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

9452194 Damiano SUN网络工作站实验室为150多名二年级和高年级学生提供10门不同数学课程的计算机支持，服务于专业和非专业的学生。数学系根据过去编写微积分的PC课件和在微积分中使用PC的经验，正在系统地将计算机的使用推广到向量微积分、微分几何、拓扑学、复分析、常微分方程组、应用数学和数值分析的二年级和高年级课程。该项目建立在系教员开发和测试课件的先前工作的基础上，包括一套矢量微积分实验模块、微分几何、应用数学和常微分方程式的练习和项目，以及一本关于微分几何的互动电子文本。本课程采用以发现为基础的教学方法，鼓励学生以数学为基础，以数字、符号和图形研究为基础，共同阐述和检验猜想。这一方法激励和加强了专业和非专业学生的学习过程。购买了20个配备数学软件的Sun Sparc工作站，可以在实验室环境中全面实施新的课件，从而实现计算机在主要高年级课程中的充分利用。该课程将通过NECUSE、AMS、MAA和MER-Network渠道传播。实验模块和课程材料将以文本和实验手册的形式提交出版。

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.