Jacob Bernstein


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Math 407: Honors Complex Analysis


Course Description

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.

References

The course text is
  • E. Stein & R. Shakarchi, ‚ÄúPrinceton Lectures in Analysis II: Complex Analysis."

Exams

There 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%.

The dates of the exames are
First Exam: Thursday, October 12.
Second Exam: Monday, November 7.

(Tentative) Schedule

Week 1 (9/5 & 9/7): Preliminaries

Read Chapter 1
No homework due.

Week 2 (9/12 & 9/14): Preliminaries

Read Chapter 2
Problem Set 1 due.

Week 3 (9/19 & 9/21): Cauchy's Theorem

Problem Set 2 due.

Week 4 (9/26 & 9/28): Cauchy's Theorem (cont.)

Problem Set 3 due.

Week 5 (10/3 & 10/5): Meromorphic Functions

Read Chapter 3
Problem Set 4 due.

Week 6 (10/10 & 10/12): Meromorphic Functions (cont.); First Exam

First Exam. Solutions.

Week 7 (10/17 & 10/19): Meromorphic Functions (cont.)

Problem Set 5 due.

Week 8 (10/24 & 10/26): Meromorphic Functions (cont.)

Problem Set 6 due.

Week 10 (10/31 & 11/2): Meromorphic Functions (cont.) and Fourier Analysis.

Read Chapter 4
Problem Set 7 due.

Week 11 (11/7 & 11/9): Fourier Analysis and Entire Functions

Problem Set 8 due.

Week 12 (11/14 & 11/16): Entire Functions

Read Chapter 5
No Problem Set due

Week 13 (11/28 & 11/30): Entire Functions and the Gamma and Zeta Functions

Read Chapter 6

Week 14 (12/5 & 12/7): Second Exam

Problem Set 9 due. (On Tuesday.)
Second Exam.

Fall 2017 -- Department of Mathematics, Johns Hopkins University.