Euclidean Division and Simple Elements

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Explores system equivalence, state-space representation, transfer functions, and Euclidean rings, emphasizing unimodular matrices and their properties.

Polynomial Methods: GCD Calculation Summary

Covers the calculation of the greatest common divisor using polynomial methods and the Euclidean algorithm.

Polynomial Factorization over Finite Fields

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

Chinese Remainder Theorem and Euclidean Domains

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

Polynomial Division: Terms and Factors

Covers polynomial division, terms, factors, and integration methods.

Rational Numbers: Construction and Properties

Covers the construction and properties of rational numbers, including fractions and equivalence, with proofs on commutativity.

Integration of Rational Functions

Covers the integration of rational functions, including the decomposition into partial fractions and the use of complex zeros.

Properties of Euclidean Domains

Covers the properties of Euclidean domains and irreducible elements in polynomial rings.

Decomposition of Fractions: Simple and Corollary Proof

Covers the decomposition of fractions into simple terms and provides a corollary proof related to the convergence of integrals.

Polynomial Factorization over a Field: Eigenvalues

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