Lectures related to Euclid and Bézout: Algorithms and Theorems

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

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

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

Introduces number theory and its essential applications in cryptography.

Covers GCD, LCM, and the Euclidean algorithm for efficient computation of GCD.

Covers commutative groups and their significance in cryptography.

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

Explores the properties of Euclidean domains, including gcd, lcm, and the Chinese remainder theorem for polynomial rings.

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

Explores polynomial roots, factorization, and the Euclidean algorithm in depth.

Introduces integer numbers, well-ordering, induction principles, GCD, LCM, and Bezout's theorem.

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

Covers GCD, LCM, and the Euclidean algorithm for efficient computation.

Covers the RSA cryptosystem, encryption, decryption, group theory, Lagrange's theorem, and practical applications in secure communication.

Explores well ordering, induction, Euclidean division, and prime factorization in integers.

Covers polynomial division and observer/controller approach with step-by-step examples.

Explores ideals in K[X], including PGCD, uniqueness, coprimality, and theorems of Bézout and Gauss.

Covers the Euclidean algorithm for GCD calculation and algorithmic complexity analysis.

Covers fundamental concepts in number theory with examples and quizzes.

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