This course covers the derivation of symmetry theory; lattices, point groups, space groups, and their properties; use of symmetry in tensor representation of crystal properties, including anisotropy and representation surfaces; and applications to piezoelectricity and elasticity.

This is a seminar based on research literature. Papers covered are selected to illustrate important problems and approaches in the field of computational and systems biology, and provide students a framework from which to evaluate new developments. The MIT Initiative in Computational and Systems Biology (CSBi) is a campus-wide research and education program that links biology, engineering, and computer science in a multidisciplinary approach to the systematic analysis and modeling of complex biological phenomena. This course is one of a series of core subjects offered through the CSB Ph.D. program, for students with an interest in interdisciplinary training and research in the area of computational and systems biology.

This game allows students to practice using dilations, rotations, reflections, and translations.  Levels start off focusing on a single skill and gradually increase in difficulty.  Levels include obstacles that students must avoid and combinations of transformations.  

Using three-dimensional scaffolds, these materials address the following topics:  - Structure & Function of DNA. - DNA Replication via Polymerase. - Transcription & Translation.  - Codons & Amino Acids Sequences. Each packet is broken into five parts - data dive, core ideas, investigations, asssessments, and life connections. Formative assessments and checkpoints are embedded throughout each packet. The final packet prepares students for a summative assessment, with a provided practice assessment. Implementation instructions are embedded for each component of each packet. PDFs are included as attachments (in case the file formats are altered by this system).