Extending and Renewing the Education of Mathematicians (EREM)

9819940迈克尔·比尔斯罗格斯大学数学系在其项目“扩展和更新数学家的教育”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。 改进后的垂直整合计划将为课程带来新的研究领域，为他们提供的各种职业道路做好准备，并增加学生获得最高水平数学研究的机会。 五个研究小组-离散数学，数论，控制理论，非线性偏微分方程和数学物理-将参与该计划。博士后研究员将被选中与这些小组合作，他们的研究和教学机会将被设计为促进大学内各级数学经验的互动。 来自这些小组的教师导师将监督博士后的研究发展。 博士后将通过大学一级的各种类型的教学提供指导进展，例如大型多节课程，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和本科生和研究生研讨会的课程模块的建设，同时与雷乌斯的本科生和研究生一起参与指导学习和微型课程。 教师导师也将看到博士后有机会跨学科界限进行互动。在适当的情况下，将提供在工业和政府部门实习的机会。被选为VIGRE实习生的研究生将参加一个旨在提供拓宽课程的计划，并尽早接触和积极参与五个核心领域的研究。 指导“轮换”-指导学习和研究参与与教师-将补充研究生课程工作的前两年。 实习生在轮换中的任务包括阅读一篇技术论文或一本书的一部分，支持教员研究工作的科学编程，或准备小规模的研讨会演讲。 学员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数学的跨学科和非学术用途。 将酌情为受训人员提供在工业界和政府部门实习的机会。学员将通过各种类型的教学，例如评分、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，获得结构化和指导性的进步，，并将参加一个正在举行的关于中学后数学教育问题的研讨会。专业沟通等领域的文档（撰写论文和发表演讲），了解和利用资助机会（阅读提案请求，撰写回复），评审和审查，受邀参加会议并充分利用它们。本科生将通过直接研究机会参与项目;研讨会活动;与教师、博士后和研究生学员的指导关系;以及课程修订。 高级本科生将被鼓励在学年期间从事REU活动，夏季REU，其中来自五个核心领域的教师将参与，将由VIGRE支持。 将在这些领域举办“初级研讨会”，以高年级本科生和研究生能够理解的水平介绍工作; VIGRE博士后将帮助组织研讨会，VIGRE受训人员将参加讲座。 除了REU的，这将提供教师，博士后和研究生实习生指导本科生，高水平的本科生将有机会与一年级学生和学生一起工作，并通过参加研讨会部分和参与数学的Gelfand外展计划。 课程模块和修订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，本科数论课程可以重新考虑，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高级本科课程，专门用于数学建模;控制理论模块可以设计为学生提供实际看到常微分方程和计算机控制相结合的机会，以预测和修改一些简单的物理情况。 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生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，该奖项的资金由数学科学部和MPS董事会多学科办公室提供。活动

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.