Fall 2025
An introduction to the theory of analytic functions of one complex variable. The complex plane, analytic functions, Cauchy Integral Theorem and the calculus of residues. Taylor and Laurent series, analytic continuation. Possible additional topics: harmonic functions, Riemann mapping theorem, special functions, geometric function theory.
Lectures: Tuesdays and Thursdays 3:30 -- 4:50pm in Small Physics Lab 235
Office hours: Tuesdays and Thursdays 2 -- 3pm (also Mondays and Wednesdays 2 -- 3pm), or by appointment
Office: Jones Hall 101C
Textbook: Complex Analysis by Donald E. Marshall (bookstore link)
Other texts if interested: Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable by L. Ahlfors
Complex Variables and Applications by J. W. Brown and R. V. Churchill
Real and Complex Analysis by W. Rudin; and many more...
Syllabus: TBA
Grades: TBA
We will use Blackboard and Gradescope. All course information and materials will be posted both here and on Blackboard. Homework should be submitted via Gradescope. You should have already been enrolled in the course on Gradescope, if you log in via School Credentials.
Here are some instructional videos for submitting homework on Gradescope: Submit homework on the Gradescope mobile app,
Submit pdfs on the Gradescope website
Please remember to assign each page of your submission to the corresponding problem, otherwise I may not be able to easily find your solutions.
LaTeX is a software system for document preparation, widely used by mathematicians and many other scientists to type their work. You are encouraged to typeset your homework in LaTeX, and required to do so for two of them.
LaTeX resources:
Overleaf Intro to LaTeX, many youtube videos (e.g. here)
Many templates on Overleaf for homework, this blog post about the homework document class
Detexify: a tool to translate handwritten symbols to LaTeX codes
TeXShop (for MacOS), TeXstudio, and of course Overleaf (recommended -- easy to use, online)
Preliminary knowledge from (real) analysis: in our textbook, a list of prerequisites is included (see the last two pages of this pdf file). It is not necessary to be familiar with all of them, but make sure you have some understanding of #1-12 for real-valued functions (and it might be worthwhile to review MATH 311). It is particularly important to have at least practical (e.g. from calculus) knowledge of power series. We will go through these again for complex-valued functions.