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 gather.town (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
arithmetic and geometry of complex numbers
complex differentiation
contour integration and Cauchy’s integral formula
residue theorem and its application
complex power series
conformal mapping
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:
Homework: assigned weekly, typically on Monday and due the following Monday. These will be posted in the Google Drive folder. Worth 30% of your final grade. You’re welcome and in fact encouraged to discuss homework problems with your classmates, but you need to write up solutions (neatly and thoroughly) yourself & in your own words. Copying is not allowed.
Midterm Exams: in class on Friday March 12 and Friday April 30, each worth 20% of your final grade.
Final Exam: Tues May 18, from 4:15-6:15, comprehensive and worth 30% of your final grade.
Further Policies, Disclaimers and Fine Print
Unsolicited advice: please be very brave about asking questions. The big majority of people (including many mathematicians) worry that they’ll seem stupid when they ask about something in a math lecture. Please ignore this worry--even if the reason you’re asking is that your attention drifted for a bit and you missed a point. Most often questions reassure the lecturer that the class is paying attention, and half your classmates are confused about the same thing you are.
Honor Code: abide by it. If you’re wondering whether or not something you’re thinking of doing in connection with this class is acceptable you should ask me about it.
Late homework, missed exams: I do not accept homework late, though I might consider discounting late assignments if the situation merits it. If, for some suitably dire reason, you need to miss an exam, you should clear it with me in advance if possible and be prepared to document the reason for missing.
Using the internet as a resource: this is generally fine with the exception that you are not allowed to seek or discuss solutions to particular homework problems on the web.
Attendance: I don’t formally take attendance, but I do notice engagement and absence over time and will feel free to take that into account when assigning final grades.