Lectures related to Quadratic Spaces and Quaternion Algebra

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

Covers linear transformations using matrices, focusing on linearity, image, and kernel.

Covers the goals and motivations of representation theory, focusing on associative algebras and homomorphisms.

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

Covers linear applications, matrices, transformations, and the principle of superposition.

Explores Lie groups, scalar fields, and vector spaces transformations.

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

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

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

Covers the topology of Adeles and their relationship with quadratic forms, polynomial varieties, and finiteness properties.

Covers various examples and general concepts related to linear applications in algebra.

Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.

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

Explores polynomial operations, properties, and subspaces in vector spaces.

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

Introduces the concept of the differential of a morphism and its applications in algebraic treatments.

Covers ideals, representations, modules, and maximal ideals in associative algebras.

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

Covers the structure of finite dimensional algebras and the characterization of semisimple algebras.