A Vertically Integrated Program for Training in the Mathematical Sciences

摘要 宾夕法尼亚州立大学数学系的目标是成为一个领先的培训 下一代数学科学家的中心 的 近年来，该部门在研究方面的突出地位使其 在一个相对适度的投资将导致 在培训效果方面的特殊回报。新闻部 规划了各级培训倡议的综合方案， 从幼儿园到博士后 它建立在该部目前的 优势：其在几个领域的卓越研究;其MASS计划， 它成立于1996年，提供一个密集的学习环境， 为来自全国各地的优秀本科生;和其独特的 流体力学实验室 该部门将扩大其最近设立的乔拉博士后 每年有一到三个三年期的任命。 这些 职位将包括一个有限的，精心设计，监督 教学内容。 许多博士后研究员将与卓越的部门中心;一些将被选为 跨学科研究;有些人将密切参与我们的 流体实验室 该部门将增加其博士课程的吸引力 通过设立三个年度奖学金， 名为VIGRE Traineeships，有特殊的任命条款。特征 将包括集中学习和论文研究的时间， 沿着一个在各个层次上密切监督教学的计划。 VIGRE学员的目标学位时间为五年。 正式 研究生培训将通过以下项目延长到夏季 密集的暑期课程和工业实习。 该部门将巩固其创新的MASS计划，扩大其 可见度和确保其资金。 它还将制定一项计划， 为期六周的本科生暑期研究经历（REU）。质量 学生和教师都应该积极参与REU项目。此外，还计划制定一项有力的计划， 数学思维和数学热情高的地区 学校学生。 该部门负责未来的数学教育 最大的本科生群体中的科学家和工程师 在宾夕法尼亚州，必须同时促进数学素养 在宾州州立大学的所有学生中。 使 当然，它会尽可能有效地应对这些挑战， 部门将进行彻底审查其整个本科 课程。 一个工作队将领导一项广泛的努力，以产生，讨论， 选择并实施最有效的课程改革，强调 数学与其他科学学科的关系， 工业应用。 该部将加强教育和研究任务， 它的普里查德流体力学实验室给予高度优先选择一些研究生和博士后 奖学金，并通过建立实验设备，可以使用 用于本科生研究项目、教师演示和K-12 外联活动。 学生、博士后研究员和教师的垂直整合， 无论是在研究和培训，已经是中心的部门， 活动：所有三个小组之间进行密集和广泛的互动 是日复一日的现实。 未来的举措将进一步加强 纵向一体化以多种非常明确的方式。 比如说， 通过VIGRE奖学金资助并作为助理参加MASS计划的研究生将受益于双重指导 关系：他们将与一位有成就的研究人员密切合作 和老师，而他们自己是导师的人才和承诺 本科生 博士后研究员附属于流体 实验室将协助教师，反过来，协助研究生， 开展本科生科研训练 实验室的活动。 为所有人计划的教学计划 博士后研究员将使他们与其他教师接触 作为导师，并与研究生和本科生在课堂上。 它提供了发展创新教学的机会， 学习策略，同时仍然提供一个结构化的环境， 明确的目标。 该项目得到了数学和物理科学局下属的数学科学处和多学科活动办公室以及教育和人力资源局下属的初等、中等和非正规教育处的支持。

ABSTRACT Penn State's Mathematics Department aims to become a leading training center for the next generation of mathematical scientists. The Department's rise to research prominence in recent years has placed it in a position from which a comparatively modest investment will lead to exceptional returns in training effectiveness. The Department has planned an integrated program of training initiatives at all levels, from K-12 through postdoctoral. It builds upon the Department's current strengths: its research excellence in several areas; its MASS program, which was founded in 1996 to provide an intensive learning environment for talented undergraduates from around the country; and its unique fluid mechanics laboratory. The Department will expand its recently instituted Chowla postdoctoral program from one to three three-year appointments per year. These positions will include a limited, carefully designed, supervised teaching component. Many postdoctoral fellows will be associated with departmental centers of excellence; some will be selected for interdisciplinary research; and some will be closely involved with our fluids laboratory. The Department will increase the attractiveness of its doctoral program to the country's best students by creating three annual fellowships, called VIGRE Traineeships, with special terms of appointment. Features will include periods of concentration on learning and thesis research, along with a program of closely supervised teaching at various levels. The target time-to-degree for VIGRE Trainees will be five years. Formal graduate training will be extended to the summer months by programs of intensive summer courses and industrial internships. The Department will solidify its innovative MASS program, expanding its visibility and securing its funding. It will also institute a program of six-week summer research experiences for undergraduates (REU's). MASS students and instructo rs are expected to be involved prominently in the REU program. In addition a vigorous program is planned to develop mathematical thinking and enthusiasm for mathematics among area high school students. The Department is responsible for the mathematical education of future scientists and engineers within the largest undergraduate student body in Pennsylvania, and must at the same time promote mathematical literacy across the full breadth of Penn State's student population. To make certain it meets these challenges as effectively as possible, the Department will undertake a thorough review of its entire undergraduate curriculum. A task force will lead a broad effort to generate, discuss, select, and implement the most effective curricular reforms, emphasizing the relation of mathematics to other scientific disciplines and industrial applications. The Department will strengthen the educational and research missions of its Pritchard Fluids Mechanics Laboratory by according it a high priority in the selection of some graduate and postdoctoral fellowships, and by building experimental apparatus which can be used for undergraduate research projects, faculty demonstrations, and K-12 outreach activities. The vertical integration of students, postdoctoral fellows and faculty, both in research and training, is already central to the Department's activities: intensive and extensive interactions among all three groups are day to day realities. Future initiatives will further strengthen vertical integration in a number of very definite ways. For instance, graduate students funded through VIGRE fellowships and participating in the MASS program as assistants will benefit from a double mentoring relationship: they will work closely with an accomplished researcher and teacher while themselves being mentors for talented and committed undergraduates. Postdoctoral fellows affiliated with the fluids laboratory will assist faculty and, in turn, assist graduate and undergraduate students in carrying out the research and training activities of the laboratory. The teaching program planned for all postdoctoral fellows will bring them into contact with other faculty as mentors and with both graduate and undergraduate students in the classroom. It presents opportunities to develop innovative teaching and learning strategies, while still providing a structured environment with defined goals. This project is being supported by the Division of Mathematical Sciences and the Office of Multidisciplinary Activities within the Directorate of Mathematical and Physical Sciences, and the Division of Elementary, Secondary, and Informal Education within the Director of Education and Human Resources.