\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2003a.00270}
\itemau{Reed, Beverly; Melton, Austin; Kasturiarachi, A. Bathi}
\itemti{Mathematics that changes lives.}
\itemso{Vakalis, Ignatios et al., 2nd international conference on the teaching of mathematics (at the undergraduate level). Wiley, New York, NY. 326 (2002).}
\itemab
We are developing a general education mathematics course that will introduce students to mathematical reasoning and applications. The one-semester course will cover the history of, motivation for, and an introduction to cryptography, fuzzy logic, graph theory, and non-Euclidean geometry. Three weeks (nine discussion-lecture hours) will be devoted to each topic and the remaining weeks will be used for intensive group work and project presentations and refinements. Classroom activities will build from the students' current knowledge to an understanding of the value and importance of each topic. Through discussion and exploration students will experience some of the insights, frustrations, and excitement experienced during the development of the four basic concepts. Group projects will enable students to work together in diverse groups applying mathematics with detailed exactness to particular problem situations, planning written descriptions of their projects, and then presenting them to the class. The cryptography unit will emphasize the classic cryptosystems and will focus on the mathematics that explains how and why the schemes actually work. The fuzzy logic unit will emphasize the basic notion of fuzziness and real-world applications. Topics in graph theory will highlight applications in management science, including Euler and Hamiltonian circuits, the traveling salesman problem, minimum spanning trees, and ideas in scheduling and planning. The non-Euclidean geometry unit will teach the basics of spherical geometry and focus on developing an understanding of an axiomatic system. Pre-service teachers will be encouraged to take this course in order to expand their understanding of the nature of mathematics. The hope is that they will begin to experience mathematics as a process of finding patterns and making and verifying conjectures, so that they will be comfortable enough to encourage their own students' explorations. We will encourage them to work on projects that can be useful in their own classrooms.
\itemrv{~}
\itemcc{D35}
\itemut{}
\itemli{}
\end