260208 VO Advanced Module Condensed Matter Physics (2008S)

The lecture will present a systematic introduction into the fundamental concepts of tree-dimensional crystallography, starting from elementary concepts of algebra, number theory and group theory. The following topics will be covered: Lattice theory and modules on the ring Z, reduction theory, reciprocal lattice and Miller indices, symmetries, stereographic projection, point groups, Laue groups and space groups. At the end of the lecture course modern extensions of classical crystallography (quasicrystals, cryptosymmetries and crystallography in higher dimensions) will briefly be introduced. The lecture is intended to supplement the basic solid state physics course, where crystallogrphy can be treated only very briefly.
It is supposed that the participants have some basic knowledge of linear algebra. Other mathemathical concepts (e.g. group theory) will be introduced within the lecture.