Professor:

Stephen B. Robinson

Calloway, room 305,

X4887

Email: robinson@mthcsc.wfu.edu

Homepage: http://web.mthcsc.wfu.edu/~robinson/

Office Hours:

One of the most pleasant parts of my job is working with students one-on-one outside of class. I know that it helps me improve my teaching, and I believe that it helps the students as well. Please feel free to drop by for help during my office hours, which are listed on my Daily Schedule. You do not need to make an appointment. I am also happy to talk to you at other times, but it is a good idea to call ahead or check with me in class to see if I am available.

 Schedule Of Daily Activities For The Class:

Texts:

Does God Play Dice?, by Ian Stewart

How To Solve It, by G. Polya

Overview: (This is an excerpt from the proposal that I submitted to the FYS committee.)

There are two interconnected goals that this course is built upon. The first is to introduce students to a mathematical point of view, as well as some specific methods, for describing and understanding the natural world. The second is to introduce students to the frustrating and exhilarating process of mathematical discovery.

The specific mathematics that will be covered is one and two-dimensional discrete dynamical systems. Little mathematical preparation is necessary in order for a student to begin learning the elementary facts of this subject. An understanding of high school level algebra, geometry and trigonometry will provide more than enough background. Also, it is quite easy, either by hand or with the aid of a computer, to develop intuition via simple numerical experiments. Still, this topic is deep enough to provide accurate models for many natural phenomena, some of which have only recently been understood. Furthermore, discrete dynamical systems are perhaps the best known tool for exploring the new and developing field of Chaos, a fascinating subject that includes many provocative questions and challenges certain traditional scientific beliefs.

Class time will be spent creating and analyzing mathematical models describing real problems in biology and related areas. More specifically, the students will begin a cycle of discovery by analyzing a specific example with several classmates. Each group will present a summary of their findings for the class. Then the class as a whole will discuss the similarities and differences in their examples and try to abstract the important ideas and methods. At this point the students must write a short report on what they have learned so far. This first stage lasts one or two weeks. The second stage provides the students with some time to reflect on their work, discuss similar problems, read and criticize their classmate’s work, and write a more polished version of their report. This approximate three-week cycle will produce a chapter for the User’s Guide to Mathematical Modeling, which is the centerpiece of the students’ work in this class.

Time will be spent discussing the books Does God Play Dice?, by Ian Stewart, and How To Solve It, by G. Polya. The first gives a fascinating history of the people involved in the discovery and the development of a new and exciting field of mathematics. It also provides a sound description of the mathematical and scientific problems that led to this new field. The second provides some insight into the use of inductive reasoning as well as some very practical suggestions for problem solving. Hopefully, the students will see that even the greatest minds must struggle, experiment, and make guesses (often incorrect) before any glimmer of understanding appears. Finally, the students should discover that mathematics is an important and exciting field of study where there is still plenty of room for future contributions.

Each student is expected to write two short research papers that will be presented to the class. I will encourage less technical topics, such as the role of mathematics in a liberal arts education, as well as more specifically mathematical investigations, such as reading and understanding an article on the role of chaos theory in biology or economics.

Technology will be helpful in our pursuits, but will not be central. We will use Excel to help test and understand mathematical models before explaining them more rigorously. We may also use some free software from the University of Arizona to help draw phase diagrams.

Evaluation:

If you consistently demonstrate an ability to solve standard problems and provide standard interpretations, then you have a good chance of earning a C or better. If you can solve more difficult problems, interpret their solutions, and justify your methods, then you have a good chance of earning a B or better. If you become adept at solving standard and nonstandard problems, if you can provide in-depth interpretations of your solutions, and if you can clearly justify all of the methods that you use, then you have a good chance of earning an A. Hard work is a prerequisite for earning a good grade (A, B, or C), but no amount of work will guarantee you a particular grade. Just do the best that you can, and then be proud of the grade you have earned. If you are ever unsure about a grading policy, or if you are not sure where you stand, then you are welcome to ask. Here are some numbers to help you judge the relative value of your assignments.

A User’s Guide To Mathematical Modeling : 50%

Individual Papers: 20% each

Participation: 10%