Algebraic Topology
Using algebraic structures (groups, rings) to classify topological spaces: fundamental group, covering spaces, simplicial and singular homology, and cohomology.
Course Overview
Textbook |
Hatcher, Algebraic Topology (free online) |
Chapters |
TBD |
Sections |
TBD |
Prerequisites |
|
Target |
Research mathematics, topological data analysis, mathematical physics |
Status |
Planned |
Chapters will be scaffolded when this course becomes active.
Why This Course
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Topological data analysis — persistent homology extracts shape from high-dimensional data
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Robotics — configuration spaces, motion planning
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Network analysis — simplicial complexes model higher-order interactions
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Physics — gauge theory, string theory, topological quantum field theory
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Pure mathematics — the gateway to homotopy theory and modern geometry