In 3.072x: Symmetry, Structure, and Tensor Properties of Materials, you will study the underlying structures of materials and you will deepen your understanding of the relationship between the properties of materials and their structures.  Topics include lattices, point groups, and space groups in both two and three dimensions; the use of symmetry in the tensor representation of crystal properties; and the relationship between crystalline structure and properties, including transport properties, piezoelectricity, and elasticity.  Two course projects will allow students to explore their particular interests in greater depth.