Course objectives/learning outcomes:
Successful students will:
-
Learn about the set of complex numbers, and gain fluency in elementary algebraic computations.
-
Master the geometric point of view on complex numbers, and understand the relationship to the algebra.
-
Understand a variety of complex-valued functions, and be able to compare them with their real-valued
analogues.
-
Master the basics of differential and integral calculus over C.
In addition, students will also:
- Thoroughly understand what definitions and theorems are. The student will be able to precisely state definitions and theorems and understand how they are applied.
- Practice writing proofs. It is expected that the student will have some, but not a lot, of experience writing proofs.
The student will gain more practice.
- Practice good mathematical writing. In mathematics, as indeed in everything else, it is important not only to be correct but to explain yourself clearly and as simply as possible.
Warning. You should expect 5-8 hours of homework a week in this class, which is more than most other instructors assign;
in my experience there is no other way to learn the material. Your consistent effort will certainly lead to improved understanding,
and it will almost certainly lead to you earning high grades.
Text:
Beck, Marchesi, Pixton, and Sabalka, A First Course in Complex Analysis. This book is available legally for free -- thank the authors for that!
Lectures:
MWF 1:10-2:00 in LeConte 348.
Microsoft Teams: I will use Microsoft Teams for announcements,
discussion, file sharing, and chat.
Please either check Teams daily, or have it forward new announcements to your email. You can ask me questions directly via teams. Although private questions are okay, please ask your question publicly if you are comfortable doing so -- maybe others will be interested in the answer as well!
Midterm Exams:
There will be two two-hour take-home, closed-book, pledged midterms. After they are handed out you will have at least a 72-hour period in which to finish them. Dates will be announced later in the term.
Final Exam: Monday, May 1, 12:30-3:00 in the usual classroom.
Homework:
Warning. I assign a lot of homework.
The homework is intended to take 5-8 hours a week. That is a lot. Please
count on making a consistent effort to do well in this class! Starting the night before is a bad idea.
If homework takes you more than 10 hours on any given week, then that is more than I intended;
please let me know.
Grading:
Please note. You will be graded both on correctness and on quality of exposition. Indeed, a major
focus of Math 552 is the ability to communicate mathematical ideas clearly.
The standard is that someone who doesn't know the answer should be able to easily follow your work.
In particular, please write in complete English sentences and draw clear diagrams where appropriate.
Any work that is confusing, ambiguous, or poorly explained will not receive full credit.
Grading scale: You are guaranteed at least the following: A = 88+, B+ = 83+, B = 75+, C+ = 70+, C = 60+, D = 50+.
This is more generous than the usual 10-point scale, and is intended to balance out the presence of some more difficult questions and/or (slightly) strict grading.
| Grade component |
% of grade |
| Homework: |
30% |
| Two take-home midterm exams: |
20% x 2 |
| Final exam: |
30% |
Contacting me:
Please contact me if you have any questions about the course, about my expectations, about my lectures,
about the homeworks, about the reading, or about anything else. The syllabus is demanding and it is my
job to help you succeed.
The best ways to get help are to come to office hours (no appointment necessary), to e-mail me (I will
usually reply within 24 hours if during the workweek), or to contact me on Teams.
If none of these work for you then please e-mail me to set up an
appointment.
Make-up policy :
In case of illness or emergency, please let me know immediately; alternative arrangements will be made.
Beyond this, late homework will be accepted once per student, up to one week late, with no excuse needed.
Academic honesty and attendance are expected of all students.
Calculators will not be needed or allowed.
Accommodations:
If you require special accommodations, please talk to the
Student Disability
Resource Center as soon as possible. If is your responsibility to advise me of any needed accomodations
a week in advance.
Important. If you have difficulty seeing the board or hearing the lectures, or
a related problem, let me know ASAP, and I will do something
about it. It is very
important to me that everyone has the opportunity to succeed.
It is my goal to create a welcoming classroom environment, free of racism, sexism, homo- or transphobia, discrimination, bullying, insults, or harassment. Please bring any concerns to me; major or repeated violations will be reported to the Office of Student Conduct.