Extending and Renewing the Education of Mathematicians (EREM)

扩展和更新数学家教育（EREM）

• 批准号: 9819940
• 负责人: R. Michael Beals
• 金额: $ 236.28万
• 依托单位: Rutgers University New Brunswick
• 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 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9819940&HistoricalAwards=false
• 关键词: Extending; Renewing; Education; Mathematicians; EREM

9819940Michael BealsThe Rutgers University Mathematics Department, in its project "Extending and Renewing the Education of Mathematicians," will change the way that postdoctoral fellows and graduate students interact with faculty, undergraduates, and each other. It will also increase opportunities for undergraduates, graduate students and post-docs to participate in applications of mathematics in other disciplines and in industrial practice. The improved, vertically integrated program will bring new research areas to the curriculum, prepare beginning mathematicians for the variety of career paths available to them, and increase the access of students to mathematical research at the highest level. Five research groups - discrete mathematics, number theory, control theory, non-linear partial differential equations, and mathematical physics - will participate in the program.Postdoctoral fellows will be chosen to work with these groups, and their research and pedagogical opportunities will be designed to promote interaction across all levels of mathematical experience within the University. Faculty mentors from these groups will supervise the research development of the post-docs. The post-docs will be provided a mentored progression through a variety of types of teaching at the university level, such as instruction in large multi-section courses, small upper level undergraduate and graduate courses, courses with non-traditional pedagogy including small group work, and courses involving appropriate use of technology. They will engage actively in the construction of course modules for undergraduate courses and seminars for undergraduates and graduate students, while being involved with undergraduates in REUs and with graduate students in guided study and minitutorials. The faculty mentors will also see that the post-docs have opportunities to interact across disciplinary boundaries. Opportunities for internships in industry and government will be provided where appropriate.Graduate students chosen as VIGRE Trainees will participate in a program designed to provide broadened curricula and early exposure to and active involvement in research in the five core areas. Mentored "rotations" - guided study and research participation with faculty members - will supplement the first two years of graduate course work. Examples of the tasks of the trainees in the rotations could include reading a technical paper or part of a book, scientific programming in support of the research efforts of a faculty member, or preparation of a small-scale seminar talk. The trainees will interact with faculty, VIGRE post-docs, and undergraduates in seminars in the five research areas, and will be exposed to the cross-disciplinary and non-academic uses of mathematics in an Outside Speakers Seminar. Opportunities for internships in industry and government will be provided for the trainees where appropriate. The trainees will have a structured and mentored progression through a variety of types of teaching, such as grading, recitation instruction, independent courses, course development, use of technology, workshops, supervision of independent study, and will participate in an ongoing seminar on Issues in Mathematics Education at the Post-Secondary Level.Additional professional development support will be provided to VIGRE trainees and post-docs in such areas as professional communications (writing papers and giving presentations), understanding and using funding opportunities (reading requests for proposals, writing responses), refereeing and reviewing, getting invited to meetings and making good use of them.Undergraduates will participate in the project through direct research opportunities; seminar activities; mentoring relationships with faculty, post-docs, and graduate student trainees; and curriculum revision. Advanced undergraduates will be encouraged to engage in REU activities during the academic year, and a summer REU, in which faculty from the five core areas will participate, will be supported by VIGRE. "Junior seminars" in these areas will be developed to present work at a level that advanced undergraduates and graduate students can understand; VIGRE post-docs will help to organize the seminars and talks will include those by VIGRE trainees. In addition to the REU's, which will provide faculty, post-doc and graduate trainee mentoring to undergraduates, upper level undergraduates will have the opportunity to work with first-year students and sophomores and through participation in workshop sections and involvement with the Gelfand Outreach Program in Mathematics. Course modules and revised courses will be designed as part of a curriculum review; such redesign will involve undergraduates (as a part of an REU activity) and graduate students. For example, the undergraduate number theory course can be reconsidered to provide more emphasis on applications (encryption, coding theory, etc.); a new year-long upper level undergraduate course devoted to mathematical modeling will be developed; control theory modules can be designed to provide students with the opportunity to actually see ordinary differential equations and computer controls combined to predict and modify some simple-appearing physical situations. Undergraduate and graduate courses involving elements of the five core areas have grown in number as faculty add new and updated courses; the VIGRE project offers the opportunity to conduct careful analysis of the content, level, and prerequisites for these courses, with the goal of designing coherent packages of such courses.Funding for this award is provided by the Division of Mathematical Sciences and the MPS Directorate's Office of Multidisiplinary Activities.

[9819940]迈克尔·比尔罗格斯大学数学系在其“扩展和更新数学家教育”项目中，将改变博士后研究员和研究生与教师、本科生以及彼此之间的互动方式。它还将增加本科生、研究生和博士后参与数学在其他学科和工业实践中的应用的机会。改进后的垂直整合课程将为课程带来新的研究领域，为初学数学家提供各种职业道路，并增加学生接触最高水平数学研究的机会。五个研究小组——离散数学、数论、控制论、非线性偏微分方程和数学物理——将参与该计划。博士后将被选中与这些小组一起工作，他们的研究和教学机会将被设计成促进大学内各级数学经验的互动。这些小组的教师导师将监督博士后的研究发展。博士后将通过大学水平的各种教学方式获得指导，例如大型多部分课程的教学，小型高级本科和研究生课程，包括小组工作在内的非传统教学法课程，以及涉及适当使用技术的课程。他们将积极参与本科课程的课程模块建设和本科生和研究生的研讨会，同时参与reu的本科生和研究生的指导学习和辅导班。教师导师也会看到博士后有机会跨学科交流。在适当的情况下，将提供在工业和政府实习的机会。被选为VIGRE培训生的研究生将参加一个旨在提供更广泛的课程、早期接触和积极参与五个核心领域的研究的项目。有指导的“轮岗”——指导教师学习和研究的参与——将补充前两年的研究生课程。在轮转中，受训者的任务可包括阅读一篇技术论文或一本书的一部分，为支持教员的研究工作编制科学方案，或准备一次小规模的讨论会。受训者将在五个研究领域的研讨会上与教师、VIGRE博士后和本科生互动，并将在外部演讲者研讨会上接触到数学的跨学科和非学术用途。在适当情况下，将为学员提供在工业界和政府实习的机会。受训者将通过各种类型的教学，如评分、背诵指导、独立课程、课程开发、技术使用、研讨会、独立学习的监督，获得结构化和指导的进步，并将参加正在进行的关于中学后数学教育问题的研讨会。将向VIGRE培训生和博士后提供额外的专业发展支持，如专业交流（撰写论文和演讲）、理解和利用资助机会（阅读提案请求、撰写答复）、评审和评审、受邀参加会议并充分利用这些机会。本科生将通过直接的研究机会参与项目；研讨会活动;与教师、博士后和研究生实习生的指导关系；以及课程修改。高级本科生将被鼓励在学年期间参与REU活动，并由VIGRE支持一个夏季REU，其中来自五个核心领域的教师将参加。将在这些领域举办“初级研讨会”，以便在高级本科生和研究生能够理解的水平上介绍工作；VIGRE博士后将帮助组织研讨会和讲座，其中包括VIGRE学员的讲座。除了REU将为本科生提供教师、博士后和研究生培训生指导外，高年级本科生还将有机会与一年级学生和二年级学生一起工作，并通过参加研讨会和参与Gelfand数学推广计划。课程单元和修订后的课程将作为课程审查的一部分进行设计；这种重新设计将涉及本科生（作为REU活动的一部分）和研究生。例如，可以重新考虑本科数论课程，以提供更多的应用（加密，编码理论等）；开设为期一年的数学建模高级本科课程；控制理论模块可以设计成让学生有机会实际看到常微分方程和计算机控制相结合来预测和修改一些看似简单的物理情况。随着教师增加新的和更新的课程，涉及五个核心领域要素的本科和研究生课程的数量有所增加；VIGRE项目提供了对这些课程的内容、水平和先决条件进行仔细分析的机会，目标是设计这些课程的连贯包。该奖项的资金由数学科学部和MPS理事会的多学科活动办公室提供。