Lectures related to Permutations and Symmetric Groups

Covers the fundamental concepts of group theory and examples of real numbers and permutations.

Explores differentiable ranking and sorting techniques for machine learning applications.

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

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

Covers the group presentation of S3, normal subgroups, generators, relations, quotient groups, and injective homomorphisms.

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

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Covers the concepts of combinations and permutations in counting scenarios.

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Covers the Symmetric group, cycle decomposition, transpositions, even and odd permutations, and group actions.

Explores the Symmetric group, cycle decomposition, Orbit-Stabilizer theorem, and properties of cycles and transpositions.

Explores the Symmetric group, cycle notation, multiplication, the sign of a permutation, and the Alternating group.

Covers the definition of a group, properties of symmetries, and group operations.

Explores the symmetric group, emphasizing cycle notation and group properties.

Covers alternating and symmetric multilinear forms in vector spaces over a field.

Explores solvable groups, group actions, normalizers, and stabilizers in group theory.

Explores permutations, signature, and alternating multilinear forms in vectors.

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.