Lectures related to Permutations and Symmetric Groups

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

Explores differentiable ranking and sorting techniques for machine learning applications.

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.

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.