# Math Colloquium Abstracts Archive '12 - '13

# Fall 2012

### September -

**9/27 Erin McNicholas, Willamette University**

*The Rubik's Cube Group * We'll examine the Rubik's Cube group, which is made up of all possible configurations of the cube. Using group theory to analyze this set, we'll determine some interesting properties of the cube. How many different configurations can the cube be in? Which transformations of the cube commute with all others? How many moves on the cube does it take to get it into a particular configuration? What are the most common solution techniques? Along the way we'll define some exotic products (direct, semi-direct, and wreath) and we'll run into some very very large numbers. If you have a Rubik's cube handy, bring it! You'll have the chance to try out a few moves and master the superflip.

### October -

**10/4 Rosa Orellana, Dartmouth**

*From Braids to Knots: An introduction to representation theory*

In this talk, I will show you how to use matrices to represent abstract objects. I will define a mathematical braid and show how we can obtain knots/links from them. I will use representations of braids to find ways to determine if the two knots/links are distinct.

*** A basic knowledge of linear algebra will be useful for this talk***

**10/11 Jim Albaugh**

*Sometimes it is rocket science: A conversation with Jim Albaugh*

Jim Albaugh graduated from Willamette in 1972 with degrees in Mathematics and Physics. His career has moved from building rocket engines to serving as the President and CEO of Boeing's Defense, Space, and Security unit and, most recently, President and CEO of Boeing's Commercial Airplanes unit. He has been a major supporter of the Mathematics and Physics departments and serves on Willamette's Board of Trustees.

Mr. Albaugh will talk about life after Willamette and answer questions. He will also stick around for a while after the colloquium to chat with anyone who cares to join him.

We are officially renaming the colloquium series the Jim Albaugh Mathematics Colloquium in honor of his many contributions* to the university, and Mr. Albaugh himself is the inaugural speaker. Please join us in this celebration.

*For example, Mr. Albaugh's support has enabled many of the activities our department has offered, including the Math Meetings course and the colloquium series. He is also the ultimate source of travel support for **six **Willamette students to the Nebraska Conference for Undergraduate Women in Mathematics.

**10/16 Oregon College Mentors**

Representatives from Oregon College Mentors will be here looking for volunteers (math majors) interested in helping to improve public education in mathematics. OCM coordinates college students from all disciplines with area high schools to provide mentoring and expertise to high school students. They will discuss how their program works and what you can expect as a OCM volunteer.

**10/25 Alix I. Gitelman, Jeremy Romer, & Carl Schreck, Oregon State University **

*Part of The Oregon Plan for Salmon and Watersheds requires the Oregon Department of Fish and Wildlife to monitor survival and migration of salmonid fishes in coastal basins. The work described in this talk supports that effort by examining estimates of smolt (juvenile migrating fish) survival under several different migration (run) distributions, survival probability schemes and sampling schemes. We simulate migration numbers using Poisson distributions, and we add random noise to several systematic survival probability models to account for daily fluctuations in survival probability. We consider three sampling schemes to compare the effectiveness of our survival estimates. All estimates are evaluated by examining estimation error (the difference between the estimate and the known survival probability) and confidence interval coverage—we expect this coverage to be 95% if the estimation procedure is valid. A systematic sampling scheme appears to perform best, though there is enough uncertainty in both the shape and timing of the run distributions and in the survival probabilities to make estimates from all sampling schemes less than optimal.*

*On Monitoring Estuarine Smolt Survival*### November -

**11/7 Heather Moreland, Dept. of Mathematical Sciences, Montana State University**

*Mathematical Models of Traveling Waves in Pancreatic Islets*

Using mathematics to model physiological processes has been very important as we attempt to gain a better understanding of these systems and treat afflictions associated with them. After providing some basic background on mathematical physiology in the form of the Hodgkin-Huxley model, we demonstrate how mathematics can be used to model insulin secretion from the pancreas. In response to an increase in blood glucose levels, insulin is released into the bloodstream by the pancreatic islets of Langerhans. As a result of this influx of glucose, the islets start what are called bursting oscillations of the membrane potential and the intracellular calcium concentration. Time delays of several seconds in the activity of distant cells in the islets have been observed, indicating the presence of traveling waves through the islets. Using the well-known Huxley equation and a homotopy parameter, we construct a relationship between the wave speed and the model parameters.

**11/15 Spring Course Review**

Come hear about the many exciting courses offered by the math department this spring. Whether you are agonizing over which math class to take out of some short list of courses (to which the answer is always ALL), or you just want to find out more about the many exciting flavors math comes in, this is the colloquium for you! Courses previewed are likely to include Knot Theory (Math 499), Real Analysis (Math 446), Combinatorics (Math 376), Probability and Statistics (Math 266), and Sequences and Series (Math153). If time permits, faculty will be on hand to answer questions about opportunities in mathematics, and Willamette's math major.

**11/29 Marla Williams, Willamette Senior Math Major**

*Accepted Elasticity in Arithmetic Congruence Monoids*

An arithmetic progression is a sequence of natural numbers in which the difference between any two consecutive terms is fixed for the entire sequence. An Arithmetic Congruence Monoid (ACM) is an arithmetic progression which is closed under multiplication, i.e. if you take any two numbers in the sequence, their product is also in the sequence. In the set of integers, each integer has a unique factorization into irreducible elements (think prime factorization). In an ACM, this is not necessarily the case. In fact, some elements will have factorizations of different lengths, giving rise to the notion of elasticity: the length of the longest factorization of an element divided by the length of its shortest factorization. An ACM has accepted elasticity whenever there is an element whose elasticity is greater than or equal to that of all other elements. We begin to explore which ACMs have accepted elasticity and which do not. Joint work with Lorin Crawford and Jason Steinberg, under the direction of Professor Vadim Ponamarenko as part of the 2012 San Diego State University Research Experience for Undergraduates program.

### December -

**12/6 Dr. Zlatko Dimcovic, Oregon State University**

*Discrete-time quantum walk on a binary tree*

We have recently constructed a framework for discrete-time quantum walks (unitary processes discrete in space and time), motivated by classical walks with memory. The framework reproduces known models, while it can be used to build walks on structures that are very difficult for current approaches. As our first example of its utility, we study a symmetric walk on the semi-infinite binary tree. For a walk starting at a given level in the tree we compute the amplitude at the root, as a function of time and starting level. The result is strikingly different from the classical case, as will be discussed. The calculation utilizes a variety of analytical techniques, of which we will see some combinatorics and path counting, regeneration sums and transforms, and steepest descent for complex integrals. The talk will not delve into much detail, but is rather meant to provide mostly an overview of the whole calculation. On the other hand, this system is rather suitable to introduce the basics of quantum theory and to directly observe some of its fundamental properties at work. We will pay due attention to the needed elements of quantum mechanics, so that this talk will also present an introduction to how elementary quantum systems behave.

# Spring 2013

### March -

**3/7 Kathryn Nyman, Willamette University **

*Cutting Cake With Linked Preferences*

Whether dealing with property, inheritance, revenue, or taxes, the question of how to divide “goods” (cake) fairly among a group of people is a ubiquitous problem. At first glance, the question of dividing a cake fairly among n people may seem to pose no problems: just cut it into n equal pieces. But, while this might work for a homogeneous chocolate cake, consider a cake which is half chocolate and half vanilla, with sprinkles in one corner, that is, a cake where each player may value different parts of the cake differently.

While the problem of dividing one cake among several players has received considerable attention, the problem of dividing multiple cakes introduces new challenges, and, despite its usefulness in economics, has yielded little ground. We consider a situation in which a player’s desired piece in the second cake depends on the piece he received in the first cake.

**3/14 Eric Gaze, Bowdoin College**

*Quantitative Reasoning: A Program For Student Success*

Quantitative Reasoning (QR) has become one of the essential learning outcomes for institutions of higher learning across the country. This talk will address how to create a coherent QR program to assess, develop, and sustain the QR needs of students and faculty alike. QR goes beyond simple quantitative skills that need to be “remediated”. These skills are certainly necessary but not sufficient for the demands of rigorous academic work requiring higher order critical thinking skills. We will explore what is meant by “quantitative reasoning” and how to assess this construct. Bowdoin College’s QR entrance test is used for advising and course placement and is one of the best predictors of academic success at Bowdoin. Next we will look at a QR course that serves as an entry point for students with weak Q-skills, and also serves as an exit point for students going on to medical school and Wall Street. Finally we will discuss the academic support systems needed to scaffold student learning as they grapple with reasoning from evidence in all their coursework.

### April -

**4/3 Steve Rhine and Heather Daniels **

*What to do after WU? Teach Math!*

**Learn more about the graduate school possibilities right here at Willamette University in the Graduate School of Education. Professor Steve Rhine and Admission Director Heather Daniels will present about the Master of Arts in Teaching (MAT) and Master of Education (M.Ed.) programs. They will also provide information about math education careers and how to accomplish professional goals related to your current undergraduate major.**

**4/18 Dr. Kenneth H. Price **

*Algebraic Properties of Relativistic Addition*

**Taking the definition of relativistic addition of velocities as a starting point, the talk will discuss multiplication as repeated addition and end with the development of a field homomorphism from the interval (-1,1) to the real number system. The discussion will use the concept of a metric space and demonstrate a novel use of the binomial theorem.**

**4/25 Mike Kimmell, Willamette University '13**

*The Bidder's Row Auction on The Price is Right*

Have you ever wondered how players are supposed to bid in the Bidder's Row Auction on the Price is Right? Which of these four players has the best chance of winning and what strategies should they use? This talk seeks to explain the findings of Berk,Hughson, and Vandezande in their paper, "The Price is Right, But are the Bids? An Investigation of Rational Decision Theory." I will also present my findings on how the propositions in their paper can be expounded upon.