A Vertically Integrated Program for Training in the Mathematical Sciences

宾夕法尼亚州立大学数学系的目标是成为下一代数学科学家的领先培训中心。近年来该部在研究方面的突出地位使它处于这样一种地位，即相对较少的投资将导致培训效率方面的特殊回报。该部门计划了从K-12到博士后各级培训倡议的综合方案。它建立在该部门目前的优势之上：它在几个领域的卓越研究；其MASS项目成立于1996年，旨在为来自全国各地的有才华的本科生提供密集的学习环境；以及它独特的流体力学实验室。该系将把最近设立的Chowla博士后项目从每年1个扩大到3个。这些职位将包括有限的、精心设计的、有监督的教学部分。许多博士后将与部门卓越中心联系在一起；其中一些将被选作跨学科研究；有些人将与我们的流体实验室密切相关。该部门将通过设立三个年度奖学金（VIGRE traineships）来增加其博士项目对该国最优秀学生的吸引力，这些奖学金被称为VIGRE traineships，具有特殊的任命条款。特色将包括集中学习和论文研究的时期，以及各级密切监督的教学计划。VIGRE学员获得学位的目标时间为五年。正式的研究生培训将通过暑期强化课程和工业实习项目延长到夏季。该部门将巩固其创新的MASS项目，扩大其知名度并确保其资金。它还将为本科生设立一个为期六周的暑期研究体验项目（REU’s）。麻省理工学院的学生和教师将在REU项目中发挥重要作用。此外，还计划开展一项积极的计划，以培养地区中学生的数学思维和对数学的热情。该系负责宾夕法尼亚最大的本科学生群体中未来科学家和工程师的数学教育，同时必须在宾夕法尼亚州立大学全体学生中推广数学素养。为了确保尽可能有效地应对这些挑战，该部将对其整个本科课程进行彻底审查。一个特别工作组将领导一个广泛的努力，以产生、讨论、选择和实施最有效的课程改革，强调数学与其他科学学科和工业应用的关系。本系将加强其普里查德流体力学实验室的教育和研究任务，根据其在选择一些研究生和博士后奖学金方面的优先地位，并通过建立可用于本科生研究项目，教师演示和K-12推广活动的实验设备。学生、博士后研究员和教师在研究和培训方面的垂直整合已经成为该系活动的核心：这三个群体之间的密集和广泛的互动是日常现实。未来的举措将以一些非常明确的方式进一步加强垂直整合。例如，通过VIGRE奖学金资助并作为助理参加MASS项目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和教师密切合作，同时自己也是有才华和忠诚的本科生的导师。附属于流体实验室的博士后将协助教师，并反过来协助研究生和本科生开展实验室的研究和培训活动。为所有博士后计划的教学计划将使他们作为导师与其他教师以及在课堂上与研究生和本科生接触。它提供了发展创新教学和学习策略的机会，同时仍然提供了一个有明确目标的结构化环境。该项目得到数学和物理科学局数学科学司和多学科活动办公室以及教育和人力资源司内的初等、中等和非正规教育司的支持。

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.