Lectures related to Relations: Definitions and Properties

Explores optimization problems in algebra and trinomial equations, focusing on maximizing area with fixed perimeters.

Explores binary relations, sequences, and summation, including arithmetic and geometric progressions, recurrence relations, and cardinality of sets.

Introduces equivalence relations, partitions, partial orderings, and total ordering concepts with examples and definitions.

Covers the analysis of functions, composition, and mathematical induction.

Explores the consequences of the Total Bell System (TBS) in a commutative body.

Explores the implicit functions theorem and the equation of the tangent plane in a graph.

Introduces the theory of categories through examples and discusses the product of categories.

Covers the fundamentals of homotopy and its applications in topology.