This will be the home page for Math 441 during Autumn Quarter, 1998. Eventually, this page will contain links to a detailed schedule of assignments and other communications about the course.
This is the place to go for the simple proof of the formula for the area of a spherical triangle.
Java software for non-Euclidean geometry
Basic information about the course can be found in UW Class Descriptions.
Additional information will appear here.
This course is aimed at advanced undergraduates and beginning grad students who are interested in learning about modern geometry for its own sake or as preparation for courses in advanced differential geometry and manifold theory or for applications to computer graphics.
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The course will introduce some large and rather abstract concepts, but will do it by studying in detail some very important examples of geometrical spaces. These spaces will be mostly surfaces: the sphere, the projective plane, the hyperbolic non-Euclidean plane, tori and quotient surfaces for example.
The concepts include the idea of distance, of geodesic paths, of curvature, and of the global properties of surfaces and how to build a quotient surface by gluing.
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Since 441 has not been taught with these particular topics for a while, the structure will be fairly conservative in that we will stick quite close to the topics and order in the textbook.
There will be some lecture presentations. However, we will use a variety of strategies including physical models and computer graphics to give hands-on experience.
Some class time will involve working on activities in small groups.
Regular homework problems will be a big part of the course.
There will also be a project assignment at the end, where students can follow their own particular interests to present some topic in geometry.
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Author: John Stillwell Title: Geometry of Surfaces Publisher: Springer-Verlag ISBN: ISBN 0-387-97743-0.
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There will be at least some geometric explorations with computer software during the course. Software such as Maple, Mathematica and Matlab can be used for general graphics demonstrations. Dynamic plane geometry programs such as Cabri Geometry and The Geometer's Sketchpad can be used for some topics, such as plane projective and non-Euclidean geometry.
No one will be required to write programs, but work with software may be included in assignments. In any event, students interested in graphics and geometrical programming can pursue this interest in their class projects.Back to Table of Contents.
The prerequisites are listed in the catalog, but this listing does not really explain what is the most important mathematics to bring into the course.
A good understanding of the geometrical aspects of linear algebra and multivariable calculus will be extremely helpful. Since this is a senior-level course which is pursuing mathematical concepts rather than techniques, some experience with rigorous and/or abstract mathematics of any kind with be very helpful.
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