Permutations and Symmetric Groups

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Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.

Explores the special linear group, matrix properties, and determinant theorems.

Explores eigenvalues of Coxeter elements, cyclic permutations, invariance, and decomposition of eigenspaces.

Explores active learning implications in understanding group structures and symmetric actions.

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Introduces algebraic structures essential for understanding mathematical objects used in science and engineering.

Explores solutions of the 2018 exam, finite fields, group theory, congruences, and polynomial irreducibility in Q[X].

Explores the applications of Lagrange's theorem in algebra, covering corollaries, cyclic groups, and quotient groups.

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