In this course we will cover Complex Analysis, which is the study of functions of a complex variable. It is a beautiful and elegant theory that unifies and reinforces various themes you have seen in the past, from both Algebra and Analysis.
We will start with an algebraic study of the complex numbers as an extension of the real numbers. We will then proceed to consider the geometry of the complex plane, then move on to functions and complex differentiability. We round up the course with a discussion of integrals in the complex plane and some truly remarkable results that follow.
In addition to the content, this course is also meant to solidify your ability to communicate in the language of mathematics, both verbally and in writing. You will learn how to use the LaTeX software to produce high quality mathematical output, and your assignments will be evaluated on more than just correctness. You will also present many of your solutions to class and comment on other students’ solutions.
On the website you will find a schedule with links to documents for each class day. In those documents you will find notes for the day’s lesson, a reading assignment, and a list of practice problems. You should work on those practice problems, and ask any questions you have about them. You do not have to turn the problems in.
15% of the final grade will be based on your class participation. This will include: asking questions in class, answering questions, presenting homework problems as well as commenting on those presentations.
There will be regular homework assignments about once per week. There will also be a list of problems that you are expected to solve but not turn in. Questions on the exams tend to be similar to the homework problems, so it is to your advantage to really understand the homework, and not merely “do it” or copy it just to get it turned in. Homework will be written using Overleaf, an online LaTeX editor, and will be evaluated for style, readability and correctness. Homework assignments are 15% of your final grade.
There will be two midterms, on Wednesday, February 17th and Friday, March 25th, and a final/3rd midterm during finals week. You have to be here for the exams. If you have conflicts with these days, let me know as soon as possible. Do not plan your vacation before you are aware of the finals schedule. In terms of your final grade, the exams you did better on will weigh more.
Your final grade depends on class attendance, homework, project, quizzes, midterms and the final, as follows:
| Component | Percent |
|---|---|
| Participation | 15% |
| Homework | 15% |
| Worst Midterm | 15% |
| Middle Midterm | 25% |
| Best Midterm | 30% |
This gives a number up to 100, which is then converted to a letter grade based roughly on the following correspondence:
| Letter grade | Percentage Range |
|---|---|
| A, A- | 90%-100% |
| B+, B, B- | 80%-90% |
| C+, C, C- | 70%-80% |
| D+, D, D- | 60%-70% |
| F | 0%-60% |