Vertical Integration of Research and Education in Applied Mathematics

应用数学研究与教育的垂直整合

• 批准号: 9810751
• 负责人: James Meiss
• 金额: $ 232.92万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-05-01 至 2006-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9810751&HistoricalAwards=false
• 关键词: Vertical; Integration; Research; Education; Applied

9810751 Meiss The Department of Applied Mathematics of the University of Colorado at Boulder's VIGRE program is focussed in the areas of computational and nonlinear mathematics. The program creates tetrahedral research groups consisting of a faculty mentor, a postdoctoral fellow, several graduate students, and undergraduate majors. Tetrahedra will focus on particular interdisciplinary research problems, hold seminars, write research proposals, and participate in the curriculum reform program. The curriculum will be integrated with computation using multi-layered case study modules. Affiliated faculty serve as co-advisors for Ph.D. theses of our students; the affiliated faculty program will be extended to government laboratories and technology companies. The program will create four tetrahedral groups in the areas of Dynamical Systems, Nonlinear Waves, Multilevel Computation, and Fast Algorithms and Modeling. The four facets of interaction within the groups include: teaching--as a seminar, and in the development of case study projects; learning--to develop mathematical, computational, and communication skills; discovering--to develop the techniques for formulation of useful and solvable research problems; and communicating--to collaborate in the joint production of research papers, grant proposals, and interim research reports. Computational mathematics provides the unifying theme for vertical integration of our training program. Computation will be integrated into lower division courses through Case Study Modules. Vertical integration will be implemented through the development of a multi-layered modeling course that has both lower and upper division undergraduate components as well as a graduate component. The VIGRE grant will support four Postdoctoral Fellows. They will receive mentoring from a faculty advisor and teach one course each semester for the Department. Twelve Graduate Trainees will be funded by the proposal. They will participate in the tetrahedra, research pro posal development, and the development and implementation of case study modules and receive teacher training through the Teaching and Learning Seminar and the Graduate Teacher Program. Four Undergraduate Research Experiences will be funded each year. Students will participate in one of the tetrahedra part-time during the academic year and for two months during the summer. These initiatives will be sustainable and lead to a number of permanent structural changes: successful tetrahedral research groups will endure and be emulated, case study modules will form an essential part of our curriculum, and the extended affiliated faculty will result in a continuing option for training of our students in application areas. Funding for this activity will be provided by the Division of Mathematical Sciences and the MPS Office of Multidisciplinary Activities.

9810751 Meiss科罗拉多大学博尔德分校应用数学系VIGRE项目的重点是计算和非线性数学领域。该项目创建了一个四面体研究小组，由一名教师导师、一名博士后、几名研究生和本科生组成。四面体将专注于特定的跨学科研究问题，举办研讨会，撰写研究建议，并参与课程改革计划。课程将与使用多层案例研究模块的计算相结合。学院教师为学生博士论文的共同指导老师；附属教师计划将扩大到政府实验室和技术公司。该计划将在动力系统、非线性波、多层计算和快速算法和建模领域创建四个四面体小组。小组内部互动的四个方面包括：教学-作为研讨会，并在案例研究项目的发展中；学习——发展数学、计算和沟通能力；发现——开发有用的和可解决的研究问题的表述技术；沟通——在共同撰写研究论文、拨款提案和中期研究报告方面进行合作。计算数学为我们的培训计划的垂直整合提供了统一的主题。计算将通过案例研究模块整合到低年级课程中。垂直整合将通过多层建模课程的开发来实现，该课程包括低级和高级本科部分以及研究生部分。VIGRE基金将资助四名博士后。他们将接受指导老师的指导，每学期为系里教授一门课程。该提案将资助12名研究生培训生。他们将参与四面体、研究提案开发、案例研究模块的开发和实施，并通过教学与学习研讨会和研究生教师计划接受教师培训。每年将资助四个本科生研究经验。学生将在学年期间兼职参加其中一个四面体，在夏季参加两个月。这些举措将是可持续的，并导致一些永久性的结构变化：成功的四面体研究小组将持续存在并被模仿，案例研究模块将成为我们课程的重要组成部分，扩展的附属教师将为我们的学生在应用领域的培训提供持续的选择。这项活动的经费将由数学科学司和MPS多学科活动办公室提供。