Permutations and Symmetric Groups

Related lectures (28)

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Explores the algebraic properties of the cross product and its linearity.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

Covers the Orbit-Stabilizer theorem, conjugacy classes, and direct products in finite groups.

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

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

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

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

Explores the reasons behind the abundance of saddle points in deep learning optimization, emphasizing statistical and geometric arguments.

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