Discovering Group Theory @Hampshire, Days 24-27

For the last two weeks of the semester students worked independently on projects which involved the material we learned in class.The class time was spent on research and discussion of their individual projects.

  • A second-year pre-med/math student researched the use of group theory in chemistry.
  • A first-year student, still undecided on her concentration, dove into a paper on applications of group theory to molecular systems biology and used what we learned in class to understand the key points made in the article (Rietman EA, Karp RL, Tuszynski JA. Review and application of group theory to molecular systems biology. Theoretical Biology & Medical Modelling. 2011;8:21. doi:10.1186/1742-4682-8-21.)
  • A first-year art student explored and identified the approximate symmetries of geometric shapes and symbols of ancient South-Western petroglyphs and rock paintings, which included dihedral groups and the translation group.
  • A third-year art student researched the connections between group theory and the tree branching patterns.
  • A third-year student with a concentration in math researched the application of group theory to Rubik’s cube.

The course concluded with class presentations.

After I complete narrative evaluations for the students in the course, I will write a post reflecting on my own experience teaching this course.

Discovering Group Theory, Days 21-23

We spent three days discussing the conceptual framework of special relativity.

We reviewed the expressions for time dilation and length contraction (we didn’t derive the latter) and discussed what they tell us about the nature of space and time.  We introduced the Lorentz boosts as a replacement for the Galilean boosts, and formally introduced the Lorentz group, SO(1,3). New concepts and ideas included

  • Spacetime events
  • Spacetime diagrams and null cones
  • Causally connected events 
  • Relativity of simultaneity

The key takeaway was that Lorentz transformations leave the causal structure of spacetime the same, just like rotations of a polygon leave the shape and the orientation of the polygon the same.