# Syllabus for Complex Dynamics

Professor: Mark McClure

## Course purpose

As a special topics course, this class is not central to your mathematics major. However, complex dynamics is an exciting area of current mathematical research that vividly illustrates applications of several topics of central importance in your curriculum. In this class we will:

- Develop our understanding of several important areas of
mathematics, including:
- Complex variables
- Real analysis
- Numerical methods

- Explore these topics theoretically and computationally
- See some very cool contemporary mathematics.

## Materials

- Text: The perfect text for a class at this level presents the theory using elementary complex variables and illustrates it concretely by having the student explore the topics on the computer. I don't think that book exists yet, so we'll make things up a bit as we go along. A couple of texts that will motivate us are But, I emphasize that you are not required to purchase a text for this class.
- Technology:
- Calculators: We won't be using calculators and they will not be permitted on quizzes or exams.
- Discourse: I'll be setting up a super fun online discussion forum for us. More on that later.
- A computing environment:
A beginning understanding of complex dynamics can benefit greatly
from a little computational experimentation. Here are a couple of
possibilities.
- Mathematica: Originally described as "A system for doing mathematics by computer", Mathematica has evolved into a huge program that integrates symbolic, numeric, and geometric capabilities very well. It is an expensive commercial program but UNCA students can download it for from the Wolfram user portal. If you don't have account, simply create one using your UNCA email address.
- Anaconda: Anaconda is a scientific Python distribution bundled with a huge number of useful, open source packages and tools. It is freely available and will remain so. You can download it from from Continuum Analytics download page. Be sure to grab the Python 3.5 version.

## Evaluation

The standard 90-80-70-60 scale will guarantee you an A, B, C, or D. However, it is quite likely that the final scale will be shifted down from this. You will be apprised of your standing as the term progresses.

- Exams: There will be two exams during
the semester worth about 100 points apiece. Likely dates for the exams are:
- Wednesday, March 8 and
- Wednesday, April 12

- Quizzes: There will be one quiz on Wednesday, February 8.
- Discourse: Discourse is an online discussion forum that we will use to facilitate discussion in this class. Participation is mandatory and will result in actual points. Discourse has three built in trust levels and you earn 15 points per trust level. There will also be several mandatory questions personalized just for you leading up to...
- Final project: There will be a final project due during finals week.
- Late work: In general, I don't accept late work.
- Cheating: I don't deal with cheating. If I suspect cheating strongly enough, I simply refer you to the provost and fail you for the class.

## Advice

- Learning Mathematics: I believe that mathematics is a wondrous but challenging field. I assume that most people in this class have interest in mathematics and appreciate its unique challenges. There will be times of frustration ahead. Buckle down and work hard.
- Help:
You are not in this endeavor alone. You have four major sources of help:
- Me: I like to talk to people about mathematics. That's why I chose this profession. My full schedule with office hours is shown below. You will almost always find me in my office during my office hours but please feel free to approach me any time you have questions.
- Your classmates: Most people learn mathematics best by talking through it with others. You will find that you can both learn from and help your fellow classmates. You should get to know one another very well.
- Discourse: A kinda combination of the previous two that never sleeps!