Counting: Combinations and Permutations

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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.