COURSE GOALS
MTH 434/534
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For students to develop a geometric understanding of line elements and
their use in describing a geometry;
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For students to develop a geometric understanding of standard surfaces
in three and four dimensions;
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For students to develop the ability to multiply differential forms;
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For students to develop the ability to differentiate and integrate
differential forms;
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For students to develop the ability to use differential forms to
describe vector calculus;
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For students to develop the ability to work with geometries of
arbitrary signature;
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For students to develop the ability to compute the connection and
curvature corresponding to a given geometry;
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For students to appreciate the unifying thread brought to these topics
by the use of the vector differential.