Lectures related to Distortion of the Hamming Cube

Explains prefix-free codes for efficient data compression and the significance of uniquely decodable codes.

Explains compression and Kraft inequality in codes and sequences.

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

Explains how entropy measures uncertainty in a system based on possible outcomes.

Explores optimal transport in heat equations and metric spaces.

Introduces erasure and error channels, Hamming distance, and error correction codes.

Covers the proof and properties of the coding theorem, focusing on maximizing the properties of lx and the achievable rate.

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

Explores variational formulation for measuring information content and divergence between probability distributions.

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

Explores distribution and interpolation spaces, showcasing their importance in mathematical analysis and the computations involved.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Explores channel coding with a focus on convolutional codes, emphasizing error detection, correction, and decoding processes.

Explores tail bounds, information bounds, and maximal leakage in the context of generalization error.

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

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

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

Explores convergence in law for random variables, including Kolmogorov's theorem and proofs based on probability lemmas.

Covers the concept of compression and distance boards.

Covers examples of direct and indirect proofs in mathematics.