Lectures related to Linear Algebra: Injections, Surjections, Bijections

Linear Algebra: Injective Functions

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

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R Programming: Conditions, Loops, Functions & Graphics

Covers conditions, loops, functions, and graphics in R programming with practical examples.

Limits of Functions: Definitions and Examples

Explains surjective, injective, and bijective functions, along with limits of functions.

Real Numbers and Functions

Introduces Real Analysis I, covering real numbers, functions, limits, derivatives, and integrals.

Definitions and Notations

Covers the definitions and notations related to functions.

Functions: properties and convergence criteria

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

Real Functions: Definitions and Properties

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

Function Properties: Injective, Surjective, Bijective

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

Limits and Infinity

Covers the concept of limits and explores limits at infinity with illustrative examples.

Functions in Python

Introduces functions in Python, covering predefined and user-defined functions, formal and effective parameters, and the importance of docstrings.

Mathematical Analysis: Functions and Composition

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

Functions: Basic Concepts

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

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Probability and Statistics

Covers mathematical concepts from number theory to probability and statistics.

Bernoulli's Hospital Rule

Covers the statement of the Bernoulli's Hospital Rule and its application.

Derivability and Composition

Covers derivability, linear applications, composition of functions, and the gradient vector.

Linear Algebra: Surjections and Bijections

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

Matlab 2: Vectorisation and Functions

Covers vectorisation, functions, and flow control in Matlab, emphasizing the importance of avoiding global variables and providing examples of simple plots and debugging techniques.

Equivalence Relations and Functions

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