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 I've been working on one of my own. You can view it online or download a PDF of your own:
- Technology:
- Calculators: We won't be using calculators and they will not be permitted on quizzes or exams.
- A web browser: Our class web page really is a central portal of information for us. Most of our class periods will follow some portion of the online version of our text, a javascript demo, or some code posted online. This is the place to keep up with the goings on in the class.
- Math & Stat HW Discuss: This is an online forum where folks at UNCA can talk about Mathematics and Statistics. There is also a special category reserved just for us and there will be several assignments that you complete through the forum. You can access:
- A computing environment:
A beginning understanding of complex dynamics can benefit greatly
from a little computational experimentation. Here are a couple of
possibilities.
-
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 Anaconda's download page. Be sure to grab the Python 3.7 version.
We will use Anaconda mainly to implement simple, straightforward algorithms to generate images. -
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 no cost from the Wolfram user portal. If you don't have account, simply create one using your UNCA email address.
There's nothing in the open source world that approaches Mathematica's ability to solve equations and systems of equations over the complex numbers. Thus, we'll often use Mathematica when trying to find dynamical systems with specified properties.
-
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 Anaconda's download page. Be sure to grab the Python 3.7 version.
Evaluation
The standard 90-80-70-60 scale will guarantee you an A, B, C, or D. However, it is quite possible that the final scale will be shifted down from this. You will be apprised of your standing as the term progresses.
- Quizzes and Exams: There will be two quizzes worth around 40 points each and two exams worth about 100 points apiece. Likely dates for these are:
- Quiz 1: Friday, February 1
- Exam 1: Friday, February 22
- Quiz 2: Friday, March 29
- Exam 2: Friday, April 19
- Final Exam: There is a final exam scheduled for 8:00 AM on Monday, May 6.
- The forum: Math&Stat HW Discuss is an online discussion forum that we will use to facilitate communication in this class. Participation is mandatory as several assignments will essentially involve forum posts.
- Homework: While there will frequenlty be homework assigned, it will only rarely be collected. There will be two or three assignments that I'll post in detail on our webpage that you will type up and turn in.
- 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.
- Our Math&Stat HW Discuss forum: A kinda combination of the previous two that never sleeps!
Your rights and responsibilities
It's worth understanding your rights and responsibilities as a student at UNCA. One of my responsibilities is to make sure you have the information that you need to do that. Since this is common to all classes, I've got that information on this legalese document.