GU4065 Honors Complex Variables, 2025
Instructor: Tang-Kai Lee Lecture: TuTh 10:10-11:25am at Hamilton 603 Office hour: TuTh 8:50-9:50am at Math 413, or by appointment Contact: tl3439 "at" columbia "dot" edu TA help room: See CourseWorks.
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- Plan:
- Week 1 (Sep 2, 4): Introduction, review, and holomorphic functions [Note]
- Week 2 (Sep 9, 11): Power series, line integrals, and Goursat's theorem [Note]
- Week 3 (Sep 16, 18): Cauchy theory and consequences [Note]
- Week 4 (Sep 23, 25): Global Cauchy theory and zeros [Note]
- Week 5 (Sep 30, Oct 2): Singularities and Laurent series [Note]
- Week 6 (Oct 7, 9): Meromorphic fucntions and residue theory [Note]
- Week 7 (Oct 14, 16): Approximation theorems and applications [Note]
- Week 8 (Oct 21): Gamma function and Zeta function [Note]
- October 23: Midterm
- Week 9 (Oct 28, 30): Normal families of holomorphic functions [Note]
- Week 10 (Nov 6): Normal families of meromorphic functions [Note]
- Week 11 (Nov 11, 13): Harmonic functions and Dirichlet problem [Note]
- Week 12 (Nov 18, 20): Conformal maps and Riemann mapping theorem [Note]
- Week 13 (Nov 25): Topology of Riemann surfaces [Note]
- Week 14 (Dec 2, 4): Uniformization and hyperbolic surfaces [Full Note]
- Dec 18: Final (9am-noon)
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