Scheduling

Week 1 (May 19): Preliminary Review
 \({\mathbf{C}}, {\mathbb{D}}, {\mathbb{H}}, {\mathbf{CP}}^1\)
 Complex arithmetic
 Arguments, branch cuts, complex log
 Elementary geometry, conic sections

Analysis Review
 Uniform (continuity, differentiability, convergence)
 HeineCantor
 Calculus review

Week 2 (May 26): Differentiation and integration
 Calculus preliminaries
 The Laplace equation,
 CauchyRiemann,
 Harmonic functions
 Contours, parameterization, primitives
 Cauchy's integral formula
 Cauchy's inequality

Week 3 (June 2): Analytic Functions and singularities
 Power series and convergence
 Laurent expansions

Isolated singularities
 Poles, meromorphic functions, essential singularities
 Riemann's removable singularity theorem
 Week 4 (June 9): Integration I
 Week 5 (June 16): Integration II
 Week 6 (June 23): Entire functions
 Week 7 (June 30): Roots
 Week 8 (July 7): Conformal Maps
 Week 9 (July 14): Schwarz lemma
 Week 10 (July 21): Omitted values
 Week 11 (July 28): Montel

Other misc topics:
 \(\mathrm{SL}_2(\mathbf{R})\), modularity and elliptic curves
 The hyperbolic metric
 Riemann surfaces
 Special functions:
 Canonical products
 Dirichlet’s problem
 Hurwitz’s theorem