Math Colloquium Abstracts Archive '14 - '15
Spring 2015
March
3/31/15 Prof. Erin McNicholas
Mathematics Course Preview 2015
Come learn about several of the exciting courses offered next fall by the math department. This special preview is open only to current Willamette students, their friends and family, and any other interested parties. Come enjoy the treats, learn a little more about such exotic topics as knot theory, and get all your math major/minor/course related questions answered. The only problem will be limiting yourself to at most 4 math classes in the fall. But never fear, if your schedule does not allow you to take every math course offered next semester, many of these courses will be offered again.
3/19/15 Heidi Andersen '11
Fantastic Groups and Where to Find Them
Starting with the fundamental concept of a group that one encounters in a first abstract algebra course, this talk aims to provide the undergraduate listener with a broader, graduate-level perspective on the huge role groups play in many other fields of math (with a focus on topology and geometry). Beyond the elementary, pretty examples like the dihedral and symmetric groups, groups also act on topological spaces and yield new manifolds in the form of quotient manifolds (also called orbit spaces), and groups themselves sometimes admit topological and/or geometric structure. Many examples will be provided.
3/12/15 Prof. Inga Johnson
All Tangled Up: Conway's Classification of Rational Tangles
Tangles are of interest to both mathematicians and biologist due to their applications in the study of DNA. We will look and a subset of tangles called rational tan
3/5/15 Prof. Josh Laison
Modern Board Games and the Math Behind Them
More people than ever are playing games, and many of those people are secretly doing math! In this talk I'll introduce the exciting world of modern board games, and give some examples of their many connections to mathematical ideas and research.
Fall 2014
December
12/4/14 Jeremy Coste and Kees McGahan
Cops and Robbers on Graphs
Join us as we explore the game of Cops and Robbers on graphs. We will take a look at cop-win and robber-win graphs, as well as finding algorithms for computing the cop number. Furthermore, we will learn some variations of the game with firefighters and helicopters!
November
11/24/14 Jared Nishikawa, Willamette '10
Hash Functions, A Soft Intro
Number theorists often talk about functions with "nice" properties (additive, multiplicative, periodic, symmetric, and so on). Hash functions are, in this sense, a mathematician's nightmare. But, in terms of cryptography and security, they are very important. This talk will gently introduce what hash functions are, their applications to cryptography (have you heard of bitcoins?), and current and ongoing work. The content will be accessible to both math and computer science majors.
11/13/14 Professor Benjamin Young, University of Oregon
Tiling an Aztec Diamond
An Aztec diamond is a diamond-shaped region of the plane, which can be completely covered with nonoverlapping dominos. We'll work out the number of ways in which this can be done, and look into what a typical tiling of a large Aztec diamond looks like.
11/6/14 Bob Milnikel, Kenyon College
A New Angle on an Old Construction
It's well known that exact straightedge-and-compass construction of a regular n-gon is impossible for most values of n, but that didn't keep people from needing to construct such polygons in the days when straightedge and compass were the principal tools of drafting. I'll introduce a historical technique for approximating a regular n-gon that works (more or less) for any value of n. Finally, I'll introduce a slight variation -- original as far as I know -- that improves the construction's accuracy. The material is very accessible! The only mathematical background needed is a little high school algebra and trigonometry.
October
10/30/14 Lexi Scheel & Eric Samelson
Lexi & Eric's Summer Research
This past summer, Willamette Math Majors Lexi Scheel and Eric Samelson, participated in mathematics summer research experiences. Lexi worked with a team of researchers at the University of Hawaii at Hilo, and Eric worked with Linfield’s research team. Lexi and Eric will share their research results and discuss the process of applying for and participating in a summer math research experience.
10/23/14 MegaMenger Mania!
We’re in the home stretch! With 4 big days of Menger, now’s your chance to participate—and take part in the big finish.
Thursday at 4:00 (Ford 204) we’ll fold MegaMenger cubes, while listening to members of the Math department talk about fractals, and watch cool fractal movies!
Friday at 3:30, during Friday Floats we’ll continue MegaMenger cube building while enjoying our usual root beer floats
Then Saturday & Sunday join us at 2pm (Math Hearth) to assemble the final Level 3! You’ll also have the opportunity to talk with the organizers of global project via Google Hangout!
Partial Differential Equations & Equivalence
Professor Sitton gives a brief, not-too-technical introduction to the geometric theory of partial differential equations (PDEs) as developed by Lie, Cartan, Goursat, Darboux, and others during the early 20th century. This theory allows us to define various geometric properties, including the notion of equivalence, of PDEs. In particular, we consider the following PDEs introduced and studied by Cartan, Goursat, (and Sitton):
9u2xx + 12uxxu3xy + 36uxxuxyuxy – 12u2xyu2xy – 32u3xy = 0
8u3xx + 24u2xxu2xy + 18uxxu4xy - 108uxxu2xyuxy – 18u2xyu3xy + 81u4xy = 0
9/11/14 Dr. Elton Graves, Rose-Hulman Institute of Technology
See the Wave: A Mathematical Simulation of the Waller Violin"
The card game SET is played with a special deck of 81 cards.
The Waller Violin, and in fact, all stringed instruments work on the basic principle that a string of length L is pinned at both ends and is under tension. The string is plucked and begins to vibrate causing a sound, usually nice music. Because of wind resistance the string will eventually stop vibrating and the music will cease. Mathematically the vibrating string is known as the “wave equation.” Our task in this talk is to simulate, mathematically, the movement of the string.
This talk will take the listener on a tour of the undergraduate mathematics needed to solve the “wave equation”. The talk will weave together topics from integration by parts, simple differential equations, along with a little matrix theory, and least squares (linear regression). These mathematical concepts will be the stepping stones which lead to the concept of the Fourier series, which is the ultimate mathematical tool used to solve the “wave equation”.
The talk will also show the derivation of the mathematical model of the “wave equation” using elementary vector addition. Once the “wave equation” had been derived, the talk will show the techniques used in solving the “wave equation” for a simulated string, using the elementary mathematics and Fourier series discussed during the talk.
The talk will conclude with a computer graphics animation which actually shows the vibrations of the string we are simulating.