Chinese Remainder Theorem and Euclidean Domains

About
Privacy
Disclaimer

Graph Chatbot

Related lectures (32)

Page 2 of 4

Polynomial Factorization over Finite Fields

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

Integers: Sets, Maps, and Principles

Introduces sets, maps, divisors, prime numbers, and arithmetic principles related to integers.

Euclidean Division: Uniqueness and Remainder

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

Polynomial Factorization: Field Approach

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

Polynomials: Definition and Operations

Covers polynomials, their operations, division theorem, and provides illustrative examples.

System Equivalence

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

Polynomial Factorization over a Field: Eigenvalues

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

Decimal Expansion: Division and Periodicity

Delves into decimal expansion of rational numbers through Euclidean division, emphasizing periodicity and illustrative examples.

Euclidean Algorithm

Explains the Euclidean algorithm for polynomials over a field K, illustrating its application with examples.

Irreducible Polynomials and Finite Fields

Explores irreducible polynomials, finite fields, cyclic unit groups, and field construction.