Lectures related to Proof of Lagrange Theorem

Explores Fermat's Theorem, factorization of integers, properties of Z[i], and Hurwitz quaternions.

Explores quadratic spaces, norms, and quaternion algebra over fields.

Explores elementary algebra concepts related to numeric sets and prime numbers, including unique factorization and properties.

Discusses Fermat's equation and Gaussian integers' properties.

Covers 3D rotations, quaternions, and matrices of direction cosines, providing an elegant solution to the limitations of rotation matrices.

Covers division rings, fields, and ideals in commutative rings with examples in Z and quaternions.

Explores idempotent elements, central orthogonal elements, commutative rings, and prime ideals in non-central rings.

Covers prime numbers, RSA cryptography, and primality testing, including the Chinese Remainder Theorem and the Miller-Rabin test.

Explores Diffie-Hellman key exchange, ElGamal cryptosystem, and their security applications in cryptography.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Explores the Class Number Formula in number theory, focusing on Lemmas, Proofs, and a significant theorem.

Covers the properties and applications of quaternion algebra, including norm calculations and distribution in different spaces.

Explores Dedekind rings, integral closure, factorization of ideals, and Gauss' Lemma.

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

Explores the additivity of dimension and height in a finitely generated k-algebra domain, showcasing its applications and implications.

Explores division rings, integral domains, fields, and ideals in rings, with examples and key theorems.

Covers the equidistribution of representations of integers by ternary forms and the conductor of X.

Explores factorisation in Principal Ideal Domains and the properties of prime numbers.

Covers prime numbers, vectors, 3D geometry, crystallography, and algebraic structures in materials science.

Covers the concept of localization in algebra, focusing on making a ring multiplicative closed.