Lectures related to Coding Theorem: Proof and Properties

Sparsest Cut: Bourgain's Theorem

Explores Bourgain's theorem on sparsest cut in graphs, emphasizing semimetrics and cut optimization.

Compression: Prefix-Free Codes

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

Compression: Kraft Inequality

Explains compression and Kraft inequality in codes and sequences.

Distributions and Derivatives

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

Optimal Transport: Heat Equation and Metric Spaces

Explores optimal transport in heat equations and metric spaces.

Generalization Error

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

Binary Coding: Channel Decoding

Explores binary channel decoding and vector spaces in coding theory.

Proofs: Logic, Mathematics & Algorithms

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

Zig Zag Lemma

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

Information Measures: Entropy and Information Theory

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

Advanced Information Theory: Random Binning

Explores random binning in advanced information theory, focusing on assigning labels based on typicality and achieving negligible error rates in source coding.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Harmonic Forms: Main Theorem

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

Error Correction Codes: Basics

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

Channel Coding: Convolutional Codes

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

Fundamental Groups

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

Sparsest Cut: Leighton-Rao Algorithm

Covers the Leighton-Rao algorithm for finding the sparsest cut in a graph, focusing on its steps and theoretical foundations.

Convergence in Law: Theorem and Proof

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

Analysis IV: Measurable Sets and Properties

Covers the concept of outer measure and properties of measurable sets.

Proofs: Direct and Indirect Methods

Covers examples of direct and indirect proofs in mathematics.