Department of Mathematics

MA0110 - Mathematical Explorations - Spring 1997

Course Synopsis

Course Overview: The goal of this course is to provide liberal students with an opportunity to develop a deeper appreciation of mathematics by exploring selected mathematical topics in a supportive, student centered environment where cooperative learning and guided discovery are the underlying pedagogical vehicles.

Course Content: The topics we shall explore include mathematical reasoning and mathematical ways of thinking, symmetry and regular figures, and topics in topology. These topics are addressed in Chapters 1, 5, and 10, respectively, of the text by Jacobs. One additional topic that we shall cover will be announced at some point during the semester.

Class Structure: As noted in the course title, we will be exploring mathematics - really the only way to develop a conceptual understanding of mathematics. Each lesson in each chapter opens with a brief introduction that I expect you to read outside of class before we begin the lesson. We will begin class by briefly discussing this reading. Afterwards you will work cooperatively in groups answering all of the questions that make up Set I and Set II of the lesson at hand. As you consider these questions, discussing any difficulties that arise with members of your groups, I will tour the room helping as I can. As we progress through the problems I will call on people to answer specific questions to insure that everyone is proceeding positively and the class is in agreement on proposed solutions. Outside of class you will be responsible for writing up detailed solutions to each of the problems. (See below for more details.)

Assignments: At the end of each chapter you are to turn in detailed solutions sets for all of the lessons we have covered. These solution sets must be detailed, complete, coherent, mathematically correct, and written with care. Your work in groups on the problems should only serve as rough drafts for your final solution sets. I strongly suggest that you work on final drafts as you proceed through the material. My expectations in regard to your solution sets are detailed in "Format and Grading of Problem Sets" which will be distributed.
While we will work cooperatively in groups during class, and while I invite people to work together outside of class, your final solutions sets must be made up of your own work which is written in your own words. Assignments that I feel have been copied from another student or another source will result in failing grades for all students involved and will be considered a violation of the college policy on academic honesty.
You will be responsible for keeping a journal throughout this course which documents your progress through this course, your thoughts about mathematics, and about your thoughts about the learning experience in which you are involved.

Grading: Grades will be based on the following:

Final Remarks: Every effort has been made for this course to be a positive, constructive learning experience. If there are any questions or difficulties, I would appreciate it if you would speak with me as soon as they arise.