# M*A*T*H Colloquium

"Mathematics is the process of turning coffee into theorems" Paul Erdös

## presents a series of informal talks open to the public.

This series is supported entirely by private donations.

### New - Syllabus for Math 175/375 Students

 Wednesdays at 4:00 p.m. Coffee at 3:45 p.m.

FEB. 4 THE MINISTRY OF SILLY WALKS
Thomas Mattman, Mathematics and Statistics, CSU Chico
The pattern your footprints leave when you walk along the beach is an example of a Frieze pattern. Using this idea, Conway has given the Frieze patterns names such as “jump” and “spinning hop”. If you’ve ever tried performing “spinning sidle” for friends or students, you’ll know that some of these walks are pretty silly. But are they REALLY silly? For this we turn to the masters of silliness, the British comedy troupe Monty Python’s Flying Circus. We will analyse the “Ministry of Silly Walks” skit to understand which of Conway’s walks are truly silly.

FEB. 11 MATH 180 PROJECTS
Bill Barnier, Professor of Mathematics, introduces students Jessica Balli, Cory Champagne, Frank Cortese, Lori Dempel, Kim Ginthum, Kristen Holub, Melissa Newcomb, and Sean Pearson from his Fall 2003 Math180 class who will present Mathematica projects examining drug dosage, biology, Pythagorean triples, water buckets, life expectancy, the lottery, blood alcohol level, and truth tables. Pizza after talk in Darwin 127

FEB. 18 A META-PROBLEM
Bill Barnier, Professor of Mathematics, SSU
will present the meta-problem: How to find a really nice cubic function. After defining “really nice” he will derive an elliptical solution similar to a circular derivation of Pythagorean triples.

FEB. 25 MATHEMATICS, NAVIGATION, AND THE GLOBAL POSITIONING SYSTEM
Bob Kleinhenz, Consultant
The talk is centered on the mathematics that lie underneath the Global Positioning System (GPS). The discussion will cover the basic measurements performed by a GPS receiver along with the model used to convert each measurement into a position solution. Along this way, elementary notions of orbits and earth coordinate systems are discussed. The dominant error sources in the GPS mathematical model are mentioned and the methods of overcoming these errors are presented. The talk concludes with a brief discussion of the algebraic and spectral properties of PN codes. PN codes are broadcast by GPS satellites and serve as identification for each satellite.

MARCH 3 PROBLEMS ON THE BORDER BETWEEN GEOMETRY & NUMBER THEORY
Don Chakerian, University of California Davis
We discuss some problems (mostly unsolved) concerning configurations of points that are at integer or rational distances from each other. For example, is there a point inside a unit square where distances to the vertices are all rational numbers?

MARCH 10 DEMONSTRATIONS OF STABILITY: UNDERSTANDING BIFURCATIONS
Elizabeth Burroughs, Mathematics, Humboldt State University
If you sit in the front row, you might get wet! Using such household items as a tennis racquet, soap bubbles, a hairdryer, and a glass of water (not all at the same time), we will consider a variety of stability problems. A physical system is described as stable when a “small” perturbation to a steady state settles back to that steady state, and unstable otherwise. A physical system undergoes a bifurcation when there is an abrupt change in the nature of the solution as a given parameter changes. Because bifurcations are associated with an exchange of stability, we can locate bifurcations by tracking the stability of solution branches. We will consider the three simplest bifurcations: the turning point bifurcation, the Hopf bifurcation, and the pitchfork bifurcation, and study a simple equation that describes each one.

MARCH 17 MAGIC SQUARES AND ORTHOGONAL ARRAYS
Donald Kreher, Mathematics, Michigan Technological University
A magic square is an n by n array of integers with the property that the sum of the numbers in each row, each column, and the main diagonals is the same. This sum is the magic sum. Magic squares have had a long and colorful history. They have attracted the attention of emperors, hobbyists, magicians, and even mathematicians. In this talk we give an introduction to recursive constructions in the context of magic squares and orthogonal arrays.

MARCH 24 MATHEMATICAL ANALYSIS OF DNA SEQUENCES
Elaine McDonald, Mathematics & Holly Skolones, Biology, SSU
will present their collaborative work using hidden Markov models applied to sequence alignment problems. This talk will begin with a brief introduction to biology and probability models, and move to a description of the algorithms used to find probable alignments between different DNA sequences. Holly will describe how she uses these powerful programs, routinely used by biologists, to identify bacterial species compositions of vernal pools. This talk is intended for an interdisciplinary audience of mathematicians, computer scientists, and biologists, including students. Pizza after talk in Darwin 127

MARCH 31 Cesar Chavez Day -- no talk

APRIL 7 Spring break -- no talk

APRIL 14 PENROSE TILINGS
Brigitte Lahme, Mathematics, Sonoma State University
The familiar tilings of the plane (or your kitchen floor) are periodic: They repeat the same pattern over and over again. Penrose tilings are infinite tilings that cannot tile the plane in a periodic manner. They are interesting to chemists because they model a recently-discovered structure called quasicrystals, and account for a previously-unexplainable 5-fold symmetry which these structures exhibit. Given a set of Penrose tiles, there are uncountably many ways in which those tiles can fill the plane — none of them periodic. We will explore properties of Penrose tilings, ways of generating them, and difficulties in working with such an unwieldy object!

APRIL 21 USING MATH IN CELL BIOLOGY: HOW DO CALCIUM CHANNELS WORK?
Bori Mazzag,Computational Biology, College of William & Mary
This talk will explore an example of how mathematics can be useful to molecular biologists. We will build a simple probabilistic model of a channel opening, releasing calcium and closing, and discuss how we can simulate such a model numerically. We will investigate how specific biological assumptions about the model translate into mathematical statements, and we will examine the prediction of the modified model. At the end of the talk, we will sneak a peak at related biological questions that can be answered using the introduced methods. The talk will assume no previous biology, and the mathematics employed will be accessible to a general audience.

APRIL 28 MATH FESTIVAL DAY SEARCHING FOR THE SHORTEST NETWORK
Ronald Graham, Mathematics, UC San Diego
There are many situations in which one would like to connect a collection of points in some space by a network having the minimum possible total length. Such problems have a long and distinguished history, and occur in such areas as the design and analysis of telecommunications networks, oil pipeline networks, and heating and air conditioning duct systems, algorithms for molecular phylogenetics, and the layout of circuits on VLSI chips, to name a few. In this talk, we survey what is known and what is not known about this problem, and how it has been impacted by current developments in theoretical computer science.

MAY 5 UNCOVERING THE LATENCY IN LATENT VARIABLE MODELS
Karen Nylund, Education & Information Studies, UCLA
Latent variable modeling is a statistical modeling framework that is widely used in the social sciences to study variables that are not directly observable. This student-friendly talk will explore latent variable models and will include: defining what a latent variable is (which include those one might know, but not consider to be a latent variable), their relationship to traditional regression models, and practical examples from education and psychology. These examples will demonstrate the flexibility and wide application of latent variable models. A basic understanding of regression is the only statistical background needed to follow this talk. Pizza after talk in Darwin 127