The following tentative schedule is subject to revision as the semester progresses.
- January 15 and 17.
- Convergence in spaces of functions. Montel’s theorem.
- January 22 and 24.
- Proof of the Riemann mapping theorem.
- January 29 and 31.
- Infinite products. Weierstrass factorization theorem.
- February 5 and 7.
- Special functions.
- February 12 and 14.
- Runge’s theorem. Mittag-Leffler’s theorem.
- February 19 and 21.
- Catch-up and review. Midterm examination.
- February 26 and 28.
- Schwarz reflection principle. Monodromy theorem.
- March 5 and 7.
- Riemann surfaces.
- March 12 and 14.
- Spring Break: classes do not meet.
- March 19 and 21.
- Harmonic functions. Poisson integral. Harnack’s theorem.
- March 26 and 28.
- Subharmonic functions.
- April 2 and 4.
- Dirichlet problem.
- April 9 and 11.
- Jensen’s formula. Order and type of entire functions.
- April 16 and 18.
- Hadamard’s factorization theorem.
- April 23 and 25.
- Picard’s theorems.
- April 30.
- This Tuesday is redefined as Friday, so Math 618 does not meet.
- May 7.
- Final examination, 8:00–10:00 in the morning.