Syllabus for Chaos and Fractals

Professor: Mark McClure

Course purpose

As a math elective, Chaos and Fractals is not central to your mathematics curriculum. However, it connects several key areas of mathematics an applies them together to generate some of the most mesmerizing images of mathematics. In this class we will:

• Develop our understanding of several important areas of mathematics, including:
  • Real analysis
  • Numerical methods
  • Linear algebra
  • Geometry
  • Complex variables
• Learn some very cool, new contemporary mathematics.
• Explore these topics theoretically and computationally.

Materials

• Text: You are not required to purchase a particular text for this class, as I will be preparing some notes as we move along. One text that will motivate us is:
  • A First Course in Chaotic Dynamical Systems by Bob Devaney
• Technology:
• Calculators: We won't be using calculators and they will not be permitted on quizzes or exams.
• Chaotic Talk: I'll be setting up a super fun online discussion forum for us. More on that later.
• A computing environment: A beginning understanding of Chaos and Fractals 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 3.6 version.
  To be clear, you should get both of these. I'll use both in class and you should be able to follow the basic code that we see.

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 in class portions are:
  • Wednesday, October 4 and
  • Wednesday, November 15
  The exams will also have take home portions due the day after the in class portion.
• Quizzes: There will be two quizzes, each two weeks before an exam:
  • Wednesday, September 20 and
  • Wednesday, November 1
• Chaotic Talk: Chaotic Talk is an online discussion forum that we will use to facilitate discussion in this class. Participation is mandatory and will result in actual points. Chaotic Talk has built in trust levels and you earn 10 points per trust level. You can move from level one to level four for a thirty points. There will also be several mandatory questions
• 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.
  • Chaotic Talk: 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.