# Foundations of Mathematics

#### W. S. (Bill) Mahavier, Spring 2008, Emory University

### Introduction

W.S. "Bill" Mahavier, circa 1972

This page was created by W. Ted Mahavier. Its purpose is to demonstrate the Moore Method as implemented by W. S. Mahavier during the Spring of 2008, the last full semester he taught at Emory University. Mahavier was teaching topology the following Fall when he had a medical set back that reduced his ability to process oxygen and forced his retirement. In these videos, you will note that he is handicapped somewhat by two factors. He often asks students to repeat themselves (sometimes this is pedagogically motivated, but most times it is due to severe hearing loss) and he stays in a chair on wheels and moves about the front of the room because standing and talking requires more oxygen than he can process without equipment.

According to the Emory University Mathematics Department website, the course titled Foundations of Mathematics
“provides the bridge from calculus to more abstract mathematics courses. It is a small
seminar
*Seminar Explaination*In an effort to improve instruction, Emory University developed a policy in the
early 2000’s whereby each department was required to implement at least one seminar style course.
Foundations is one such course as indicated by its number, Math 250S.
intended to develop the
student’s ability to work with fundamental logical and mathematical concepts. Emphasis will be placed on the careful and
precise expression of ideas. The students and the instructor will construct proofs of theorems and present them in class.”
As described, such a course is perhaps the optimal setting for the Moore Method, since the goal of the class is the
development of mathematical maturity and because the class consists of a relatively homogenous, small number of
well-prepared students. Still, as the early clips demonstrate, few of these first-rate students began the course prepared
to write or speak mathematics correctly.

This chronological video diary of the course consists of video clips where some aspect of the method is demonstrated. One might ask how we decided what to include and what not to. We have only omitted excerpts where:

1. the filming or audio was not clear,2. the discussion was excessively lengthy,

3. the student dropped or missed more than twenty-five percent of the classes,

4. the presentation was perfect and the presenter had already shown many perfect proofs,

5. the discussion was dependent on previous classes so that following the thread of the problem was challenging,

6.the board work was illegible and insufficient oral statements were made to follow the problem, and

7. the class was experiencing dead time (passing out of papers, waiting for students to hand in papers, discussing of who had what problems ready to present, etc.).

Each video is interspersed with a small amount of text to offer our impression of what might be gained by watching the
clip. While studying this page in its entirety should provide an understanding of the culture in the classroom and the
pedagogical tools and strategies that Mahavier used in the classroom, we recognize that some may not need or wish to view
the entire page. The Viewing Suggestions indicate how one might review portions of the page
to optimize the time/learning ratio.