Box optimization problems (how to find the maximum volume of a box from its dimensions) have been discussed in calculus classes for years. This talk will discuss the insights given by an article, written by Vincent E. Coll, Jeremy Davis, Martin Hall, Colton Magnant, James Stankewicz, and Hua Wang...
Mean curvature flow is the $L^2$ gradient flow of the volume functional on embedded surfaces. As a nonlinear system of parabolic equations, its behavior is quite complicated, but generally solutions become more spherical over time as their volume decreases. The evolution of tori under this flow is...
Differential geometry is the use of the techniques and tools of calculus to study the geometric properties of manifolds. One of the most commonly studied properties of manifolds their curvature. We can measure the curvature of a manifold at a point by using a metric called an algebraic curvature...
We explore and compare, via geometric methods, the topology of the hyperbolic-unit interval and the spherical-unit interval with respect to the Euclidean-unit interval. We do so using analysis of the density of rational and irrational numbers in the real plane by employing methods of refraction...
The representation of a sphere, or spherical object such as the Earth, on a Euclidean plane has been of interest to mathematicians, cartographers, and navigators for centuries and, as a result, many different spherical projection methods have been developed. This presentation will explore the...
Starting with a one unit circle, circumscribed by a regular triangle, circumscribed by a circle outside, circumscribed by a square, circumscribed by a circle, circumscribed by a regular pentagon and so on by circles and regular polygon. Will the radius of the circle diverge or converge when we...
Alvaro Francisco Manuel*, Western Oregon University
Many people are familiar with the game of Billiards, commonly known as pool. We will consider a simple version of this game consisting of just the cue ball, cue stick, and table. The ball is shot at a 45 degree angle from the lower left hand corner. In this talk, we will find a general formula for...
Simple estimates of the level of uncertainty in a measurement (usually as relative or absolute error) are easy to calculate and understand, but when doing any sort of computation or inference using these measurements, things become quite a bit more complicated. This project explores several models...
Our talk explores the effect of the spinner size on the length of a game of Chutes and Ladders. Starting by considering the size of the game board, and then integrating the effects of the chutes and the ladders, one can predict the length of the game through mathematical process. This general idea...
Ryan writes two distinct real numbers on two separate piece of papers and puts them into two envelopes. Ruth chooses one of the envelopes randomly and she must guess whether the other real number in the closed envelope is less than, or greater than, the one she picked. Most people would think that...
I shall briefly introduce what Markov Chains are and some theory behind how the transition matrix can be used. I will then apply the theory to an example that models the movement of pieces on a Monopoly board. Some examples of the theory I will demonstrate are finding and interpreting powers of the...
Alan Thuy*, Lake Washington Institute of Technology
Narayani Choudhury, Lake Washington Institute of Technology
Social media platforms offer excellent opportunities for real life Mathematical modeling, Data science and Math education. We carried out detailed descriptive statistics and a Poisson regression analysis of Facebook data. We used cluster sampling to infer about the population. The five number...
Perfect shuffles on a deck of cards perfectly interleave the cards. Out-shuffles leave the top and bottom card in the same positions, while in-shuffles do not. When in and out shuffles are combined, a card can be moved from any place in the deck to any other position the shuffler desires. This...
In our talk, we will present the idea of a multicrossing projection of a knot and the specific projection called the petal projection. A petal projection is a projection of the knot containing a single crossing. Imagine that we have such a diagram where we do not know which strand is on top of...
Lattices are collections of points in 3-space generated by integral linear combinations of vectors in 3-space. Lattices naturally occur as the centers of solid polyhedra that tesselate 3-space. The simple hexagonal lattice is the collection of centers of hexagonal prisms that tesselate 3-space, or...
Everyone is familiar with the standard base-10 representation of numbers; others may also be familiar with the binary representation of natural numbers useful for computing. In this talk, we discuss our summer research, which involves representing natural numbers using a rational number as the base...
Peg solitaire is a board game that has been played and studied for many years. Examination of the game offers an opportunity to explore a practical application of group theory. Through the use of the Klein Four Group, the insolvability of different board configurations will be examined. We will...
This talk explores using matrix algebra techniques to solve modulo restricted finite linear games. All finite linear games possess a definite number of game states; the state changes are predictable, tied to specific actions, and obey the commutative law. Solving these puzzles with a structured...
Luis Solis-Bruno*, University of Washington Tacoma
PageRank is an algorithm used by Google to present the user with the most important, helpful, or relevant pages first when they enter keywords or phrases into the search engine. We will introduce the algorithm, highlight key subjects of Linear and Matrix Algebra the algorithm implements, and run...
Non-negative matrix factorization (NMF) is a technique in matrix algebra used to factor a matrix into 2 sub-matrices. NMF proves to be very useful in data clustering and analyzing raw data. We will discuss research on the work of Berry et al. regarding factorization and analysis of the Enron email...
Subject Area: Mathematical Aspects of Computer Science
Many turn based board games played by computers use game state trees to determine what moves to make. Traversing through game state trees can be extremely time consuming, especially if the game involves random factors such as a deck of cards. Battle Line is a game where two players are competing...
Competitive Tiling consists of two players, a tile set, a region, and a non-negative integer $d$. Alice and Bob, our two players, alternate placing tiles on the untiled squares of the region. They play until no more tiles can be placed. Alice wins if at most $d$ squares are untiled at the end of...
The purpose of this project is to represent mathematical summations and recurrence relations, visualizing the sum by generating a work of art. This project was inspired by recurrent complex patterns in both art and nature. Simple manipulations of famous recurrence relations, such as the Fibonacci...
Race to the Origin is a two player game where players take turns moving from a coordinate in the first quadrant toward the origin according to a specific set of rules. The first player to the origin wins. This is a variant of the game NIM. We will discuss the rules of play and give winning...
Motivated in part by anti-magic labeling and similar schemes, we introduce a new graph labeling and derive from it a game on graphs called the \emph{1-relaxed modular edge-sum labeling game}.
The players, Alice and Bob, alternate turns with Alice going first. Each turn, the player chooses an...
Games are a great way to learn a new subject. Sprouts is a game that uses graph theory in many ways. In order to explore how moves are made, and how to restrict the bound for the number of moves requires graph theory. Along with graph theory, combinatorial game theory plays a role in determining a...
Imagine yourself on a beach, playing in the sand. You begin to make a sandpile by adding handfuls of sand. Now you consider dropping another grain of sand onto the pile but you don’t know what will happen. It may cause nothing to happen or it may cause the entire pile to collapse in a massive...
Though some may be familiar with the topic of coloring from graph theory, few may be familiar with list coloring. List coloring is a generalization of coloring, where each vertex is assigned a list of available colors. In this talk, we will discuss the similarities and differences between coloring...
Trapezoidal numbers are those which can be written as a sum of consecutive positive integers where the smallest number must be at least two. We will look at the mathematics behind trapezoidal numbers and how to find all such representations. We will give a clever construction which shows how each...
Pell's equation is the famous equation $dx^2+1=y^2$. We will use the continued fraction representation of the irrational numbers $\sqrt{d}$ to find solutions to this famous equation when $d$ is square-free.
Subject Area: Ordinary Differential Equations and Dynamical Systems
We present a few rudimentary and general methods of solving first order linear and nonlinear differential equations which satisfy a specific form. We present general tests which can be run on the differential equations in question. If the equations satisfy the tests, the solutions to the...
In this talk we discuss the danger of ignoring uniqueness criteria when solving an initial value problem either by a traditional pencil and paper approach or with computer algebra systems (CAS's). In particular, we consider both an exact ordinary first-order differential equation and one that...
The idea of agricultural intensification is what defines modern agriculture in that it uses technological advances in order to increase productivity. The goal of this project was to examine through mathematical modeling how agricultural intensification through driving herbivore-predator...
The United States Air Force has a need for parachute operations which will work outside the scope of the current parachute systems. These operations can be constructed to mimic certain egress conditions, the end goal is always to obtain complete, unhindered openings of the parachute and a safe...
Locating aircraft that have crashed in open water is a monumental task. The recent disappearance of Malaysian Airlines Flight 370 underscores the importance of having a robust, yet flexible response system in place. In this paper, we outline a recommendation to the Obama Administration for the...
We construct and analyze three models for the spread of ebola within a single city. One model
was a standard Susceptible, Infected, Recovered (SIR) model with natural births and deaths
(deaths not due to ebola) and deaths due to ebola. We then extended this model two other
models that...
We present a model developed for the COMAP Mathematical Competition in Modeling to assist in searching for aircraft assumed to have crashed in open water. We began by determining all potential and most probable crash locations based on the plane’s trajectory and when and where its ACARS ‘handshake...
In this talk we develop a mathematical model that not only fits the current Ebola outbreak, but also extrapolates the situation by considering the spread of the disease, the quantities of drug necessary, rate of drug synthesis, systems and locations of drug delivery, and any other critical factors...
Our approach for finding a missing oceanic flight begins with modeling the most probable locale of said flight. To do so, we use our model to plot a projected region in which the plane likely first made contact with the water. Then our model breaks this region into smaller objects that flow with...
Investing is critical in the business world and is an avenue to make profit for many. Making the decisions of what to invest in involves intricate mathematics in order to reduce risk. We investigate portfolio optimization, which is a branch of economic and financial modeling that typically has the...
Subject Area: Mathematical Physics
Anthony Podvin*, Heritage University
David Laman, Heritage University
Aric Washines, Heritage University
Sarah Moats, Pacific Northwest University of Health Sciences
The relationship between the oscillation period and the length of a simple pendulum is well known. Other more complex pendulums such as physical, double, and inverted pendulums have been thoroughly examined as well. We present here, for the first time to the best of our knowledge, a systematic...
Knots have been used throughout human history, from tethering boats to tying your shoes. Knot theory formalizes the nature and properties of knots. This talk will introduce participants to the history, fundamentals, and applications of a subset of knot theory, stick knots, using interactive...
In this talk we describe our research into stick knots and projections of stick knots undertaken by our undergraduate research group at Eastern Oregon University during Summer 2014-Winter 2015. Our goal was to find a method, or several methods, for identifying which 2-D projections of stick knots...
We are taking Jason Rosenhouse's article "Knights, Knaves, Normals, and Neutrals" (The College Mathematics Journal Vol. 45, No. 4 (September 2014) (pp. 297-306)) and applying his concepts to various paradoxes.
This talk explores subsets of the integers, called chipsets, that are subject to an iteratively defined constraint. We will establish a test to determine whether a subset of the integers is a chipset and use this to determine whether various sets are chipsets.
Many Calculus I instructors often do not prove the The Intermediate Value Theorem because it seems intuitive and obvious to both the instructor and the students. Moreover, the proof can be complicated. The talk addresses why the IVT is not as obvious through examples and the benefits of having the...
For several years, I have been collecting ``Math Fun Facts'', which are juicy math tidbits that I have been using to start off math classes as a warm-up activity. Math Fun Facts are can be from any area of mathematics, can be presented in less than 5 minutes, and are meant to arouse my...
The Brouwer fixed point theorem and the Borsuk-Ulam theorem are beautiful and well-known theorems of topology that admit combinatorial analogues: Sperner's lemma and Tucker's lemma. In this talk, I will trace recent connections and generalizations of these combinatorial theorems,...
Weaving beads with a needle and thread provides an excellent method for creating aesthetically pleasing mathematical models. Many sorts of mathematical objects can be represented with woven bead work, including those from geometry, tiling theory, algebra (symmetry), and topology. In this talk, I...
The geometry of special relativity can be neatly described using hyperbolic trigonometry. The geometry of general relativity can be similarly described using differentials and differential forms.
This talk presents an excursion through both special and general relativity, emphasizing geometric...
Linfield College requires an Inquiry Seminar of all first-year students. The purpose of this course is to introduce students to academic discourse through writing. As the course title suggests, it motivates writing as a means of posing interesting questions and providing reasoned arguments to...
Research on pre-service elementary school teachers’ (PSTs’) understanding of the multiplicative structure of number shows that PSTs struggle to use prime factorization to identify a number’s factors. This study investigates the benefits of a sequence of three instructional tasks aimed at...
I will discuss two courses I have developed and led with undergraduate mathematics students. The first follows in the footsteps of Leonhard Euler and considers a small part of his impact in a few fields of mathematics. The course starts in St. Petersburg, Russia, then moves to Berlin, Germany,...
This discussion contains a description of my experiences flipping undergraduate mathematics and statistics courses for the first time with some advice for any fellow novice flippers. I discuss ways to start small and build up to a completely flipped class over the span of a few terms with advice on...
A measured value of total hydraulic conductance in the tank bromeliad Guzmania lingulata is decomposed into separate conductances in the axial and radial directions. This decomposition uses the numerical solution of a second order initial value problem where an unknown parameter is selected to...
As evident from the recent events in Japan, Chile, and Sumatra, tsunamis are destructive waves that can devastate coastal communities. The best defense is an early warning system that gives people time to reach higher ground. But how exactly does one predict a tsunami?
The root growth process is characterized by the plant cells absorbing water which, in turn, generates pressure on the cellular wall. This pressure forces the cell to grow by inflating it like a water balloon, stretching the cellular wall to the point that the expansion is irreversible. The primary...
Laura Matrajt*, Fred Hutchinson Cancer Research Center
Avian influenza A (H7N9), emerged in China in April 2013, sparking fears of a new, highly pathogenic, influenza pandemic. In addition, avian influenza A (H5N1) continues to circulate and remains a threat. Currently, influenza H7N9 vaccines are being tested to be stockpiled along with H5N1 vaccines...
In this talk, we will introduce the architecture of the visual system in higher order primates and cats. Through activity-dependent plasticity mechanisms, the left and right eye streams segregate in the cortex in a stripe-like manner, resulting in a pattern called an ocular dominance map. We...
Two major mistakes that a business can make are pursuing a new line of business that is not actually worthwhile, and not pursuing a new line of business that is actually worthwhile. The likelihood that a firm decides to make one of these two mistakes is modeled as a function of a firm's...
We will discuss travelling wave solutions to reaction-diffusion equations of the form:
$u_t=u_xx+ u^p (1-u^q)$
which can be used as a mathematical model for various biological phenomena, as well as to model problems in combustion theory. We identify conditions on the wave speed so that travelling...
I am a professor in the mathematics department at UW, and the founder of SageMath, Inc. In 2005, I founded SageMath, which is the main large open source pure mathematics research software (and is often used in undergraduate teaching), with many hundreds of contributors. Sage is an open source...
Despite there being many excellent tools for authoring, producing and distributing open source textbooks, it is still a technical challenge to self-publish a mathematics textbook. This is especially true now that there are so many options for output formats: print, PDF, web, and EPUB to name some...
WeBWorK is a well-tested, free homework system for delivering individualized problems over the web. It was originally developed in 1995 by Professors Arnold Pizer and Michael Gage at the Department of Mathematics at the University of Rochester. A team of developers from a number of institutions now...
Tacoma Community College recently adopted Kathryn Kozak's "Statistics Using Technology" for its introduction to statics course. In addition to saving the students significant expense (under \$20 vs over \$190), we're finding it empowers a return to an ancient now nearly lost...
We will describe experiences in teaching a course titled Calculating the Value of Reparations and the History of Mathematics. The issues of reparations is in the recent news, e.g. fourteen Caribbean nations suing for slavery reparations and Greece requesting additional WWII reparations. Reparations...
Many institutions, including the University of Washington, Seattle, require that a student has successfully completed an Intermediate Algebra course in order to be considered for admission.
An yet the world is full of people who say things like "I never could pass that algebra course"...
A lion and a man in a closed circular arena have equal maximum speeds. The lion wishes to catch the man while the man tries to evade capture. Who has the winning strategy? We will discuss the incorrect "solution" which stood for more than 20 years, its error, and the surprising answer...
Binomial coefficients, when defined as quotients of partial products of the natural numbers, can be generalized to any nonzero integer sequence, but the resulting ratios cannot be expected to be integers. As will be demonstrated in another talk, if a sequence is both multiplicative and divisible,...
The binomial coefficient $\binom{n+m}{n}$ can be thought of as $\dfrac{f(1) \cdots f(n+m)}{\left(f(1) \cdots f(n)\right) \left( f(1) \cdots f(m) \right)}$, where $f(j) = j$. We can generalize the binomial coefficient by considering functions $f$ other than the identity function. In particular,...
Help students explore the rules of probability with one interesting data set. Is there a statistically significant dependence between variables? What is joint and marginal probability? Is there an easy way to comprehend conditional probability? All of these questions and more can be answered...
Abstract: On the television show, Let’s Make A Deal, the announcer, Monty Hall, asks a contestant to pick one of three curtains/screens. A new car is hidden behind one the curtains. Monty Hall opens one of the two remaining curtains, showing it does not have the car. He asks the contestant if he/...
Continuous maps on Cantor space induce maps between measures on the space. Mauldin has answered the question of when two Bernoulli measures are related by such a map by giving a purely number-theoretic condition on the parameters of the measures. The proof of this result is constructive and hence...
Subject Area: Geometry
Jennifer McLoud-Mann*, University of Washington Bothell
The problem of classifying the convex pentagons that admit tilings of the plane is a long-standing unsolved problem. There are 14 known distinct kinds of pentagons that admit tilings of the plane. Five of these known types admit tile-transitive tilings. The remaining 9 known types admit either 2-...
We examine straightedge and compass constructions in spherical geometry. We show via examples that the starting conditions affect the outcome. Although current tools do not allow for a complete solution, we take a tour through group theory and real analysis to show that, in general, the set of...
Klein links form a classification of links which may be embedded across the surface of a Klein bottle. That is, a Klein link is a set of interlocking mathematical knots which may be drawn across the surface of a Klein bottle without intersection. This particular classification of links has not...
Orbifolds are generalizations of manifolds that allow certain singularities. They were originally defined using charts and atlases, similar to manifolds, but working with these atlases is hard, particularly when dealing with maps between orbifolds. Orbifolds can alternatively be defined using...
I will give a survey of what's known (very little!) about the mod-p cohomology of the general linear groups over finite fields of order $p^r$. I'll briefly describe a recent construction of a new class in (lowest possible) degree $r(2p-3)$, valid more generally for finite groups of Lie...
In this short contribution we will briefly mention:
(i) So called side-channel attacks on RSA public cryptosystem, one of the most frequently used ciphers;
(ii) Impact that scalable quantum computers will have, once they become available, on all deployed public key cryptosystems and electronic...
The use of differentials in introductory calculus courses provides a unifying theme which leads to a coherent view of calculus. We show in particular how differentials can be used to determine the derivatives of trigonometric and exponential functions, without the need for limits, numerical...
Subject Area: Algebra
Robert Benim*, Pacific University
Mark Hunnell, North Carolina State University
Amanda Sutherland, North Carolina State University
In this talk, we consider the order m k-automorphisms of Sl(2,k). We first characterize the form that order $m$ k-automorphisms of Sl(2,k) will take and then we find simple conditions on matrices $A$ and $B$ involving eigenvalues and the field that the entries of $A$ and $B$ lie in that are...
Faced with growing demand from very different student populations, The College of Idaho developed a three-year plan to redesign its entry level mathematics courses. Our objective two years ago was to streamline the sequence of courses for our bimodal audience of students with and without calculus...
The math faculty at University of Washington Tacoma have proposed a Bachelors of Science in Mathematics that is in the final review process. As the primary author of the proposal, I will present the structure of the new major, highlighting influences from the Committee on Undergraduate Programs...
The MAA Committee on the Undergraduate Program in Mathematics and the MAA have released the 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences. The speaker, a member of the CUPM, will present a high level overview of the guide and its development.
At all levels (elementary, high school, and university), doing mathematics is at once about discovering truth and getting the right answer. It is interesting that getting the right answer is often possible without understanding why the method works. Using examples from all levels of mathematics, I...