Discovering Group Theory, Day 15

On Day 15, we continued working with complex numbers, but now in exponential or polar form. After an introduction to complex numbers exponential form and its relation to the rectangular form, students worked on exercises covering:

  • Complex numbers in the polar form and their relation to the rectangular form
  • Complex conjugation and modulus
  • Complex numbers as points in a complex plane

About half of the class managed to get to the proof that the complex numbers form a group under multiplication, which was easier to do in the polar form.

We ended the class by watching a TED talk by Murray Gell-Mann,  “Beauty, truth, and …, physics?”.

Discovering Group Theory, Day 14

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,+).