Lectures related to Counting: Combinations and Permutations

Introduces Cartesian product and induction for proofs using integers and sets.

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

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

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

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

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

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

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.

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

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

Explores sets and subsets in linear algebra, emphasizing counting elements and subsets.

Covers the concepts of permutations and combinations, explaining how to calculate them with examples.

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

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

Explores the Steinitz Lemma and the concept of cycles in linear algebra.

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

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