Lectures related to Fermat's Theorem: Sums of Squares

Covers the proof of Lagrange Theorem and explores quaternions, prime numbers, and equations.

Discusses Fermat's equation and Gaussian integers' properties.

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

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

Covers the ring of polynomials, focusing on coefficients and multiplication.

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

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

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

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

Explores algebraic structures of morphism spaces, including stability properties and injective ring homomorphisms.

Discusses Fourier expansion, quaternion algebra, and Whittaker model in automorphic forms.

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

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

Explores abelianization examples, homomorphisms, and isomorphisms in group theory.

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

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

Introduces sub-rings and morphisms in ring theory, emphasizing stability by multiplication.

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

Discusses irreducible factors in rings and the properties of Noetherian rings.

Explores F-G sheaf morphisms, sheafification, and localization in ring theory.