Math 101 Term Projects

Math 101 - Fractals and Chaos
Dr. Monks

As noted on the syllabus, one fourth of your grade in the course is determined by a term project.  This page gives the specific requirements for the term project.

1. Each term project must include a typewritten report.  The length of the report should be at least five pages. Collaborations are allowed and increase the length of the report by three pages per additional person in the group, e.g. 5 pages for one person, 8 pages for two people, 11 pages for three people, etc.
2. The report should include references to at least one mathematics book or article besides our required textbook, Chaos Under Control. The recommended textbooks are fine for this purpose (see the syllabus for a list of recommended textbooks).
3. The report should contain a section which briefly explains any mathematical concepts which are used in the project, even ones which we covered in the course.
4. The project should not just be a "book report" on something that is said in another text or article but must include a creative or investigative component that is the result of your own thoughts and efforts.   I intend for you to have a lot of freedom in this regard and the purpose is for you to choose a topic that interests you. Thus for example,

• If you are curious about some topic we discussed in class you might explore that topic further... "What happens if I alter a fractal construction method slightly?"... "How can we use fractal methods to determine the coloring of fractals and what would the results look like?"... "How can I produce a fractal that looks like (some object)?" etc.  In these cases you would most likely have some fractals which you produced by computer to test your theories or explore your questions as a result of the project.  You do not have to write your own software to do this, but rather can use existing programs we have used in the course in order to produce your results.
• You can create an artistic project if you wish. For example, you can paint or carve a painting or statue based upon principles of fractal geometry. In this case your report would describe the mathematical principles you used, how you implemented them in your project.  If you are interested in music you can produce a musical composition based on fractal principles and again the report would describe the mathematics behind your creation.
• You can perform an analysis of literature or stock market data or natural phenomena like rivers or forests that you have data for, using principles from fractal geometry.  Examples might be to compute and compare the fractal dimension of some natural objects you are interested in, or test some important sequences of numbers or letters for randomness via the chaos game. You might analyze the distribution of words or sounds in a poem or other literary work for self similar patterns.
• If you are very good with computers and want to write some software to implement some topic related to fractal geometry, that is fine as long as you explain the mathematics behind the program and use the program to explore some topic in your own creative and investigative manner (i.e. not just another plain Mandelbrot set generating program).
• The course's recommended reading books are excellent sources of topics which we will not have time to cover in this course.  If you get one of those books and look through it, you are bound to find some topic that you are interested in learning about and reporting on.  The topics are far too numerous to list here.
• Other topics of your own choosing are also acceptable as long as they relate directly to the mathematical principles of fractal geometry and chaos theory.  I encourage you to be creative, but all topics should be approved by me before working on them.

Due Dates:

• The final project is due on Thursday, December 6, 2001 at 4:10pm in class. Any component of the project which cannot be conveniently brought to class should be brought to my attention BEFORE that time so we can work out the logistics of handing them in. (If you carved a 300 ft tall granite Sierpinski Tetrahedron, it wouldn't be easy to bring to class, for example.) Any project handed in after that time will not be accepted and will be given a zero grade for the term project.

If you have any questions, feel free to ask me via email or after class.

Here is a list of projects done in this course by students in the past:

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This page was last  updated on Monday, December 10, 2001 09:40:44 PM. © Ken Monks