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Nov 15, 2024
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MATH 742 - Topology (3 units)
Topological structures, uniform spaces, metric spaces, compact and locally compact spaces, connectivity, function spaces, topological algebra, elementary homological algebra, singular homology theory, cell complexes, homotopy groups.
Units of Lecture: 3
Offered: Every Fall - Even Years
Student Learning Outcomes:
Upon completion of this course:
1. Students will be able to use long exact sequences to compute homology and cohomology groups of topological spaces.
2. Students will be able to compute homology groups and cohomology groups of a space from the Mayer Vietoris sequence for a decomposition into subspaces.
3. Students will be able to use the Kunneth formula to determine the cohomology of a product space. hmidt algorithm, Thomas algorithm and Newton’s divided difference formula.
4. Students will be able to recall and define terminology including error, condition, number, matrix, norm, machine epsilon, unitary matrix, Haar subspace, order of convergence positive, definite matrix, and stability.
5. Students will be able to write practical computer programs.
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