Brian Sherson*, Oregon State University****Numerical Inversions of the Broken Ray Transform with fixed initial and terminal directions**

The Broken Ray transform is a transform used in single-scattering tomography, and was introduced by Lucia Florescu, Vadim A. Markel, and John C. Schotland, in 2009, and shown to be invertible in the case of fixed initial and terminal directions. An inversion formula for this case, involving a...

### Subject Area: Probability and Statistics

**Curtis Feist*, Southern Oregon University****Jake Scott, Southern Oregon University****If You Must Gamble: Minimizing Expected Loss**

We consider a typical gambling situation such as red/black roulette bets of a fixed size, with a limited bankroll, a fixed goal (such as doubling oneâ€™s money), and a maximum time of play. Through the use of Markov chains, we analyze the expected value of this game for various bet sizes. Unlike in...**Chris Hallstrom*, University of Portland****First to Toss N Heads Wins**

Two players play a game, taking turns tossing a coin; the winner is the first to reach $n$ heads for some agreed upon value of $n$. What is the probability that the player to go first wins? In this talk, we will consider this question as well as its application to your lunch-time half-court...

### Subject Area: Combinatorics

**Roger MadPlume*, University of Montana****Examining Matroids with Unique Addresses**

In the September 2013 issue of Math Horizons Gary Gordon posed the following problem:

For a finite set of points in the plane, write down the following data: For each point P, record the number of 3-point lines through P, the number of 4-point lines through P, and so on. Is there a finite set of...**Gerald Todd*, University Of Montana****Breaking Bad Symmetries**

Point-line configurations in the plane can have many types of symmetries. We will investigate bijections of point-line configurations that preserve a certain structure (automorphisms). Of course, to 'break' these symmetries, we can simply fix all points, but we are interested in the...

## Session: Research in Undergraduate Mathematics Education

**Nicole Wessman-Enzinger*, George Fox University****Prospective Teachersâ€™ Reasoning about Integers and Temperature**

Ninety-eight elementary and middle school prospective teachers participated in a study focusing on integer addition and subtraction while enrolled in an introductory mathematics content course emphasizing number concepts and operations. Across two academic semesters, the prospective teachers posed...**Kristen Vroom*, Portland State University****Kate Melhuish, Teachers Development Group****Student Conceptions of Isomorphism**

During creation of the Group Concept Inventory (GCI), we discovered that the initial question related to isomorphism adapted from Weber & Alcock (2004) (Are Q and Z isomorphic?) contained a number of hidden complexities related to student understanding of isomorphism. We developed two new...**Emily Cilli-Turner*, University of Washington Tacoma****Impacts of Inquiry Pedagogy on Undergraduate Studentsâ€™ Conceptions of the Function of Proof**

Mathematicians and mathematics educators agree that proof has many different roles in mathematics beyond that of verifying the truth of a statement. For instance, some proofs can not only show that a statement is true, but also explain why it must be true. However, students may not appreciate...**Ekaterina (Katya) Yurasovskaya*, Seattle University****Improving algebra skills of university students through participation in academic service-learning**

Seattle University has a long history and a solid institutional structure for implementing academic service-learning in its courses. For the present study, we developed a Precalculus course with a service-learning component, allowing university students to work in the tutoring labs at a local...**Allison Dorko*, Oregon State University****What do students attend to when first graphing planes in R3?**

This talk considers what students attend to as they first encounter R3 coordinate axes and are asked to graph y = 3. Graphs are critical representations in single and multivariable calculus, yet findings from research indicate that students struggle with graphing functions of more than one variable...**Elise Lockwood, Oregon State University****John Caughman*, Portland State University****Zackery Reed, Oregon State University****Deconstructing and Reconstructing the Multiplication Principle**

The multiplication principle ("MP") is fundamental to combinatorics, underpinning many standard formulas and providing justification for counting strategies. Given its importance, the way it is presented in textbooks is surprisingly varied. In this talk, we identify key elements of the...**Robert Ely*, University of Idaho****Reasoning with "dx" in the integral**

Research indicates that in order for students to be able to successfully interpret and flexibly model with definite integrals, they must conceptualize the integral as â€śadding up the piecesâ€ť of a quantity, rather than as (a) a symbolic template, (b) an anti-derivative, or even just (c) an area under...**Zackery Reed*, Oregon State University****Student Generalizations of Distance and the Cauchy Property**

The Cauchy Property is an important characterization of convergent sequences in complete metric spaces. Students were observed reflecting on the nature of Cauchy Sequences on R, and were then prompted to generalize the definition of a Cauchy sequence into more abstract settings. Their...**Sarah Erickson*, Oregon State University****Student Attitudes Toward Listing as a Strategy for Solving Counting Problems**

While researchers have found that students at a variety of levels struggle to solve counting problems correctly, listing has been shown to be a potentially effective remedy to student difficulties. Motivated by its importance in helping students solve counting problems, this presentation describes...

## Session: Panel Discussions

**Manny Hur*, Oregon State University****Matthew Sottile*, Galois****Elise Lockwood*, Oregon State University****Career Panel**

Youâ€™re about to earn a degree in mathematics, now what? You may be surprised to know that teaching isnâ€™t your only option; in the â€śreal worldâ€ť mathematical knowledge is a valued commodity and there are many interesting job opportunities for mathematicians in non-academic settings. So, whether you...

### Subject Area: Other

**Kelsey Jewell*, Western Washington University****Maureen Sturgeon*, Western Washington University****Leading a Successful Math Club**

This session will be an open discussion led by the student leaders of Western Washington Universityâ€™s math club, Kelsey Jewell and Maureen Sturgeon. The topic of discussion will be leading academic clubs on campus. The goal of the session is to allow clubs throughout the Pacific Northwest to...

## Session: Teaching Tricks, Techniques and Discoveries -- Share what works for you!

**Jean Marie Linhart*, Central Washington University****Stimulating Students to Succeed with Standards Based Grading**

Students often don't master required prerequisite material in foundational courses, and then they struggle in later courses that

require mastery of earlier concepts. To move students towards mastery learning and full proficiency, I implemented Standards Based Grading in Discrete Mathematics...**Jeffrey Stuart*, Pacific Lutheran University****Specific Examples, Generic Elements and Size Tuning - Overcoming Student Roadblocks in Linear Algebra**

Linear algebra is the often the first math course in which sets play an explicit and fundamental role. Consequently

students typically struggle with writing proofs for set-based results. In this talk, I focus on four key strategies to improve student success.

1. Emphasize the role of specific (...**John Hossler*, Seattle Pacific University****Wanna Play? Gamifcation of STEM Courses in Higher Education**

While the word "gamification" may sound like it means playing games in class, it means something entirely different: the infusion of game principles into an otherwise non-game situation. Gamification is the addition of game elements, mechanics, and principles to non-game contexts--the...**Nick Lassonde*, Klamath Community College****Creating Websites about Math - Not Just for Mathematicians**

Even undergraduate students can create websites with beautiful mathematics displays. MathJax is a free tool that can be used to render math on web pages, and CodeCogs is a free online equation editor with LaTeX translation and HTML embedding of images. Teach your students how to create their own...**Kristin Lassonde*, Klamath Community College****Beyond Email: Reaching Students Where They Are**

Email is not always the most effective way to reach our students. To improve instructor-student rapport and ultimately student success, consider implementing alternate methods of contact in your classes. Google Voice for texting and social media for other messaging are two powerful tools available...

## Session: Thinking Outside the Circle: Alternate Outreach

**Brandy Wiegers*, Central Washington University, National Association of Math Circles****The Diversity of the national Math Circle movement**

Originating in Eastern Europe, Math Circles spread to the United States in the 1990s. They emerged approximately at the same time on both the east and west coast, and have spread to almost every state, numbering around 200 today. While the first wave of Math Circles in the United States started...**Annie Raymond*, University of Washington****Girls' Day or MĂ¤dchen-Zukunfstag**

We discuss what happened when a whole country decided to reach out to its teenage girls to get them to be more involved in math, science and technology.**Matthew Junge*, University of Washington****Inside the box: college in prison**

Prisoners that receive college education in prison have drastically lower recidivism rates. Mathematicians are in short supply here, and can make a great difference. I will discuss my experience designing and teaching the first-ever for-credit math course in the Washington Corrections Center for...**James Morrow*, University of Washington****Mathday at University of Washington**

Mathday is a day in which 1600 high school students and teachers are on the UW campus to attend lectures and activities. We have grants to support the attendance from remote schools and schools with under-represented populations. This is its twenty-sixth year.