This is a first semester graduate course in functions of one complex variable. Topics to be covered include the CauchyRiemann equations, Cauchy Integral Formula, Liouville theorem, meromorphic functions, residues, normal families and Montel's Theorem, Riemann mapping theorem, harmonic functions, Poisson Integral Formula, subharmonic functions, Dirichlet problem, Weierstrass products, MittagLeffler Theorem, Blaschke products.
Instructor: Email: Office Hours: 
Hang Xu TTh 1:002:00 at Krieger 220 
TA: Office Hours Email: 
Cheng Zhang Wed 34 pm at Krieger 211 and 57 pm at Krieger 213. 
Lecture Time: 
TTh 10:3011:45 
Classroom: 
Krieger 204 
Text: 
Greene & Krantz, Function
Theory of One Complex Variable, Third Edition 
Grading: 
Grades will be based on 350 points distributed as follows: 11 homework assignments, worth 10 points each, due in the lecture on the following Thursday. The lowest score will be dropped. A midterm exam (100 points) and a final exam (150 points). 
Syllabus (will be updated 
as the course progress): 
week 
beginning 
reading 
assignment (due the following Thursday) 
1. 
Jan. 30 
(review Chapter 1) 
Ch. 1: 16, 17, 36, 42, 43 
2. 
Feb. 6 
3.13.3 
Ch. 2: 21 
3. 
Feb. 13 
3.43.6, 4.14.3 
Ch. 3: 32, 33, 37, 38, 39, 42, 44 
4. 
Feb. 20 
4.44.6 
Ch. 4: 9, 21, 27abc, 33abc, 34bdh, 40, 50, 59 
5. 
Feb. 27 
4.7, 5.15.3 
Ch. 4: 30, 31, 51, 60. 
6. 
Mar. 6 
5.4, 5.5, 6.2 
Ch. 5: 5, 8, 10acf, 12, 13, 14, 16. Ch. 6: 17 
7. 
Mar. 13 
6.1, 6.3 
Midterm, Thursday, Mar. 15 

Mar. 20 
Spring Break 

8. 
Mar. 27 
6.46.7 

9. 
Apr. 3 
7.17.3 

10. 
Apr. 10 
7.47.6 

11. 
Apr. 17 
7.7, 7.8 

12. 
Apr. 24 
8.1, 8.2 

13. 
May. 1 
8.3, 9.1 
Final, 2:005:00 pm
Thursday, May. 17 