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 The goal of the lecture (and the only take-away point, as far as the rest of the course is concerned!) was to prove the following two theorems:
 
-Theorem 1: If $f:A \to \C$ is a holomorphic function on an annulus, then it has a Laurent series expansion
+Theorem 1: If $f:A \to \mathbb{C}$ is a holomorphic function on an annulus, then it has a Laurent series expansion
 $$ f(z) = \sum_{n = -\infty}^{\infty} c_n z^n = \cdots \frac{c_{-2}}{z^2} + \frac{c_{-1}}{z} + c_0 + c_1 z + c_2 z^2 + \cdots $$ 
 
-Theorem 2: If $f: D \to \C$ is a holomorphic function on a disk, then it has a power series expansion
+Theorem 2: If $f: D \to \mathbb{C}$ is a holomorphic function on a disk, then it has a power series expansion
 $$ f(z) = \sum_{n = 0}^{\infty} c_n z^n = c_0 + c_1 z + c_2 z^2 + \cdots $$
 
 The reason we discussed convergence of Fourier series was to give some taste for the type of mathematical analysis that goes in to proving things rigorously using Fourier series.