# matthias beck

professor of mathematics
san francisco state university
 MATH 380: Introduction to Complex Analysis Spring 2023

 Lecture Mon/Wed/Fri 1:00-1:50 p.m. TH 210 Prerequisites MATH 228 & 301 with grades of C or better or consent of the instructor Instructor Dr. Matthias Beck Office Thornton Hall 933 Office hours Mondays 4-5, Wednesdays 11-12, Fridays 10-11 & by appointment

Course objectives. Our goal is to study the calculus of functions in one complex variable. That is, we will look at concepts of real-variable functions and see which of these concepts and their accompanying theorems can be transferred into the complex realm, which have to be modified, and which don't exist in the world of complex numbers. We will see that there are concepts and theorems in all of these three categories.

Syllabus. Topics in this course will include:

• complex numbers and functions
• differentiation
• integration
• Cauchy's theorem and its consequences
• power and Laurent series
• residues

Textbook. M. Beck, G. Marchesi, D. Pixton, and L. Sabalka, A First Course in Complex Analysis, version 1.54 (2018).

Homework. I will assign homework problems as we go through the material. You may (and should) work together with your class mates. We can discuss the homework problems at any time during class, and you can hand any of your solutions for feedback. We will have a homework quiz every Monday at the beginning of class, in which you will be asked one definition and one problem given in the previous week.

Sage. You will be expected to use the open math software sage in some of your homework assignments. Here is a good introduction to sage.

 Homework quizzes 60% Midterm Exam (March 29, in class) 20% Final Exam (May 22, 12:30 p.m.) 20%

I want to ensure that each of you accomplishes the goals of this course as comfortably and successfully as possible. At any time you feel overwhelmed or lost, please come and talk with me.

The math. The way to learn math is through doing math. It is vital and expected that you attend every class meeting. You will get a good feel for the math from there, but it is even more crucial that you do the homework. Working in groups is not only allowed but strongly recommended. Our class is based on Federico Ardila's Axioms:

1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering mathematical experiences.
3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.

This syllabus is subject to change. All assignments, as well as other announcements on tests, policies, etc., are given in class. If you miss a class, it is your responsibility to find out what's going on. I will try to keep this course web page as updated as possible, however, the most recent information will always be given in class. Always ask lots of questions in class; my courses are interactive. You are always encouraged to see me in my office.

department of mathematics
san francisco state university
1600 holloway ave
san francisco, ca 94132

 becksfsu @ gmail.com