### Complex calculus

1. The Cauchy Riemann Equations: what do they really mean?
2. Contour Integration I: Cauchy and Morera's integral theorems
3. Contour Integration II: Everything about singularities and the origin of Pi + Picard's theorem
4. Conformal maps, preserving angles, etc.
5. Power series and disks of convergence
6. Analytic continuation, monodromy theorem
7. Random properties of holomorphic functions, Maximum modulus principle, FTA, etc.
Resources
• Visual Complex Analysis (Needham)

Why "disk" of convergence? Why singularity at $i$ affects 1? Why do quaternion singularities not matter?