Structure of AlgebrasCovers the structure of finite dimensional algebras and the characterization of semisimple algebras.
Lie Algebra: Group TheoryExplores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Group Algebra: Maschke's TheoremExplores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Analytical Study of SpaceExplores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.
Vertex Operator AlgebrasCovers the basics of Vertex Operator Algebras, including normal ordering, fields, and product fields.
Number of Solutions in Linear SystemsExplores the number of solutions in linear systems of equations and the conditions for no solution, a unique solution, or an infinite number of solutions.