Mathematics Projects 2010

Fun with Graph Theory

Faculty Mentor - Dr. Charles Lam

Graph Theory is the study of mathematical structures of "dots" and "lines". In mathematical terms, they are referred to as vertices and edges. Many practical problems, such as matching, map coloring, network flows, and database management are modeled using graph theory techniques.

In this program, you will learn the basics of graph theory. Algebra II background is required. We will utilize software such as Maple and Geometer's Sketchpad in our work.

Explore the World of Chaos

Faculty Mentor - Dr. Maureen Rush

This workshop is for high school students who want to explore the mathematical phenomenon known as chaos. Chaos is what results when very small changes in the initial conditions of a system lead to very large discrepancies over time. This phenomenon can account for our inability to predict weather, spread of disease, among other things.

You will learn the basics of iteration, both linear and nonlinear, with only an algebra background. Much of our work will utilize graphing calculators and software spreadsheets. We'll even show movies!

Connections between coccidioidomycosis incidence, land development, and climatic fluctuations

Faculty Mentor - Dr. Jorge Talamantes

Coccidioidomycosis (valley fever) is a fungal infection found in the southwestern US, northern Mexico, and some parts of Central and South America. The fungi which cause it (Coccidioides immitis and Coccidioides posadasii) are normally soil-dwelling but, if disturbed, become air-borne and infect the host when their spores are inhaled. It has long been surmised that activities which disturb the environment (such as construction of new housing, new roads, etc.) cause the fungal spores to become air-borne and infect humans when the right climatic conditions are given. We will investigate this hypothesis by examining satellite images of Kern County taken by NASA since 1982, and archived by the US Geological Survey. We will then connect those data with weather and valley fever incidence records.

We will use state-of-the-art image processing software. Project participants will learn skills used in a wide range of disciplines such as medical imaging, astronomy, ecology, environmental resource management, and epidemiology. Furthermore, participants will learn techniques in computational and statistical analysis.