Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Covers the Zig Zag Lemma and the long exact sequence of relative homology.
Covers entropy, source coding, encoding maps, decodability, prefix-free codes, and Kraft-McMillan's inequality.
Explores generalization error in machine learning, focusing on data distribution and hypothesis impact.
Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.
Explores probability convergence, discussing conditions for random variable sequences to converge and the uniqueness of convergence.
Covers the Fourier inversion formula, exploring its mathematical concepts and applications, emphasizing the importance of understanding the sign.
