Math 40480: Complex Variables

Spring `21

Weekly schedule

Instructor: Jeffrey Diller (click for contact info, etc.)

Time and place: MW 3:30-4:45 PM (Note change as of 2/8), Bond Hall 104

Office Hours:  F 3:30-??. I will hold these in our Bond 104 classroom and open up the Zoom mtg (no recording) for the class at the same time. So you can ask questions in person or virtually.

Math Bunker: Sun-Thurs 7-9 in Hayes-Healy basement (recently former math library) or virtually via (url and pwd available in the contact file in Google Drive). The math bunker provides peer-help for proof-based math courses and is staffed by upper class math majors with a lot of experience with these. It’s perhaps less useful for this particular class, but if nothing else, you can go work on your homework in good & sympathetic company.

Textbook: Complex Variables with Applications (9th edition) by James Ward Brown and Ruel V. Churchill.

Why this course: complex numbers were originally introduced as a sort of fantasy construct that would a allow one to pretend that negative numbers have square roots. Fantastic or not, people rapidly came to appreciate the convenience of complex numbers throughout math and its applications. Eventually, mathematicians realized that complex numbers are just as real as real numbers and that things as diverse as prime numbers and quantum mechanics are nearly impossible to understand without them. In this course, our main aim is to understand complex numbers from various points of view: algebra, geometry and calculus, digressing occasionally to see how they are useful for solving problems outside the subject.

What we'll cover: in brief, as much of chapters 1-10 of the textbook as time allows. Topically speaking, this amounts to

Note of thanks: many past incarnations of this course were taught by recently emeritized Professor Dennis Snow, and he has kindly given me access to all the material he developed for it over the years. I will make shameless and copious use of it all. My general strategy is to follow his excellent model closely, tarnishing his legacy as little as possible in the process. In any case, I’m very grateful for his help.

How you will be evaluated:

Further Policies, Disclaimers and Fine Print