Lectures related to Functions: Introduction and Terminology

Introduction to Functions

Covers the basics of functions, including domain, codomain, image, and range, as well as injections, surjections, and bijections.

Linear Algebra: Surjections and Bijections

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

Definitions and Notations

Covers the definitions and notations related to functions.

Injectivity and Surjectivity

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

Operations on Sets: Parts, Intersection, and Difference

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

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.

Real Functions: Definitions and Properties

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

Set Theory: Operations and Functions

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

Graphical Definition: Level Sets and Domains

Covers the graphical definition of functions, focusing on level sets and domains.

Mathematical Analysis: Functions and Composition

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

Functions: Limits, Continuity, Differentiability

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

Functions: properties and convergence criteria

Explores convergence criteria, function properties, and unique element association.

Functions and Periodicity

Covers functions, including even and odd functions, periodicity, and function operations.

Taylor Series: Convergence and Applications

Explores Taylor series convergence and applications in approximating functions and solving mathematical problems.

Mapping Functions and Surjections

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

Functions: Basic Concepts

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

Mathematics: Analysis and Algebra Overview

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

Linear Algebra: Injections, Surjections, Bijections

Explores injections, surjections, and bijections in linear algebra, highlighting their significance in mathematics.

Real Functions: Graphs and Properties

Explores real functions, their graphs, properties, and transformations, including symmetry and surjection.

Closure Conversion: Representation and Transformation

Explores the representation and transformation of values, focusing on closure conversion and the challenges of representing functions in functional languages.