VIGRE Heartland REU Summer 2007 Workshops


Workshops are as follows:


Linear Algebra

Instructor: Prof. Juan Gatica, The University of Iowa
Pre-requisite: It is suggested that students have taken one year of Calculus.

This will be a basic introduction to linear algebra. Specialized topics covered in the Linear Algebra Workshop will prepare participants to work on research projects

Graph Theory

Instructor: Prof. Michael Lang, Bradley University
Pre-requisite: It is suggested that students have taken one year of Calculus.

Description: A graph [not the same as graphs y=f(x) that you studied in pre-calculus] is a mathematical structure consisting of a set of vertices and connections between some of them, called edges. For example, a triangle is a graph with 3 vertices and 3 edges; the complete graph on 5 points has 5 vertices and 10 edges.

Many real-world situations can be modeled as graphs, for example personal relationships in an organization, computers passing messages, components of a large project that feed into one another, or bonds in chemical molecules. We can view the graphs as mathematically abstract structures, and ask combinatorial questions such as how many sub-graphs there are with various properties, or how many graphs exist with certain properties; or we can view graphs as tangible geometric objects and ask questions such as whether a particular graph can be drawn on a given surface.

In this Workshop, we will first have a basic introduction to the subject, and then work on topics related to instructor's and student's interests, along with the needs of the research projects. The specialized topics covered in the Graph Theory Workshop will prepare participants to work on research projects led by Camillo, Manderscheid, Anderson, and Simon.

Orthogonal Polynomials

Instructor: Prof. Karen Shuman, Grinnell College
Pre-requisite: It is suggested that students have taken one year of Calculus and a course in Linear Algebra.

Each workshop day, a new topic will be introduced with a short lecture. After the short lecture, workshop participants will work through examples, problems, and proofs in small groups. Sometimes, different groups will work on different problems, and groups will present their findings to the entire workshop.

The workshop will start with basics (for example, what is a set of orthogonal polynomials? What does "orthogonal" mean?) and will then work toward specialization (for example, why do orthogonal polynomials arise in the solutions of differential equations associated with physical phenomena? how can orthogonal polynomials be used in signal processing?). The specialized topics covered in the Orthogonal Polynomials Workshop will prepare participants to work on research projects led by Curto, Han, Jorgensen, and Simon.