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Academic Year 2005/2006

Topics in Geometry: Geometric Analysis and Discrete Groups
MATH 251 FA

The theory of discrete groups is especially beautiful as it intertwines geometry, analysis, and topology. This class will introduce undergraduates to this exciting and fast-moving field. We will start with the study of a geometry that is very different from the usual geometry. For instance, in this geometry (hyperbolic geometry) the sum of the angles of a triangle is strictly smaller than 180 degrees (and in fact could be zero!) We then consider ways of building more complicated shapes with this geometry (the theory of Kleinian groups). Though Kleinian groups are easy to define objects, their behavior can be quite complicated and beautiful.

MAJOR READINGS

Regular classroom handouts, roughly in the format of chapters for a future textbook.

EXAMINATIONS AND ASSIGNMENTS

Between two and five examinations. Enough computational homework for the student to become familiar with incidence matrices and finite fields.

ADDITIONAL REQUIREMENTS and/or COMMENTS

This course should be a good introduction or companion course for Mathematics 261. The geometric constructions will emphasize the applications of matrix groups, matrix rings, and matrix fields to geometric structures.

COURSE FORMAT: Seminar

REGISTRATION INFORMATION

Level: UGRD    Credit: 1    Gen Ed Area Dept: NSM MATH    Grading Mode: Graded   

Prerequisites: NONE Links to Web Resources For This Course.

Last Updated on MAR-30-2006

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