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Homological Algebra: Basics and Applications
Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.
Regular Implicit Functions
Discusses regular implicit functions, rings, ideals, sheaves, and ring operations.
Lifting properties and model categories
Covers the study of lifting properties in categories, focusing on the left and right lifting properties.
Regular Functions on Quasi-Affine Varieties
Explores regular functions on quasi-affine varieties, defining morphisms, local rings, and rational functions.
Local Rings and Residues
Covers the proof of theorem 4.2 on multiplicities and the special structure of local rings at a simple point of a plane.
Information Theory: Source Coding & Channel Coding
Covers the fundamentals of information theory, focusing on source coding and channel coding.
Compression: Kraft Inequality
Explains compression and Kraft inequality in codes and sequences.
Linear Maps: Injectivity and Surjectivity
Explores injectivity and surjectivity in linear maps through examples and proofs.
Sheaf Morphisms and Localization
Explores F-G sheaf morphisms, sheafification, and localization in ring theory.