Symmetry, Structure, and Tensor Properties of Materials
MIT OpenCourseWare offers this advanced materials science course on how symmetry governs the physical properties of crystals. Lectures build up symmetry theory from lattices through point groups and space groups, then apply it to tensor representations of crystal properties, covering anisotropy, representation surfaces, piezoelectricity, and elasticity. The course includes lecture notes and problem sets drawn from MIT's Department of Materials Science and Engineering curriculum, aimed at students who already have a background in crystallography or solid-state physics. Materials are free to access under MIT's open license, with no enrollment or certificate offered, since OCW publishes course content rather than a taught, credentialed version of the class. Good for anyone who needs a rigorous, self-contained treatment of how symmetry constrains the tensors that describe real material behavior.