Circling the Desks: A Weekly Discussion in a Liberal Arts Mathematics

Course

Josh Laison, Colorado College

ABSTRACT: During the spring of 2002, the presenter taught a new course at Kenyon College entitled ``Topics in Contemporary Mathematics'' to 23 non-mathematics majors. One of the goals of this course was to introduce students to the culture of mathematics. To accomplish this goal, weekly readings were assigned from two mathematics books written for a popular audience. Students wrote one-page papers on philosophical questions based on the readings. On the days these papers were due, the class was spent discussing students' responses. In this talk, we will describe some advantages these weekly discussions had, both in making this course more attractive to non-mathematics majors, and in providing them with a more fulfilling intellectual experience.

This course was a new course in the department, designed for non-mathematics majors. In part, this course was a response to the anticipated increase of non-majors in mathematics courses, following a new college quantitative reasoning requirement. It had no prerequisites and itself was not a prerequisite for any other course.

The main goal of this course was to give the students an opportunity to see mathematics as a beautiful subject in its own right, and not merely as a tool used for other sciences. Topics were chosen for their interest and beauty alone. Topics included Fibonacci numbers, prime numbers, the RSA encryption algorithm, the Pythagorean Theorem, the Art Gallery Theorem, tilings of the plane, the Platonic solids, topological equivalence, graph theory, geodesics on surfaces, and knot theory. The text for the course was "The Heart of Mathematics," by Edward Burger and Michael Starbird.

A second goal of this course was to give the students an idea of the culture of mathematics. To accomplish this goal, two books were assigned other than the main text. These were "Fermat's Enigma," by Simon Singh, and "The Man Who Loved Only Numbers," by Paul Hoffman. Readings were assigned once a week. Students wrote weekly one-page papers on topics based loosely on the reading, meant to provoke thought and discussion about philosophical ideas surrounding mathematics. Roughly once a week, or 11 times during the 14-week course, the class was a discussion class. We spent the hour discussing the topics that students had written about in their papers.

The students in this course learned that mathematics is not a static and dry field. They formulated strong opinions about, for example, what makes a mathematical proof, the role collaboration should play in mathematics, and the beauty of a mathematical idea. In this way, they became emotionally invested in the mathematics, and felt a sense of ownership over the conclusions the class reached, in these discussions and in other class meetings. These discussions afforded a rare and valuable opportunity for the students and I to exchange philosophical ideas and opinions about mathematics. At the end of the course, the students had a much better understanding of what mathematics is as a field, and how it is changing. I believe the students' attitudes towards mathematics changed drastically, and positively, over the semester.