Lectures related to Range of a function

Real Functions: Definitions and Graphs

Covers real functions, definitions, graphs, parity, periodicity, and boundedness.

Operations on Sets: Parts, Intersection, and Difference

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

Recognizing a Quotient

Discusses the recognition of a quotient in topology and the properties of the quotient topology.

Linear Algebra: Bijections and Cardinality

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

Linear Algebra: Surjections

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

Continuous functions on a closed bounded interval

Covers limits, range of continuous functions, and uniform continuity on closed intervals.

Directed Graphs: Introduction and Categories

Covers the fundamental notion of composition in directed graphs and provides examples of their representation.

Injectivity and Surjectivity

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

Functions: Limits and Continuity

Explores functions, limits, continuity, differentiability, and important notions of limits and divergence.

Sets, Functions and Relations: Summary of Week 4

Covers sets, functions, and relations, including functions' properties and binary relations.

Linear Transformations: Matrices and Applications

Explores linear transformations, matrices, injective and surjective functions, and their applications.

Set Theory: Operations and Functions

Covers set theory operations and functions, including injections and surjections.

Linear Algebra: Properties of Injective and Surjective Functions

Covers the properties of injective and surjective functions and the concept of bijections.

Functions: Limits, Continuity, Differentiability

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

Functions: Introduction and Terminology

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

Linear Algebra: Surjections and Bijections

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

Introduction to Linear Transformations

Introduces linear transformations, mapping vectors to unique terms and exploring matrix equations.

Linear Applications: Some Basic Concepts

Introduces the basic concepts of linear applications, including injective, surjective, and bijective functions, along with function composition.

Proofs and Sets: Applications

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

Cartesian Products and Equivalence Relations

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