Lectures related to Decimal Expansion: Division and Periodicity

Explains polynomial division, factor decomposition, and rational function simplification.

Explores algebraic geometry, focusing on rings, bodies, quotient rings, and irreducible polynomials.

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

Delves into infinite decimal numbers, exploring convergence and divergence, and showcasing examples of rational and irrational numbers.

Explains the conversion between decimal and fractional writing, including division with remainder and a trick for periodic numbers.

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

Covers algorithms for big numbers, Z_n, and orders in a group, explaining arithmetic operations and cryptographic concepts.

Introduces number theory and its essential applications in cryptography.

Explores the construction of rational numbers, irreducible fractions, equivalence, and simplification rules.

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

Explains decimal and periodic numbers, illustrating with examples and discussing rational numbers.

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

Explores Euclidean division for polynomials, emphasizing uniqueness of quotient and remainder.

Explores the Chinese remainder theorem, systems of congruences, and Euclidean domains in integer numbers and polynomial rings.

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

Covers the factorization of polynomials over a field, including division with remainder and common divisors.

Covers the Chinese remainder theorem for commutative rings and integers, polynomial rings, and Euclidean domains.

Explores polynomial factorization over a field, emphasizing eigenvalues and irreducible components.

Explains the conversion process from fractions to decimal numbers and vice versa.

Introduces polynomial factorization over finite fields and efficient computation of greatest common divisors of polynomials.