A graduate course on complex analysis, equivalent to an incoming graduate student one-semester (or a bit more) class.

We prove the Riemann mapping theorem which says that all simply connected domains in the plane, except the plane itself, are biholomorphic to the disc (or in other words, conformally equivalent). (Subsection 6.3.1 in the book).

The course is based on the book "Guide to Cultivating Complex Analysis", which is available freely online at

https://www.jirka.org/ca/

(You can also buy an inexpensive paperback copy, the best way to support this project)

See the course playlist:    • Cultivating Complex Analysis