Lectures related to Rational Numbers: Definitions and Operations

Algebraic Operations

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Understanding Equivalence Relations and Integer Construction

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

Division in Rational Numbers

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

Division and Multiplication in Rational Numbers

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

Group Theory: Basics

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

Modular Arithmetic: Introducing Z/mZ

Introduces Z/mZ for writing equations with congruence classes in modular arithmetic.

Definition of Complex Numbers Field

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

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Natural Numbers

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

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.

Addition of Fractions

Covers the addition of fractions and properties of rational numbers, emphasizing associativity and summing fractions with the same denominator.

Linear Algebra in 3D: Matrices and Determinants

Covers linear algebra in three dimensions, focusing on matrices and determinants.

Linear Algebra: Matrices and Operations

Covers the basics of linear algebra, focusing on matrices and 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.

Subtraction: Properties and Definitions

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

Rational Numbers: Amplification and Simplification

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

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Complex Numbers and 2x2 Matrices

Covers complex numbers, quadratic equations, solutions in C, and 2x2 matrices.