Coding Theorem: Proof and Properties

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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.