Lectures related to Symmetric Group and Cycle Decomposition

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

Explores Lie algebras, representations, tensor products, and commutation relations in mathematics.

Covers a review of algebraic structures such as rings, fields, and groups, including integral domains, ideals, and finite fields.

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

Covers alternating and symmetric multilinear forms in vector spaces over a field.

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.

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