Incoporating Experimental Results into the Undergraduate Mathematics Curriculum Using Web-Based Technology

该项目将改善和扩展弗吉尼亚理工大学数学商场的数学建模实验室的设施，以提供生产，监控，传输和显示实验结果的能力，作为本科数学课程中数学建模组件的一个组成部分。 这些设备还将提供制作高质量网络产品的能力，这些产品的特点是可供计算机下载和分析的流式视频和数据集。这将是使实验提供给弗吉尼亚理工大学和其他机构的大群学生的主要手段。 新设备将使一系列三个不断扩大的学生圈子与数学和科学丰富的实验。 第一个也是最小的圆圈将参加数学建模实验室的动手实验。 第二个更大的圈子将参加一个“现场”演示在商场的100个座位的演示室。 最大的圈子将通过录像带和万维网异步参与，或使用视频会议设备和联网计算机同步参与。 实验将被设计为在广泛的大招生本科课程的模块使用： 二年级的常微分方程， 初级现代代数， 高级课程：动力系统与混沌、偏微分方程、工程师操作方法、工程师数值方法。我们要求实验/可视化设备用于： 质量弹簧系统、弦、梁、板和膜的振动分析， 群论概念的可视化， 流体流动和混合问题。

This project will improve and extend the facilities of the Mathematical Modeling Laboratory in Virginia Tech's Mathematics Emporium to provide the capability to produce, monitor, transmit, and display experimental results as an integral part of a mathematical modeling component in the undergraduate mathematics curriculum. The equipment will also provide the capability to produce high quality web-based products featuring streamed video and data sets that can be downloaded and analyzed by computer. This will be the primary means for making the experiments available to large groups of students at Virginia Tech and other institutions. The new equipment will enable a series of three expanding circles of students to work with mathematically and scientifically rich experiments. The first and smallest circle will participate in hands-on experimentation in the Mathematical Modeling Laboratory. A second and larger circle will participate in a "live" demonstration in the Emporium's 100 seat presentation room. The largest circle will participate asynchronously via videotapes and the World Wide Web or synchronously using videoconferencing equipment and networked computers. Experiments will be designed to be used as modules in a wide range of large enrollment undergraduate courses: Sophomore-level Ordinary Differential Equations, Junior-level Modern Algebra, Senior-level courses in Dynamically Systems and Chaos, Partial Differential Equations, Operational Methods for Engineers, Numerical Methods for Engineers. We request experimental/visualization equipment for: Vibration analysis of mass-spring systems, pendulums, strings, beams, plates, and membranes, Visualization of group theoretic concepts, Fluid-flow and mixing problems.