Summer 2009 Workshops
All workshops will run for approximately 4 weeks, meeting daily for 2 hours in the morning with the professor and 2 hours in the afternoon with graduate student mentors. Students will be placed in a workshop depending on their background and research project choice. There may be one or two cases where a student's background already includes the material in the workshop associated to the research project. In such cases, we will consult with mentors and students to confirm which workshop would be best for the students.
Workshops are as follows:
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Instructor: Prof. Paul-Hermann Zieschang, Professor of Mathematics
University of Texas, Brownsville
Curves and surfaces play a fundamental role in our life. They occur in engineering (car construc-
tions, highway and roller coaster design, the development of the curve ball in baseball), in computer
science (standard graphic programs such as Adobe Illustrator, construction of computer fonts such
as PostScript fonts, computer-aided design), in physics (paths of particles run on curves), in optics
(eye surgery), and in biology (investigation of DNA strands).
This course is a friendly and smooth introduction to the geometry of curves and surfaces. It is accessible for students who know Calculus II.
Click here for further description.
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Instructor: Prof. Chris French, Assistant Professor of Mathematics
Grinnell College
Groups have become one of the most fundamental objects in all of mathematics even though they were not defined until the nineteenth century. As with all important mathematical concepts, it is necessary to develop methods and machinery to study groups. One of the most useful approaches to the study of groups is to “represent” the elements of the group using matrices. These representations are called just that: representations. The study of these representations is called the representation theory of the group. In this workshop, we will start by explaining what a group is and then explaining what a representation is. (We will also study certain functions associated to representations: these are called characters.) We will introduce these ideas by looking at concrete examples of groups and then studying their representation theory.
There are several ways of building new representations out of old ones. We will look at these constructions and determine just how the matrices of these new representations correspond to the matrices of the old representations out of which they are built. We will then go on to study characters and certain relations between them called orthogonality relations.
Toward the end of the workshop, we will pick some additional topics in the area depending on students’ interests and on their projects. One possible topic would be applications to chemistry or physics.
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Instructor: Prof. Mariah Birgen, Associate Professor of Mathematics
Wartburg College
Mathematical Modeling
Pre-Requisite: 1 year calculus, some programming experience is a plus.
This workshop will introduce students to mathematical modeling using difference equations, Monte Carlo simulations and other techniques. We will use several software products to help us simulate complicated models.
The workshop will combine lecture and student-led learning. Students will work through several warm-up modeling projects on their way to their main research project.