Math 519: Complex Analysis
Time/place: MWF 9–9:50 a.m. in Engineering E205
Course website: www.math.colostate.edu/∼bates/courses/S12/519
Text: I will follow Stein & Shakarchi’s Complex Analysis, especially Chapters 1, 2, 3, 5, and 8, after
which I will hit various topics covered in this book, Ablowitz & Fokas, Conway, and/or elsewhere.
Instructor info: Prof. Dan Bates, bates@math.colostate.edu, Weber 221 (1-1037)
Office hours: None yet, but that can change if necessary.
Prerequisites: None. This is a basic (QE) graduate course. (This course is very calculus-related;
I assume you’ve had that.)
Topics to be covered: Complex analysis is a beautiful, classical subject which touches many areas of mathematics and is essential in a number of applications. As a qualifying exam (QE) course
for the math department, we have five general topics that must be covered carefully: functions,
Cauchy’s theorem(s), meromorphic functions, entire functions, and conformal mappings. Each of
these has several subcategories – see the topics to be covered at:
http://www.math.colostate.edu/programs/graduate/qexamsyllabi.shtml.
That will take about 80% of the time, after which we’ll hit various topics. I would like to hit “optional topics” 1 (asymptotic evaluation of integrals), 6 (Fourier transforms), 7 (gamma functions),
and 16 (Riemann zeta function) at least. If you have favorites, just let me know.
Structure of the class: This will be a fairly standard lecture class. I certainly welcome your
comments and ideas during lectures. Work-wise, you should expect a homework assignment of
10-15 problems due every other week, a midterm (date TBD), and a final exam. You are absolutely
welcome (and encouraged) to work on the homework together, though your homework MUST be
written up individually. Please refer to the student handbook for a definition of plagiarism and
the consequences of plagiarizing. (Just don’t do it!) As this is a QE course, there will be two final
exams: A qualifier (which will thoroughly test whether you have mastered the main five topics
above) and a gentler one (maybe take-home) for people not taking this course as a QE course. (I
will gladly be flexible on the amount of work done by graduate students who have finished their
suites! Undergrads should plan on doing all the homework, the midterm, and the easier final.)
Grading: The homework is worth 30% (each assignment will be equally weighted), and the midterm
and final are worth 30% and 40%, respectively. Do your homework and turn it in on time! I’ll just
use the standard scale (90–100 A, 80-89 B, etc. with +’s and -’s as appropriate) to assign final
letter grades. I don’t expect to curve anything. QE evaluations will be based on performance on
the final exam (only).
Feedback: I want it!
Final Note: You should know that I have insulin-dependent diabetes and may therefore need to
sit down and take it easy occasionally. There is also the very slight risk that I could have very low
blood sugar at some point, causing me to pass out. If that happens (the probability of this is very
low), I will need somebody to call 911. Please don’t worry: I haven’t passed out yet and don’t
intend to! Even if I do pass out, I am not in any significant danger.