MATH 251
Fall 2006 not offered
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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. |
Essential Capabilities:
None |
Credit: 1 |
Gen Ed Area Dept:
NSM MATH |
Course Format: Seminar | Grading Mode: Graded |
Level: UGRD |
Prerequisites: None |
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Fulfills a Major Requirement for: None |
Major Readings:
Regular classroom handouts, roughly in the format of chapters for a future textbook.
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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. |
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