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,+).