Disclaimer: As I said in class, I only post these notes due to students requests. I typically type them rapidly and right before class, so they are extremely likely to have mistakes!

1. Session 1: Introduction to complex numbers
2. Session 2: Complex derivatives
3. Session 3: The Cauchy-Riemann equations
   You can read more about domain coloring in this excellent paper.
4. Session 4: Harmonic functions
   The Bimbo theorem: when does an analytic function map boundary to boundary? (without proof)
5. Session 5: Möbius Transformations and multi-valued functions (the later part is incomplete and more will be described in class)
   Möbius transformations applet to help you develop intuition to the geometry behind Möbius transformations.
   Möbius Transformations Revealed by Douglas N. Arnold and Jonathan Rogness