Lectures related to Permutation

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

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

Covers permutation, combination, and the pigeonhole principle in counting problems.

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.

Covers permutations and combinations with and without repetition, including examples with letters, fruits, bills, and equations.

Covers the concept of enumeration and counting subsets of a finite set with examples and factorial notation.

Covers the concepts of combinations and permutations in counting scenarios.

Covers the simplified notation for expressing permutations and their applications in mathematics.

Covers symmetric groups, transpositions, sign of a permutation, and conjugacy classes in permutations.

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

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

Provides a recap of group theory, defining a group as a set with a multiplication operation.

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

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

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

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

Covers preservation, substitution, weakening, and sequencing in type systems.