Lectures related to Counting: The Product Rule

Explores binary relations, Cartesian products, and applications between sets, emphasizing their properties and significance.

Explores properties of operations, equivalence relations, and logic basics.

Introduces the theory of categories by generalizing the Cartesian product and disjoint union of sets to any category.

Covers the foundation of mathematics through set theory concepts like membership and unions.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Covers equivalence relations, functions, injectivity, surjectivity, and bijectivity with illustrative examples.

Covers propositions indexed by vectors, proof by induction, and Cartesian products of sets.

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.