Group Theory
In 2017, I taught an introductory course titled "Symmetries of Nature: An Introduction to Group Theory" at Hampshire College, which I designed as a hands-on, interactive course accessible to all students, even those without much math background. In an effort to keep a record of what we did and share the pedagogy with other interested educators, I posted our daily activities, along with the pictures, and links to resources. Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
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Discovering Group Theory, Day 2
Topics:
- Rotational symmetry
- Identity
- Inverse
- Formal definition of a group
- Group product
On Day 2, we considered only rotations of various polygons around their geometric centers. After a systematic hands-on investigation and cataloguing of rotations which leave a polygon unchanged, we identified the identity transformations and the inverse of each rotation. The class concluded we the formal definition of a group.
Cataloguing rotations of various polygons which leave them unchanged. -
Discovering Group Theory, Day 1
Topics:
- What is symmetry?
- How do we quantify it?
- Symmetries of polygons.
On Day 1, we looked at examples of polygons and tried to rank them based on their symmetry. First we had to come up with a sensible criteria for something to be symmetric, which we agreed had to do with the number and kind of operations which leave the polygons looking the same. Then as a class we used those criteria to rank the polygons based on the number of such possible transformations, which we found to be rotations and flips.
Students investigating symmetries of polygons. 
Summarizing the observations from the investigation as a whole class. Materials: Construction paper and some magnets.