Lectures related to Equivalence Classes and Relations

Definitions and Notations MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Covers the definitions and notations related to functions.

Relations in Computer Science

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

Function Properties: Injective, Surjective, Bijective

Explains injective, surjective, and bijective functions using examples and graphs.

Mapping Functions and Surjections

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

Equivalence Relations: Relations, Sequences and Summations

Explores equivalence relations, functions, subsets, and De Morgan's laws.

Sets and Functions

Introduces sets, functions, and their properties, including injective and surjective functions, composition, and inverse functions.

Mathematics: Analysis and Algebra Overview

Provides an overview of analysis and algebra courses, focusing on real numbers, limits, functions, and exams.

Discussion of Surjectivity MOOC: Analysis I (part 1): Prelude, basic concepts, real numbers MOOC: Analysis I

Discusses the concept of surjectivity in functions and its implications.

Functions: Injectivity and Surjectivity

Explains injective, surjective, and bijective functions with examples and graphical representations.

Relations and Sequences

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Real Functions of Real Variables: Properties and Domains

Covers the properties of real functions, domains, and types of functions, including periodicity.

Functions: Definitions and Notations

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

Composition of Applications in Mathematics

Explores the composition of applications in mathematics and the importance of understanding their properties.

Linear Algebra: Injective Functions

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

Algebraic Identities and Trigonometry

Covers algebraic identities, trigonometry, and real functions, including injective, surjective, bijective, and reciprocal functions.

Tangent vectors without embedding space: Making tangent spaces linear

Explores making tangent spaces linear, defining tangent vectors without an embedding space and their operations, as well as the equivalence of different tangent space notions.

Mathematical Analysis: Functions and Composition Log in to Mediaspace to watch this video

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

Real Functions: Definitions and Properties Log in to Mediaspace to watch this video

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

Equivalence Relations and Functions Log in to Mediaspace to watch this video

Covers equivalence relations, functions, injectivity, surjectivity, and bijectivity with illustrative examples.

Functions: Basic Concepts Log in to Mediaspace to watch this video

Covers the basic concepts of functions, including definitions, notations, and discussions on injectivity and surjectivity.