Salisbury University, in collaboration with California State University Fresno, Humbolt State University, Kennesaw State University, New College of Florida, and Pittsburg State University, is developing online materials to enhance several mathematics courses, including those for prospective teachers. Students frequently find abstract mathematics difficult to visualize. They rarely see links between coursework and independent mathematical inquiry. The PascGalois Project provides an interesting class of discrete dynamical systems generated over algebraic structures, such as groups, and color graphical representations of these systems that allow students to see algebraic and number theoretic properties intertwined with the dynamics.
The primary objectives of this project are to: develop online activities including Java applets that provide a visual component for courses including abstract algebra, discrete mathematics, number theory, dynamical systems, and computer graphics; develop students' visual and intuitive understanding of difficult mathematical concepts; model effective use of technology for prospective mathematics teachers and better prepare them to implement the NCTM standards; and create a bridge between upper-level courses and undergraduate research by providing a source of interesting and accessible research projects.
The intellectual merit of the project is in the innovative activities designed for upper-level mathematics courses, revealing connections between courses that otherwise may appear unrelated, and the undergraduate research projects that are generated. Two summer PascGalois retreats highlight the undergraduate research efforts.
Broader impacts follow from online dissemination of the Java applets and activities through a venue such as MathDL. These activities will be integrated throughout the mathematics curriculum.
