MA0110 - Mathematical Explorations - Fall 1995

Course Syllabus

Course Content: As stated in the course description, this course is designed to give the liberal arts major an appreciation of mathematical reasoning and content. The topics we shall study are mathematical ways of thinking, symmetry and regular figures, topics in topology, and number sequences. These are chapters 1, 5, 10, and 2 respectively in the text. (Note: Ch. 2 might be replaced by a unit on dimension theory and fractals from outside of the text.)

Class Structure: As noted in the course title this course is an exploration of mathematics. Mathematics can only be learned through active exploration. Most of class time will be spent on exploration in small groups. The text will map out the course of this exploration. I will play a limited role, serving mostly as a guide in this exploration.
Each section of each chapter we shall cover will be treated in the following way. You are to read and be prepared to answer questions on the reading in the section. (Which is generally only 2 or 3 pages.) We will discuss the readings in class. In groups you will then complete the questions that make up Set I and Set II. As we progress through the problems, I will call on people to explain the questions to insure that we are all proceeding in a positive direction. Any problems with the questions should first be addressed within the groups. At the beginning of each class there will be an opportunity for groups to ask about problems with the questions. In about half of the chapters you will complete Set III for homework.

Assignments and Grading: At the end of every chapter you are to turn in complete answer sets for the problems in Set I, Set II, as well as the Set III's that have been assigned. Your work in groups on these problems should only be treated as rough drafts. Your final submissions must be final drafts that completely and coherently express your solutions to the questions. In particular, your work should be neatly presented and well labeled. Your work will be graded on completeness, mathematical correctness, clarity of presentation and effort. Your final submitted work must be your own. Assignments I feel have been copied will be given failing grades. Your grades on these assignments will make up the majority of your final course grade.
As noted above, each class I will ask questions about the readings and the questions from Sets I and II. People who do not routinely volunteer to answer these questions will be called on by name. Your responses to these questions will partially determine a class participation grade. Hence, your attendance, preparation, and timely completion of assignments will substantially effect your grade.
Lastly, you are expected to keep a journal of your mathematical exploration. You should write in your journal at least once a week, detailing specific thoughts about the material, interactions within your group, the structure of the course, applicability of the mathematics we treat, and any other relevant details of your learning experience in this class or regarding mathematical topics in general. Your journals will periodically be collected and graded. At the end of the course you will write a reflective essay on a specific topic related to your journal entries.

Final remark: Subsequent handouts will explain the issues treated here in finer detail. If you have any questions, now or in the future, please ask.