In preparation for the discussion of continuous groups and their applications in physics, we began the class with a short and a bit of a handwaving introduction of the more abstract notion of symmetry, namely that of a symmetry of a physical law. We then moved on to complex numbers, which most students have seen before. After a brief introduction, students practiced working with:
- Complex numbers in the rectangular form
- Operations with complex numbers
- Complex conjugation and modulus
- Complex numbers as points in a complex plane
Finally, students showed that complex numbers form a group under addition, (C,+).