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Final exam The final oral exam will be held on Monday December 13th. All students are asked to meet at 10.00 to get individual times. Place: B81, Niels Henrik Abels hus.

Mandatory assignment: the assignment will be released Oct. 11, and the deadline is Oct. 28.

September 8. we will finish our discussion of conformal equivalence and prove rigidity in the family of annuli. We will move on to approximation problems, starting with Chapter 5 in Narasimhan.

So far we have covered elementary properties of holomorphic functions. The key tool is the generalized Cauchy Integral Formula deduced from Stoke's Theorem. We have proved Montel's Theorem and Schwarz's Lemma, and together with elementary properties of automorphisms of the disk and Koebe's Lemma, we have used the results to prove the Riemann Mapping Theorem.