Lectures related to Algebraic Operations

Rational Numbers: Definitions and Operations

Covers the definition and operations involving rational numbers.

Division in Rational Numbers

Explores division in rational numbers and the extension of addition from integers.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Division and Multiplication in Rational Numbers

Explores division and multiplication in rational numbers, emphasizing the concept of multiplying by the inverse.

Mathematical Notations: Recap and Rational Numbers

Covers a recap on mathematical notations and introduces rational numbers and basic algebraic operations.

Complex Numbers: Operations and Applications

Covers the properties and operations of complex numbers and their applications.

Modular Arithmetic: Operations and Polynomials

Covers modular arithmetic operations and polynomial calculations modulo N with various examples.

Multiplication in Rational Numbers

Covers the extension of addition and multiplication operations in rational numbers.

Rational Numbers: Amplification and Simplification

Covers rational numbers, amplifying and simplifying fractions, and calculating values.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Subtraction: Properties and Definitions

Covers the properties and definitions of subtraction using addition and multiplication as a basis.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Element by element operations

Covers element by element operations in MATLAB and Octave for beginners.

Complex Numbers: Operations and Representations

Explores complex numbers, their operations, and representations in Cartesian and polar forms.

Element-Wise Operations

Covers element-wise operations in MATLAB and Octave using matrices and vectors.

Group Theory: Basics

Covers the basics of group theory, including definitions, examples, and isometries.

Definition of Complex Numbers Field

Introduces complex numbers and defines their field, emphasizing properties and operations.

Natural Numbers

Covers the concept of natural numbers, including properties like commutativity and associativity.

Matrix Multiplication

Covers matrix multiplication, properties, and the identity matrix in algebraic operations.

Linear Equations and Matrices: Solution Methods, Elementary Operations

Explores solution methods and elementary operations for linear equations and matrices, demonstrating techniques to simplify systems and obtain solutions.