Lectures related to Equivalence Relations and Construction of R

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

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

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

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

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

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

Covers the properties and sets related to linear algebra, emphasizing the importance of understanding these concepts.

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

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

Explores the Cartesian product of sets, subsets, and recurrence in mathematics with examples and exercises.

Explores sets and subsets in linear algebra, emphasizing counting elements and subsets.

Explores independence in infinite coin tosses, covering sets, shifts, and T-invariance.

Introduces logic, proofs, sets, functions, and algorithms in mathematics and computer science.

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

Covers the basic concepts of sets, functions, and number systems.

Explains group representation, character, and theory, emphasizing orthogonality and equivalence.

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

Introduces sets, functions, and proofs in mathematics, covering set equality, subsets, Cartesian products, and truth sets of predicates.

Covers the definition of applications, image of elements, and direct and reciprocal images.

Covers basic notations related to sets and subsets, including elements and subsets.