Cohomology: Cup Product

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The Degree of a Covering Space

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.

Stein Algorithm: Polynomial Identity Testing

Explores the Stein algorithm for polynomial identity testing and the minimization of a cut problem.

Tensor Products of Modules

Covers tensor algebras, symmetric and exterior algebras, and tensor products of modules.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Injective Modules: Ox-Modules and Injectives

Covers injective modules, Ox-modules, and their relevance in algebraic structures, emphasizing their importance in resolving acyclic resolutions and computing cohomology.

Directed Networks & Hypergraphs

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Irreducible Polynomials: Degree and Roots

Explores irreducible polynomials, focusing on their degree and roots in different fields.

Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.

Fundamental Groups

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