Fall 2003 Meeting: November 21-22, 2003

3:30-3:45 Euler Goes Beyond Isosceles
               Ed Sandifer, Western Connecticut State University

We all know what happens if a triangle has two equal angles, say A and B. Such triangles are isosceles, and there is a simple relation on their sides, a = b. But what if one angle is an integer multiple of another angle, say B = 2A, or B = 3 A?

3:45 – 4:00 Mathematical Models and Art in the Early 20th Century
                  Angela Vierling, Boston University

For thousands of years, artists, as well as mathematicians, have been interested in solid geometric forms. The drawing and painting of polyhedral models can be simply a teaching tool, but, for others, these forms have represented perfection and truth itself. In the nineteenth century, mathematicians began to produce less regular and more startling solid figures. The strange beauty of these forms had an effect on many artists, particularly those associated with the constructivist and surrealist movements.

4:00 – 4:15 A Mathematician at a K-8 School
                 Debbie Borkovitz, Wheelock College

Last year I spent a portion of my sabbatical at the Young Achievers Science and Math School in Boston, where I worked primarily with Wheelock College graduate students, but also with children, teachers, and administrators at the school.  In the talk, I will share some of the children’s work, some anecdotes about working with the new teachers, and a few thoughts on how the school experience affected my work in preparing future elementary teachers in mathematics.

4:15 – 4:30 Group Quizzes using the Think-Share-Write Method
                  Hema Gopalakrishnan, Sacred Heart University

Group Quizzes using the Think-Share-Write strategy can be effective in engaging students and enhancing their learning in the classroom. In this talk, I describe my experiences with implementing this method in lower division and upper division mathematics courses. 

3:30 – 3:45 The Formulation of Vector Analysis Valid in All Coordinate Systems
                   Domina Eberle Spencer and Terri L. Mascardo, University of Connecticut

The paper presents a formulation of vector analysis valid in all coordinate systems. The pedagogical value of this formulation is easily seen when compared to the established formulation, which is valid only in rectangular coordinates and is being taught in elementary calculus classes. Historical development is traced back to Hamilton, Grassmann, Heaviside and Gibbs and the implications of their efforts when considering extending vector analysis to curvilinear coordinates and non-uniform fields. Proper definitions are given for the unit vectors, the gradient and the divergence and curl.

3:45 – 4:00 Using a Partial Singular Value Decomposition to Approximate a Large Sparse Rectangular Matrix
                  James Baglama, University of Rhode Island

4:00 – 4:15 An Application of Logic to Combinatorics
                    Rehana Patel, St. John’s University

Roughly speaking, first order logic is a language with which we can talk about properties of mathematical structures. A class of structures (eg. graphs, partial orders) is said to have a 'first order 0-1 law' if almost all its members look the same, when described in the language of first order logic. It is known that the class of all graphs has a first order 0-1 law. For any configuration H, for instance a triangle, or a pentagon, we say that a graph G is 'H-free' if the configuration H doesn't appear anywhere inside G. I will give a simple condition on a configuration H, which ensures that the class of H-free graphs has a first order 0-1 law. Many new examples arise from this condition.

4:15 – 4:30 Further Remarks on Systems of Interlocking Exact Sequences
          Joanna Su, Providence College

This is a joint paper with Professor Peter Hilton. It is a sequel and further discusses the paper "On Systems of Interlocking Exact Sequences" written by Hilton in 1967.