MA 423 Topics in Geometry: Differential Geometry
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This course is an introduction to the field of differential geometry.
We will mainly focus on the intrinsic and extrinsic properties of curves
and surfaces, but time permitting we will look at the extension of these
ideas to higher dimensions and Riemannian geometry; the geometry of n
dimensional manifolds.
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For instance, in this course, we will examine the geometry of
objects such as the Costa surface depicted in the snow scultpure
to the left by Helaman Ferguson. This surface is an example of a
minimal surface (locally it has the smallest area possible among
all other surfaces). In terms of differential geometry, it is a
surface with mean curvature equal to zero.
The mathematics used in investigating of the geometry of such a surface is used in computer
graphics, imaging science, general relativity, high-energy physics, and in more advanced forms
of mathematics.
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Evaluation will be by homework sets, quizzes, class participation, and a final project. [No exams].
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