Decimal Expansion: Division and Periodicity

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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.