Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.
Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.
Explains k-means clustering, assigning data points to clusters based on proximity and minimizing squared distances within clusters.
Covers the Lebesgue integration of simple functions and the approximation of nonnegative functions from below using piecewise constant functions.
Explores weak derivatives in Sobolev spaces, discussing their properties and uniqueness.
Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.
Explores the proof of the Weyl character formula for finite-dimensional representations of semisimple Lie algebras.
Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.
Covers manifolds, topology, smooth maps, and tangent vectors in detail.
Explores the properties of relations in computer science, including equivalence relations and the partition of a set.
