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Related lectures (27)

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Explores the composition of applications in mathematics and the importance of understanding their properties.

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Explores proof concepts, techniques, and applications in logic, mathematics, and algorithms.

Explores linear similarities and similitudes, demonstrating their properties and applications in geometry.

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Covers distributions, derivatives, convergence, and continuity criteria in function spaces.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Explores the convergence of Fourier series in L² space with trigonometric polynomials and approximation theorems.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Explores the Rockafellar Theorem in optimal transport, focusing on c-cyclical monotonicity and convex functions.

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

Discusses bases in vector spaces of known dimension and how to determine if a given set is a base.

Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.

Covers the multivariate normal distribution, properties, and sampling methods.

Introduces Cartesian product and induction for proofs using integers and sets.