Lectures related to Euclidean domain

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

Chinese Remainder Theorem and Euclidean Domains

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

Decimal Expansion: Division and Periodicity

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

Chinese Remainder Theorem: Rings and Fields

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

System Equivalence

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

Number Theory: GCD and LCM

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

Number Theory: GCD and LCM

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

Open Balls and Topology in Euclidean Spaces

Covers open balls in Euclidean spaces, their properties, and their significance in topology.

Number Theory: Foundations and Applications in Cryptography

Introduces number theory and its essential applications in cryptography.

Euclidean Algorithm

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

Euclidean Correlation Functions

Explores Euclidean correlation functions and the transition to real-time correlators, emphasizing analyticity and time ordering in thermal n-point functions.

Algorithms for Big Numbers: Z_n and Orders

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

Euclidean Norm: Properties and Special Cases

Explores the Euclidean norm properties, special cases, and applications of the Cauchy-Schwarz inequality.

Polynomial Factorization: Field Approach

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

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Properties of Euclidean Domains

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

Polynomial Factorization over a Field: Eigenvalues

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

Quantum Field Theory in Ads and CFT Correlators

Covers the concept of Quantum Field Theory in Ads and CFT correlators.

Chinese Remainder Theorem and Polynomial Rings

Covers the Chinese remainder theorem, polynomial rings, and Euclidean domains among other topics.

Irreducible Polynomials and Finite Fields

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