M 180, Fall Semester 1999

Patterns and Phenomena in Mathematics


Tuesday + Thursday, 9 - 10:40 AM, EE203
Instructor: Chris Peterson (with occasional guest lectures by Rick Miranda)
Office: 211EE (Engineering Building)
e-mail: peterson@math.colostate.edu
Phone: 491-6751
Office Hours: MWF: 10:00-11:00
Text: Excursions in Modern Mathematics (Third Edition)


Course Description:
This course is designated "Experimental". What this means is that the course is under development. Some of the major consequences of this are:

1) Student input and participation is vital to the success of the course.

2) There is a fair amount of flexibility in the course material.

3) The class size is limited, this allows more individualized attention.

4) There is no perfect textbook for the course.

The text that was chosen for the course is also used in another course. This means there should be a number of used copies floating around the campus. You are encouraged to buy a used text.

We are lucky to have a class size of 40 students, please take advantage of this and let me get to know you and your interests (both mathematically and otherwise).
The present plan for the course is to give a sampling of four broad areas of mathematics. Some of the mathematics that will be covered will relate directly to your interests but others may veer far away from what you have seen before. I will try to mix the abstract with the concrete and can adjust the mixture as the course progresses.
The four broad areas that will be covered are:

1) Symmetry: This section is covered somewhat in the text. There will be a fair amount of additional material relating to art, music, architecture, weaving, braids, knots, melody, sentence formation, etc.

2) Computation: This section is not covered well in the text. While it sounds very dry, bear with the material and you may be quite surprised. There is much more here than meets the eye. First of all we will try to answer the question ``what is a computation?" In trying to answer this question mathematically, one is lead to several rather philosophical issues. We will discuss Turing machines, the halting problem, complexity, coding theory, cryptography, recursion, iteration, growth, etc.

3) Fair division and apportionment: This section is covered well in the text and we will not stray too far from the material presented in Part 1 of the text. We will discuss the prisoner's dilemma, paradoxes of democracy, fair division, etc.

4) Some ``pure" mathematics: This section is not covered well in the text. The purpose is to give some examples of topics I find particularly interesting in areas of mathematics seldom covered in 100, 200 and 300 level math courses. We will discuss several problems from number theory, topology and geometry and find that these quite abstract areas have several concrete applications.

It is quite likely that too much material is listed in the above areas. It is also quite likely that the class will have some great suggestions for topics to discuss (or perhaps some of the topics above will want to be seen in more detail). In any case, I will be asking for a great deal of input from the class and from individuals. Again, class participation is vital and integral to the course. You may be surprised at how much mathematics you already know and how relevant it is to everything around you.
Please note that I put listed office hours. During these hours you are guaranteed to find me. Do not interpret these office hours as a restriction on when you can come and discuss mathematics. You are certainly welcome to come at other times but it may be wise to call first to make sure that I am in my office (or of course we can arrange for other times to meet). I look forward to getting to know you, please do not remain anonymous.