Date  Lecture  Topics  References (Stein Shakarchi) 
Remarks 
1/20  1  Review of analysis and topology  Ch 1, Sections 1.1–2.1  
1/22  2  Review of analysis and topology
The complex plane 
Ch. 1, Sections 1.1–2.1, p.88  
1/27  3  Cauchy–Riemann equations Power series 
Ch.1, Sections 2.2, 2.3  
1/29  4  Power series Curves in the plane 
Ch. 1, Sections 2.3, 3  
2/3  5  Curves in the plane Integration over curves 
Ch. 1, Section 3 Appendix B 
Homework 1 Due 
2/5  6  Goursat's theorem Cauchy's theorem 
Ch. 2, Sections 1–3 Ch. 3, Section 5 

2/10  7  Cauchy's theorem Cauchy integral formula 
Ch. 2, Section 4  
2/12  8  Corollaries of Cauchy integral formula  Ch. 2, Sections 4, 5  Homework 2 Due 
2/17  9  Corollaries of Cauchy integral formula Isolated singularities 
Ch. 2, Sections 4, 5 Ch. 3, Sections 1–3 

2/19  10  Isolated singularities Meromorphic functions 
Ch. 3, Sections 1–3  
2/24  11  Meromorphic functions 
Ch. 3, Sections 1–3 Ch. 2, Section 3 
Homework 3 Due 
2/26  12  The residue theorem Evaluation of some integrals 
Ch. 2, Section 3 Ch. 3, Section 2 

3/3  13  The argument principle and applications 
Ch. 3, Section 4  
3/5  14  The complex logarithm Review 
Ch. 3, Section 6  Homework 4 Due 
3/10  Midterm  
3/12  15  Infinite products
Weierstrass's theorem 
Ch. 5, Sections 1–5  
3/17  16  Weierstrass's theorem
Functions of finite order 
Ch. 5, Sections 1–5  
3/19  17  Functions of finite order Hadamard's factorization theorem 
Ch. 5, Sections 1–5  Homework 5 Due 
3/23–3/27  Spring break  
3/31  18  Conformal mappings  Ch. 8, Sections 1–3  
4/2  19  Conformal mappings Introduction to groups 
Ch. 8, Sections 1–3  
4/7  20  Möbius transformations  Ch. 8, Sections 1–3  Homework 6 Due 
4/9  21  Automorphisms of the disk and upper half plane 
Ch. 8, Sections 1–3  
4/14  22  Normal families  Ch. 8, Sections 1–3  
4/16  23  Riemann mapping theorem  Ch. 8, Sections 1–3  Homework 7 Due 
4/21  24  Prime number theorem  Gamelin Ch. XIV  
4/23  25  Prime number theorem  Gamelin Ch. XIV  
4/28  26  Prime number theorem  Gamelin Ch. XIV  Homework 8 Due 
4/30  27  Prime number theorem  Gamelin Ch. XIV  
5/4  RRR Week  
5/5  RRR Week  
5/6  RRR Week  
5/7  RRR Week  Homework 9 due  
5/8  RRR Week 