Algebraic Structures and Crystallography

This lecture covers algebraic structures such as fields and vectorial spaces, prime numbers, basics on vectors, 3D geometry, crystallography, and crystal structures. It introduces the concept of crystallography, crystal planes, reciprocal space, and the distance between crystal planes. The lecture also explains the organization of materials in a crystalline state, the Bravais lattice, lattice points, coordination, density, and fill factor. Additionally, it discusses the cubic system, primitive, body-centered, and face-centered cubic lattices, as well as the basics of Euclidean geometry, vector spaces, and the cross product of vectors.