Math 407: Honors Complex Analysis
This is a rigorous introduction to complex analysis and is considered an Introduction to Proofs (IP) course. Topics covered in the course will include, review of complex numbers, Cauchy's theorem, holomorphic and meromorphic functions and some applications of complex analysis. There will be 10 problem sets (30% of final grade), and two in class exams (70% total -- your higher score will count for 40% and your lower score for 30%).
Lectures are Tuesday and Thursday 12-1:15pm in Krieger 306.
Problem sets will be due in class on Thursday (see below for dates and the assignments). No late homework will be accepted. Your lowest grade will be dropped.
Lecturer office hours: Tuesday 1:30-3:30pm or by appointment, in Krieger 408.
TA (Xiangze Zeng) office hours: Wednesday, 3-4pm in Krieger 211.
The syllabus is here.
ReferencesThe course text is
ExamsThere will be two in class exams. The exam you score higher on will count for 40% of your final exam and the one you score lower on will count for 30%.
Week 1 (9/5 & 9/7): Preliminaries
Week 2 (9/12 & 9/14): Preliminaries
Week 3 (9/19 & 9/21): Cauchy's Theorem
Week 4 (9/26 & 9/28): Cauchy's Theorem (cont.)
Week 5 (10/3 & 10/5): Meromorphic Functions
Week 6 (10/10 & 10/12): Meromorphic Functions (cont.); First Exam
Week 7 (10/17 & 10/19): Meromorphic Functions (cont.)
Week 8 (10/24 & 10/26): Meromorphic Functions (cont.)
Week 10 (10/31 & 11/2): Meromorphic Functions (cont.) and Fourier Analysis.
Week 11 (11/7 & 11/9): Fourier Analysis and Entire Functions
Week 12 (11/14 & 11/16): Entire Functions
Week 13 (11/28 & 11/30): Entire Functions and the Gamma and Zeta Functions
Week 14 (12/5 & 12/7): Second Exam