Lectures related to Equivalence relation

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

Covers integers, rings, subrings, invertibility, divisors of zero, and equivalence relations in formal fractions.

Explores Lagrange's theorem in commutative groups and the concept of equivalence relations, demonstrating their practical applications.

Classification of Extensions

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

Equivalence Relations: Classes, Partitions

Covers equivalence relations, classes, and partitions of a set.

Markov Chains: States Classification

Explores the classification of states in Markov chains, emphasizing equivalence classes and periodicity.

Equivalence Relations: Classes, Partitions

Explains equivalence relations, classes, and partitions in sets.

Equivalence Relations and Partial Orderings

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

Equivalence Relations and Partitions

Explores equivalence relations, reflexivity, equivalence classes, and constructing new sets based on equivalent elements.

Logical Expressions and Equivalence Relations

Covers logical expressions, sets, elements, and equivalence relations.

Quotients of Groups by Relations of Equivalence

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Cartesian Product and Equivalence Classes

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

Fractional Elements and Equivalence Relations

Explores fractional elements, equivalence relations, and injective mappings in commutative rings.

Equivalences de Catégories et Adjonctions

Explores category equivalences, adjunctions, and group actions in category theory.

Equivalences of Categories

Explores examples of natural transformations, equivalence of categories, and adjunction with specific instances involving Un.

Groups and Numbers: Mathematical Elements on Groups

Explores fundamental properties of groups and numbers, emphasizing equivalence classes and subgroup concepts.

Properties of Operations: Equivalence Relations and Logic Basics

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

Cartesian Products and Equivalence Relations

Introduces Cartesian products, equivalence relations, and functions, emphasizing the importance of order and discussing injective, surjective, and bijective functions.

Quotient Spaces: Three Ways

Explores three ways to form quotient spaces using group actions and equivalence relations.

Elementary Matrices: Operations and Equivalence

Explores elementary matrices, operations, equivalence, and echelons in matrices.