Inverse Problems: A Curricular Resource for the First Two Years of Mathematical Science

全国各地的学院和大学正在开发课程材料，以补充头两年的数学课程。这些材料的统一主题是数学科学中反问题的主题。所有材料都是为了将科学知识与数学分析和基本建模相结合而设计的，这些单元将在适当的时候利用图形计算器和现代数学软件。其目的是提供数学分析和基本物理原理的无缝结合。该课程指南的目标是为教师提供激发物理直觉、培养模型建立、鼓励猜测、刺激基本数学分析的应用以及促进学生批判性思维的工具。该课件按数学课程级别进行分类，并按应用领域和所使用的数学工具进行交叉索引。它由相关练习、项目和计算经验的模块组成，所有这些都受到(但不一定严格限于)逆问题的启发。此外，在一些模块中还提供了软件程序。这些材料将以印刷品和电子形式广泛传播。一个本科教师网络，他们参加了本科教师关于逆问题的数学强化研讨会，美国数学协会关于本科课程中逆问题的区域特别会议，或美国数学协会关于本科生课堂中逆问题的小型课程，将组成材料的初始分发和测试的核心小组。

Curricular materials are being developed that complement mathematics courses in the first two years at colleges and universities throughout the nation. The unifying theme of these materials is the subject of inverse problems in the mathematical sciences. All materials are designed to integrate scientific knowledge with mathematical analysis and basic modeling and the units will exploit graphing calculators and modern mathematical software when appropriate. The aim is to provide a seamless blending of mathematical analysis and basic physical principles. The curriculum guide has the goal of providing instructors with tools for kindling physical intuition, fostering model building, encouraging conjecturing, stimulating the application of basic mathematical analysis, and generally promoting critical thinking by their students. The courseware is classified by mathematics course level and cross-indexed by application area and mathematical tools used. It consists of modules of related exercises, projects, and computational experiences, all inspired by (but not necessarily strictly limited to) inverse problems. In addition, software programs are provided in some modules. The material will be widely disseminated in print and electronic forms. A network of undergraduate teachers who took part in the Undergraduate Faculty Enhancement Workshop on the Mathematics of Inverse Problems, the regional Mathematical Association of America special session on Inverse Problems in the Undergraduate Curriculum, or the Mathematical Association of America's Mini-course on Inverse Problems in the Undergraduate Classroom will form the core group for initial distribution and testing of the materials.