Certificate in Math Topology for Data Science
-- ViewingNowThe Certificate in Math Topology for Data Science is a comprehensive course that bridges the gap between advanced mathematics and data science. This certification program highlights the importance of topology in data analysis, machine learning, and artificial intelligence.
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โข Topological Spaces: Introduction to topological spaces, open and closed sets, basis, and subbasis.
โข Continuity: Definition and properties of continuous functions, sequential continuity, and uniform continuity.
โข Compactness: Compact topological spaces, Heine-Borel theorem, and compactness in metric spaces.
โข Connectedness: Connected and disconnected spaces, path components, and locally path-connected spaces.
โข Convergence of Functions: Pointwise and uniform convergence, Dini's theorem, and Arzela-Ascoli theorem.
โข Homotopy and Homology: Definition and properties of homotopic functions, homology groups, and singular homology.
โข Fixed-Point Theorems: Brouwer's fixed-point theorem, Schauder's fixed-point theorem, and Lefschetz fixed-point theorem.
โข Manifolds: Definition and properties of manifolds, differential forms, and integration of differential forms.
โข Algebraic Topology: Fundamental group, covering spaces, and van Kampen's theorem.
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