Extending and Renewing the Education of Mathematicians (EREM)

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其他学科的数学应用和工业实践的机会。改进后的垂直整合计划将为课程带来新的研究领域，为初学数学的人提供各种职业道路的准备，并增加学生接触最高水平的数学研究的机会。五个研究小组-离散数学、数论、控制理论、非线性偏微分方程式和数学物理-将参与该计划。博士后研究员将被选为与这些小组合作，他们的研究和教学机会将被设计为促进大学内所有层次的数学经验的互动。这些团体的教师导师将监督博士后的研究进展。将通过大学一级的各种教学形式为博士后提供指导，例如教授大型多节课程、小型高级本科和研究生课程、采用包括小组合作在内的非传统教学方法的课程，以及涉及适当使用技术的课程。他们将积极参与为本科生和研究生建立课程模块，并为本科生和研究生举办研讨会，同时与REUS的本科生和研究生一起参加指导学习和微型课程。教师导师还将看到，博士后有机会跨越学科界限进行互动。被选为Vigre实习生的研究生将参加一个项目，该项目旨在提供更广泛的课程，及早接触和积极参与五个核心领域的研究。有指导的“轮换”--与教职员工一起指导学习和研究参与--将补充研究生课程头两年的工作。受训者在轮换中的任务可以包括阅读一篇技术论文或一本书的一部分，支持教员研究努力的科学规划，或准备一次小规模的研讨会演讲。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，并将在外部演讲研讨会上接触到数学的跨学科和非学术用途。在适当的情况下，将为学员提供在行业和政府实习的机会。学员将透过不同类型的教学，例如评分、复习指导、独立课程、课程发展、科技应用、工作坊、独立研究的督导等，有系统及有指导地取得进步，并将参加一个有关专上数学教育问题的研讨会。此外，Vigre学员及博士后将获提供其他专业发展支援，包括专业沟通(撰写论文及发表报告)、理解及利用资助机会(阅读建议书、写作回应)、评审及检讨、受邀出席会议及善用这些机会。本科生将透过直接研究机会参与计划；研讨会活动；与教师、博士后和研究生实习生的指导关系；以及课程修订。将鼓励高级本科生在学年期间参与REU活动，Vigre将支持五个核心领域的教师参加夏季REU。这些领域的“初级研讨会”将被发展到高级本科生和研究生可以理解的水平；Vigre博士后将帮助组织研讨会，演讲将包括Vigre实习生的演讲。除了REU将为本科生提供教师、博士后和研究生实习生指导外，高水平的本科生还将有机会与一年级和二年级的学生合作，并通过参加研讨会部分和参与Gelfand推广计划数学。课程单元和修订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(作为区域教育联盟活动的一部分)和研究生。例如，可以重新考虑本科生的数论课程，以提供更多的重点应用(加密、编码理论等)；将开发一门新的为期一年的、致力于数学建模的高级本科生课程；可以设计控制理论模块，使学生有机会实际看到常微分方程和计算机控制相结合，以预测和修改一些简单的物理情况。涉及五个核心领域元素的本科生和研究生课程的数量随着教员增加新的和更新的课程而增加；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，目的是设计出连贯的课程包。该奖项的资金由数学科学部和MPS董事会的多学科活动办公室提供。

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.