Computing in Mathematics Courses After Calculus: A Discovery-Based Approach

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9452194 Damiano A laboratory of networked Sun Workstations provide computer support in ten different mathematics courses servicing majors and non-majors for over 150 sophomore and upper division students. Based upon past experience in writing PC courseware for calculus and using PC's in the calculus, the faculty in the Department of Mathematics are systematically extending the use of the computer to the sophomore and upper division offerings in vector calculus, differential geometry, topology, complex analysis, ordinary differential equations, applied mathematics and numerical analysis. The project builds on previous work of department faculty in developing and testing courseware, including a set of laboratory modules for vector calculus, exercises and projects in differential geometry, applied mathematics, and ordinary differential equations, and an interactive electronic text for differential geometry. This courseware utilizes a discovery-based approach, encouraging students to work together to formulate and test conjectures based on numeric, symbolic and graphic investigations primarily with the software package Mathematica. The approach invigorates and strengthens the learning process for majors and non-majors alike. The purchase of 20 Sun Sparc Stations equipped with Mathematica allow full implemention of new courseware in a laboratory environment which achieves full utilization of the computer in major upper division courses. The courseware will be disseminated through NECUSE, AMS, MAA and MER-Network outlets. Laboratory modules and curriculum material will be submitted for publication in texts and lab manuals.