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.

Syllabus for Math 175/375 Students

 Wednesdays at 4:00 p.m. Darwin Hall Room 108 Coffee at 3:45 p.m.

September 1: It s Knot Math. Maria Robinson, Seattle University

Knot Theory is an exciting area of Mathematics. One of the fundamental questions that mathematicians strive to answer is Are these the same knots? We will explore that question during the talk. We will also look into some of the current open questions in Knot Theory.

September 8: Math & Statistics Anxiety: Their Causes and Treatment. Diane Johnson, Humboldt State University

Math (or statistics) anxiety is defined as a feeling of tension, apprehension or fear that interferes with math (or statistics) performance. While it is most prevalent in remedial math students, math majors and even math professors may have traces of it. The causes and treatments are individual and often complex, but certain trends seem to stand out. I will discuss recent research findings concerning these trends.

September 15: The Statistical Paleontology of Charles Lyell and the Coupon Problem. Neil Schwertman, CSU Chico

Lyell, a founder of the science of geology, used statistical models to describe the changes that had occurred in the earth and its environment. From this model he attempted to establish a time frame for each epoch. We will show that Lyell s model is equivalent to the classic coupon problem included in many probability texts. Furthermore, the time frame deduced by Lyell is inconsistent with the model he was using.

September 22: A Mathematical Theory of Ecological Traps. Roland Lamberson, Humboldt State University

Habitat selection theory suggests that individuals should occupy those available habitats that maximize fitness; ecological traps result when they do not. Using a differential equations model, we study an ecological system in which patches may differ in fitness and appeal to organisms. Our results indicate that if the order of habitat preference corresponds to the expected fitness (that is, if the individuals know what s good for them!), then there can be at most one stable distribution of population. Multiple stable possibilities can exist only when lower-quality patches are preferred over higher quality patches, as in ecological traps.

September 29: Hubris, Weird Numbers, a Missing Asterisk, and Paul Erdos. Stan Benkoski, West Valley College

This is the true story of a young mathematician who, in a fit of hubris, discovered weird numbers and, with the help of a missing asterisk, ended up with an Erdos number of 1.

October 6: How does one see? Joe Latulippe, Montana State University (Pizza after talk in Darwin 127)

Although we cannot answer this question we can begin to examine how the brain processes visual information, usually light. This talk will explore different cells in the layers which compose the visual system and identify them as On-Center, Off -Center, or Simple cells based on their receptive fields. We will discuss how we can use mathematics to model these cells, & obtain numerical results to verify this model.

October 13: A Few Surprises from Calculus. Scott Farrand, Sacramento State University

As calculus students often notice, and , but and . So what's the deal with round things? We'll look at an unexpected connection between this and the standard calculus problem about building an open-top box using a rectangular piece of cardboard. One additional surprise from another standard calculus problem should serve as a reminder to anticipate the unexpected, even in a classical subject like calculus.

October 20: A Gentle Introduction to Trigonometric Series. Sheldon Axler, San Francisco State University

This talk will present an introduction to trigonometric series. Approximating a function by combinations of sines and cosines often leads to useful insights. Questions about the convergence of trigonometric series have led to many crucial concepts in modern mathematics.

October 27: Mathematical Models and Spotted Owl Populations. Dan Munton, Santa Rosa Junior College

Spotted Owls have inspired strong feelings and have been a source of controversy in California and the Pacific Northwest. We will blend the natural history of the spotted owl with mathematics and statistics to form and explore several mathematical models. We will discuss the assumptions of the models and their sometimes contradictory conclusions.

November 3: Serendipity: Robots, DAGs, and Salmon Biology. Peter Baker, Stillwater Science

There is something especially satisfying about turning up connections between ostensibly unrelated fields. I will discuss a few occasions on which I was able to make progress on a problem with the help of knowledge acquired more or less accidentally from an unexpected source.

November 10: Phase Locking in Nature. Sunil Tiwari, Sonoma State University (Pizza after talk in Darwin 127)

Phase locking of oscillators in nature is quite common. When a given oscillator fires, it pulls the other oscillators up by a fixed amount or brings them to the firing threshold. This interaction between the oscillators causes them to lock into mutual synchrony. Examples of oscillators in nature include synchronously flashing fireflies, and crickets that chirp in unison. This talk is about developing a mathematical model to explain this physical phenomenon.

November 17: Unfolding Hyperbolic Polyhedra. Rick Scott, Santa Clara University

Compact surfaces are classified by their genus (the number of holes in the surface) and whether they are orientable or not. Surfaces with genus > 1 turn out to be hyperbolic, meaning that one can define a distance between points on the surface in such a way that the curvature at every point is -1. A nice proof of this fact uses regular hyperbolic polygons to build the surface. We will begin the talk with a description of this construction then consider an analogous construction in three dimensions.

November 24: No talk; Thanksgiving break.

December 1: Mathematics of Protein Folding. Ben Ford, Sonoma State University

Proteins are the tools by which DNA does its work; a protein s function is determined largely by its physical shape (and many diseases are caused by misfolding). The folded (least energy) shape of a protein is determined by its coding DNA sequence but the resulting calculus minimization problem has thousands of variables and is not tractable. Many mathematical techniques can be brought to bear on this “protein folding” problem, including statistical, algorithmic, and dynamical systems approaches.