General Information
Time 
MWF, 2:303:20 p.m. 
Location  Vincent Hall, Room 206 
Professor 
Ben Brubaker (brubaker@math.umn.edu)
Office: Vincent Hall, Room 233
Office Phone: 56380
Office Hours: W 12, Th 12:301:30, and always available by appointment 
Textbook  Lars Ahlfors, Complex Analysis (3rd. Ed., McGrawHill) 
Course Assignments  Weekly problem sets (35% of total grade), a midterm (20%), an integration quiz (10%) and a final exam (35%). 
Syllabus Syllabus II Syllabus III  (linked at left as PDF files) The first syllabus is an outline of the course through the first midterm on Wednesday, October 16. The second is through the integration quiz on Monday, November 18. 
TakeHome Final Exam
Midterm I
Here is the review sheet of problems for the first midterm, one of which will appear on the test itself.
There will be one question on the midterm asking you to state and prove one of the following results:
 Differentiability is equivalent to the CauchyRiemann equations (p. 26)
 Open sets are connected iff joined by a rectilinear path (p. 56)
 Cauchy's theorem for rectangles (p. 109)
 Cauchy's theorem for disks (p. 113)
 Liouville's theorem (p. 122)
All section and problem numbers in the following assignments refer to Ahlfors' book.
 Problem Set 1 (Due Friday, Sept. 13):
 Find the fifth roots of 3 + 3i.
 Section 1.1.4 (p. 9): 3, 4
 Section 1.1.5 (p. 11): 1, 4
 Section 1.2.2 (p. 16): 5
 Section 1.2.3 (p. 17): 1, 2
 Section 1.2.4 (p. 20): 1, 2
 Problem Set 2 (Due Friday, Sept. 20):
 Section 2.1.2 (p. 28): 2, 4, 7
 Section 2.1.4 (p. 32): 2, 3, 6
 Section 2.2.3 (p. 37): 3, 5
 Section 2.2.4 (p. 41): 2, 4, 6, 8
 Problem Set 3 (Due Friday, Sept. 27):
 Section 2.3.2 (p. 44): 1
 Section 2.3.4 (p. 47): 5, 6, 10
 Section 3.1.2 (p. 53): 1, 7
 Section 3.1.3 (p. 58): 3, 4
 Section 3.1.4 (p. 63): 3, 4
 Section 3.1.5 (p. 66): 1, 3
 Section 3.2.2 (p. 66): 1, 2
 Problem Set 4 (Due Friday, Oct. 4):
 Section 4.1.3 (p. 108): 1, 2, 3, 4, 6
 Section 4.2.2 (p. 120): 1, 3
 Problem Set 5 (Due Friday, Oct. 11):
 Section 4.2.3 (p. 123): 1, 2, 3, 5
 Section 4.3.2 (p. 130): 1, 2, 3, 4 (DUE: Nov. 8)
 Problem Set 6 (Due Friday, Oct. 25):
 Section 4.3.3 (p. 133): 1, 2
 Section 4.3.4 (p. 136): 1, 2
 Problem Set 8 (Due Friday, Nov. 8):
 Section 4.3.2 (p. 130): 1, 2, 3, 4
 As a linked pdf
 Problem Set 9 (Due Friday, Nov. 15):
 Section 4.5.2 (p. 154): 1, 2 (assigned previously)
 Section 4.5.3 (p. 161): 1 (b,e,f only), 3 (c,d,e,g,h)
 Problem Set 10 (Now Due Monday, Dec. 9):
 One extra problem as a linked pdf
 Section 5.1.2 (p. 184): 3
 Section 5.1.3 (p. 186): 4
 Section 5.2.1 (P. 190): 1, 5
 Problem Set 10, PART II (Also Now Due Monday, Dec. 9):
 Section 5.2.2 (p. 193): 1
 Section 5.2.3 (p. 197): 1, 3
 Section 5.2.4 (p. 200): 1, 2
