Vertical Integration of Research and Education in Applied Mathematics

小行星9810751 应用数学系的科罗拉多大学博尔德分校的VIGRE计划的重点是在计算和非线性数学领域。 该计划创建四面体研究小组，由一名教师导师，一名博士后研究员，几名研究生和本科专业组成。 四面体将专注于特定的跨学科研究问题，举办研讨会，撰写研究提案，并参与课程改革计划。 该课程将使用多层案例研究模块与计算相结合。 附属教师担任博士的共同顾问。我们的学生的论文;附属教师计划将扩展到政府实验室和技术公司。 该计划将在动力系统，非线性波，多级计算和快速算法和建模领域创建四个四面体组。 四个方面的相互作用组内包括：教学-作为一个研讨会，并在个案研究项目的发展;学习-发展数学，计算和沟通技能;发现-发展的技术制定有用的和可解决的研究问题;和沟通-合作，在联合生产的研究论文，赠款建议，和临时研究报告。 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较低的部门课程。 垂直整合将通过一个多层次的建模课程，既有较低和较高的师本科组件，以及研究生组件的发展来实现。 VIGRE赠款将支持四名博士后研究员。 他们将接受指导教师的指导，并教一门课程，每学期为部门。 该提案将资助12名研究生受训人员。 他们将参与四面体，研究方案开发，以及案例研究模块的开发和实施，并通过教学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研究经验。 学生将在学年期间兼职参加其中一个四面体，并在夏季参加两个月。 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并被模仿，案例研究模块将成为我们课程的重要组成部分，而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。 这项活动的资金将由数学科学部和MPS多学科活动办公室提供。

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.