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Related lectures (31)

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Homology of Riemann Surfaces

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.

Markov Chains: Basics and Applications

Introduces Markov chains, covering basics, generation algorithms, and applications in random walks and Poisson processes.

Homotopy Lifting

Explains homotopy lifting, paths, proofs, constant paths, discrete spaces, and monomorphisms.

Advanced Numerical Analysis: Space Discretization

Explores advanced space discretization techniques in numerical analysis for solving differential systems efficiently and accurately.

Sheaves: Hartshorne I.1

Covers the concept of sheaves, emphasizing the unique determination of functions by local data and the importance of direct limits.

Image manipulations: Affine transforms and Interpolation

Covers affine transforms, rotation, shear, and bilinear interpolation for image manipulations.

Fractal Uncertainty Principle and Spectral Gaps

Delves into the Fractal Uncertainty Principle for the Fourier transform and spectral gaps, including specialized cases for Cantor sets.

Interior and Closure in Topology

Covers the concepts of interior and closure of a set in a topological space, as well as isolated points and accumulation points.

Metric Spaces: Topology and Continuity

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Dimension theory of rings

Covers the dimension theory of rings, including additivity of dimension and height, Krull's Hauptidealsatz, and the height of general complete intersections.