Lectures related to Set Theory: Operations and Functions

Explores operations on sets, Cartesian products, and functions' properties.

Explains surjections and bijections in linear algebra, focusing on function properties and inverse identification.

Covers the introduction and terminology of functions, including injections, surjections, and bijections.

Covers the basics of functions, including domain, codomain, image, and range, as well as injections, surjections, and bijections.

Covers injectivity, surjectivity, and bijectivity in mathematical functions, explaining unique mappings and pre-image existence.

Introduces categories as collections of objects with morphisms and identity morphisms.

Covers the definitions and notations related to functions.

Covers the Pigeonhole Principle, its applications, and examples of its guarantees.

Explores real functions, covering parity, periodicity, and polynomial functions.

Explores the origin of functions, continuity, differentiability, and the physical representation of chemical bonds.

Explores injective functions in linear algebra, demonstrating how to prove injectivity step by step.

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Covers the properties of Euclidean spaces, focusing on R^n and its applications in analysis.

Explores surjections in linear algebra, demonstrating their importance in mapping elements between sets.

Covers the basics of proofs, defining sets, and applications between sets.

Covers functions, including even and odd functions, periodicity, and function operations.

Explores the properties of relations in computer science, including equivalence relations and the partition of a set.

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Explores convergence criteria, function properties, and unique element association.

Covers open balls in Euclidean spaces, their properties, and their significance in topology.