Date    Chapter.Section/Topics   or   Page/Problems

M  Jan 9    Lecture 1: Introduction: Complex Numbers
            Assignment 1 Due Wednesday January 25
W   11      Lecture 2: Complex Numbers Continued
            Assignment 2 Due Wednesday February 1
M   16      Holiday 
W   18      Lecture 3: Powers and Roots
            Assignment 3 = Exam 1 Due Wednesday February 8
M   23      Lecture 4: 
            Assignment 4 Due Wednesday February 15
W   25                  Lecture 5: 
            Assignment 5 Due Wednesday February 22
M   30      Lecture 6:
            Assignment 6 = Exam 2 Due Wednesday March 1
W  Feb 1    Lecture 7: 
            Special Project: Mike's hyperbola(s) Due Wednesday May 3, 2023
            Assignment 7 Due Wednesday March 8
M    6      Lecture 9:  RuiRui:  inequalities
                        Gleb: triangle inequality
W    8      Lecture 9:  Leo:  open and closed sets
                        Carol's birthday problem: intersection of circles
                        Jose's hyperbola
M   13      Lecture 10: Comments on elementary functions (chapter 3)
                        Ethan: Wirtinger derivatives
                        Yinan: equivalent conditions for injective and surjective functions
W   15      Lecture 11: More comments on elementary functions (chapter 3)
                        Leo:  Cauchy-Riemann equations but not complex differentiable
                        Carter: quadratic factorization of z^(2n) -1 over the reals.
                        Xuanqi: discontinuous complex square root
M   20      Lecture 12: 
            Assignment 8 Due Wednesday March 15
W   22      Lecture 13:
            Assignment 9 Due Wednesday March 22 (This should probably be changed to March 29.)
M   27      Lecture 14: 
            Assignment 10 Due Wednesday March 29 (This should probably be changed to April 5.)
            Assignment 11 Due Wednesday April 5
            Assignment 12 Due Wednesday April 12
W  Mar 1    Lecture 15: 
M    6      Lecture 16: 
W    8      Lecture 17: 
M   13      Lecture 18: 
W   15      Lecture 19: 
M   20      Spring Break
W   22      Spring Break 
M   27      Lecture 20: 
W   29      Lecture 21: 
M  Apr 3    Lecture 22: 
W    5      Lecture 23: 
M   10      Lecture 24: Moore's proof of Goursat's theorem = Stein's proof (Leo)
W   12      Lecture 25: 
            Take any and all of what you find below as a final assignment
            UC Davis Practice Final 
            Description:  If you've followed what we've discussed in class, 
                          you should be able to work almost all of these 
                          problems.  You might need to learn a little something                          new, but not much.
            Michigan State University Second Exam 
            Description:  The first two problems should be relatively easy.  
                          The last three might require you to pick up 
                          something new, but they are not difficult.  
            University of Illinois Final Exam 
            Description:  About half of this should be no problem.  You need 
                          something like Liouville's theorem for Problem 4.  
                          Problem 10 is of special interest.
            MIT Practice Final 
            Description:  Only three problems!  You'll need to learn a little 
                          something for the first two.  Once you know what 
                          meremorphic means, the first one should be very 
                          (or at least relatively) easy.  I think you need 
                          Rouche's theorem for the second one.  The third 
                          one should be (relatively) easy for you, if you 
                          remember our discussion of the complex sine function.
            Harvard Final Exam 
            Description:  This one is just quite comprehensive and 
                          quite difficult.  If you can do it, 
                          you know complex analysis.  
            Due Wednesday May 3
                        Claire:  Computed a real integral of a complex function.
                                 Assignment 12 Problem 1
                        Linus:   Assignment 12 Problem 10
                                 Assignment 9 Problem 7
                        Ashton:  Assignment 11 Problem 2
                                 Assignment 11 Problem 4
                                 Note:  Ashton used formulas for the 
                                        complex arctangent and arccotangent 
                                        without really understanding these formulas.  
                                        This is only mentioned to suggest that 
                                        when/if you use a formula, you may want to 
                                        understand that formula.
M   17      Lecture 26: Nathan:  quantum mechanics
                        Sergey:   isolated singularities
W   19      Lecture 27: Yiting:  Attempted to derive a formula for the 
                                 complex arctangent involving the complex 
                                 logarithm.  The basic problem with this 
                                 presentation is that the proper domain 
                                 of the complex logarithm (and the corresponding 
                                 branches) were not taken into account.
                        Zihan:   Computed a complex integral (of (z+2)/2 over a 
                                 semicircle of radius 2 centered at zero in the 
                                 upper half plane.
                        Carter:  UC Davis practice final Problem 3.  
                                 Found radii of convergence for three complex 
                                 power series using the ratio and root test.  
                                 We could have used a more comprehensive 
                                 introduction to complex power series as well 
                                 as proofs of the specific tests used.
                        Tommy:   Assignment 12 Problem 9 
M   24      Lecture 28 (last lecture):  
W  May 3    Final Exam 11:20-2:10
Th May 4    Game Over