Lectures related to Counting: Permutations and Combinations

Counting: Permutations and Combinations

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

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Enumeration: Counting Subsets

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

Steinitz Lemma and Cycles

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

Counting: Combinations and Permutations

Covers the concepts of combinations and permutations in counting scenarios.

Symmetric Group and Cycle Decomposition

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

Symmetric Group and Group Actions

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

Linear Algebra: Sets and Subsets

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

Symmetric Group and Alternating Group

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

Why are there so many saddle points?: Loss landscape and optimization methods

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

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Group Theory: Basics

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

Properties of Cross Product: Algebraic Aspects

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

Linear Equations and Matrices: Solution Methods, Elementary Operations

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.

Permutations and Symmetric Groups

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

Algebraic Structures: Groups and Rings

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

Determinants: Special Linear Groups and Matrix Properties

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

Local structure of totally disconnected locally compact groups I

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

Permutation of In: Simplified Notation

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

Permutations and Adjacency

Explores permutations preserving adjacency, linear transformations, groups, and sub-groups.