Department of Mathematics

MA0110 - Mathematical Explorations - Spring 1998

Course Synopsis

Course Overview: The goal of this course is to provide liberal arts students with an opportunity to develop a broader appreciation of mathematics by exploring ways in which the artistic, aesthetic, intellectual, and humanistic aspects of mathematics are as important as its utility. This exploration will be carried out in a supportive, student centered environment where cooperative learning and guided discovery are the underlying pedagogical vehicles and written work is the dominant vehicle for assessment.

Course Content: The topics we shall explore include mathematical reasoning and mathematical ways of thinking, topics in topology, the infinite, and dimension theory. The former topics are addressed in Chapters 1 and 10, respectively, of the text by Jacobs. The latter topics are addressed in supplemental "Chapters" 11 and 12, respectively, that have been written by Fleron. These chapters will be distributed to the class.

Class Structure: As noted in the course title, we will be exploring mathematics. Mathematics cannot be learned passively, and every attempt has been made to structure this course in a way that provides a supportive, active learning environment. The text and supplemental chapters have been designed to guide your discovery and exploration of mathematics in a variant of the Socratic teaching style. That is, these materials provide you with a series of leading questions that allow you to (re-)discover and explore specific mathematical topics for yourself. The majority of class time will be devoted to cooperative group work on the questions posed in these materials.

Assignments, Quizzes, and Journals: 80% of your grade in this course will be determined by your work on the questions posed in the materials we cover. This work will be assessed in two ways: through written solution sets and written quizzes.
For alternative lessons in each chapter (generally the 1st, 3rd, and 5th lessons) you will be required to submit a solution set which provides detailed, complete, coherent, mathematically correct, and well written solutions to each of the problems from that lesson. Your work in class in groups and individually at home on these problems should only serve as rough drafts for your final solution sets. The solution sets you hand in should be final drafts. My expectations in regard to your solution sets are detailed in "Format and Grading of Solution Sets" which will be distributed.
For the remaining lessons in each chapter (generally the 2nd, 4th, and 6th lessons) there will be an in class quiz that asks you to answer, by number only, several questions from the lesson under consideration. These quizzes will be open note but will be closed book. Therefore, it is imperative that your progress through these problems is complete and well documented in your notebooks.
You will be responsible for keeping a journal throughout this course which documents your progress, your thoughts about mathematics, and your thoughts about the learning experience in which you are involved.

Student Responsibilities: Each class day you must come prepared for class and must work faithfully during class. In part this means that your work must be up to date, excluding questions that you have specific difficulties with; you must bring your notebook; and you must have your text or the supplemental materials. Because you will generally be unable to complete all of the lessons during class time, you should expect to spend about one hour working on problems outside of class for every hour of class time. All of your work must be recorded in your notebook. Work not included directly in your notebook cannot be utilized for quizzes. Most days I will call on people by name to share their solutions to specific problems with the class. You must be prepared to provide not only mathematically correct solutions with justification, but to provide clear and concisely written solutions as well. Students who are not participating actively in class will be asked to leave so they are not detrimental to their groups progress. Finally, attendance is required. If you are absent for more than three classes during the semester, each class you miss beyond the limit of three will reduce your final course grade by one-third of a letter grade.

Grading: As noted above, absenteeism will adversely effect your grade in this course. Final grades will be based on the following:

Academic Honesty: 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 have been copied from another student or another source will result in failing grades for all students involved. Moreover, such dishonesty will be considered a violation of the college policy on academic honesty and will be dealt with severely.

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

This and other documents related to this course can be found via the World Wide Web at the URL