Lectures related to Cardinality and Group Theory

Covers the basics of sets and operations in mathematics, from set properties to advanced operations.

Introduces fundamental concepts of linear algebra, focusing on sets and operations.

Covers the generalities of functions, including the definition of an application between sets and the uniqueness of elements in the image set.

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

Explores bijections in linear algebra and the concept of cardinality between sets.

Covers sets, propositional language, reading, writing, containment, and cardinality.

Introduces the basics of group theory, defining groups, categories, and groupoids.

Covers simplicial and cosimplicial objects in category theory with practical examples.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers the basics of group theory, including sets, applications, and examples like permutations and rotations.

Introduces cardinality and mapping in linear algebra, illustrating concepts with examples and visual aids.

Explores concrete examples of group actions on sets, focusing on actions that do not change the set.

Introduces sets, functions, Cartesian products, and compositions, discussing images, preimages, and function properties.

Covers sets, subsets, and their notation, including the power set concept.

Covers the basics of analysis, including real numbers, proofs, sets, and operations.

Introduces sets and functions, covering union, intersection, complement, functions terminology, and set operations analogies.

Explains the union of sets, its properties, operations, and intersection.

Explores adjunction between functors, composition of applications, G-equivariance, and natural transformations in G-sets.

Covers the Cartesian product of sets and binary relations with detailed examples and graphical representations.

Introduces sets in discrete mathematics and explores proof techniques like direct and indirect proofs.