Vertical Integration of Research and Education in Mathematics at Columbia University

哥伦比亚大学数学研究与教育的垂直整合

• 批准号: 9810750
• 负责人: Robert Friedman
• 金额: $ 228.88万
• 依托单位: Columbia University
• 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: 1999-07-01 至 2005-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9810750&HistoricalAwards=false
• 关键词: Vertical; Integration; Research; Education; Mathematics

9810750PinkhamThe main goal of the Columbia University VIGRE award is to offer mathematical training that is better aligned with contemporary scientific needs and job opportunities for mathematicians. These require a more cohesive teaching of traditional branches of mathematics, with an exposure at an early stage to other scientific disciplines and to non-academic environments. Thus a central feature of this proposal is a restructured "core curriculum", for the first year of the Ph.D., which will provide all new math graduate students with a broad, yet tightly interwoven introduction to the basic themes and techniques of modern mathematics. The material ranges from classical topics to state-of-the-art developments, and cuts across the traditional subdivisions of mathematics into algebra, analysis and topology. It is covered in a series of one-year courses, with large overlaps, where the same ideas occur repeatedly in different guises. Besides lectures, the courses all incorporate round table discussions led by advanced graduate students and postdoctoral fellows supported by the proposal.The project focuses on three areas in the mathematical sciences, in which Columbia has particular strength: 1) core mathematics, with an emphasis on geometry; 2) the mathematics of theoretical physics; 3) probability, with an emphasis on the mathematics of finance. In each area, we offer (a) a restructured curriculum and research activities reflecting cutting edge developments in the subject. (b) joint postdoctoral-Ritt Assistant Professor positions structured to provide better support for young mathematicians beginning their careers as teachers and researchers. These positions will have half the teaching load of the ordinary Ritt Assistant Profressor positions in the Department. (c) internship positions in allied institutions such as other departments or financial or industrial firms. (d) increased emphasis at all levels on pedagogical issues in mathematics, much of this through collaboration with the mathematics department of Teacher's College. (e) improved funding for graduate students in order to shorten time to degree. (f) improved research activities and funding for mathematics undergraduates. This will be done through Columbia University's I.I. Rabi scholarship program, which already has an established track record of promoting undergraduate reseach in science and mathematics, in particular through a summer internship program allowing Rabi scholars to join active research groups and participate in the actual process of mathematical and scientific investigation and discovery. (g) seminars and other activities designed to increase the amount of interaction between students at different levels and faculty at different stages of their careers.Mathematics in the urban environment of New York will be an important aspect of our efforts. It will include outreach to both mathematics high school teachers and high school students in New York City, with an emphasis on disadvantaged students and teachers working in schools with a high percentage of disadvantaged students. Here we will work in collaboration with two well-established and nationally recognized Columbia University programs: a) the Double Discovery Center (DDC), founded in 1965 at Columbia University, a youth service agency serving over 1,000 at-risk high school students in New York City. The undergraduate and graduate students supported by this proposal will collaborate with the DDC on math courses and tutorials for these youths. b) the Columbia Saturday Science Honors Program (SHP), a long-standing, highly selective program for high school students who have exceptional talent in mathematics and the sciences. This proposal will allow the SHP to hire high school math teachers as "teaching partners" in the mathematics courses offered by SHP, with the goal of enabling them to offer similar courses in their own schools. It will also allow students and postdocs supported by the proposal to participate in the design and teaching of innovative new mathematics courses.This project is being funded by the Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities and the Division of Elementary, Secondary, and Informal Education.

哥伦比亚大学VIGRE奖的主要目标是提供更好地符合当代科学需求和数学家就业机会的数学培训。 这些都需要一个更有凝聚力的数学传统分支的教学，在早期阶段接触到其他科学学科和非学术环境。 因此，这一建议的一个中心特点是重新调整了博士第一年的“核心课程”，这将为所有新的数学研究生提供一个广泛的，但紧密交织的介绍现代数学的基本主题和技术。 材料范围从经典主题到最先进的发展，并跨越传统的数学细分为代数，分析和拓扑。 它包含在一系列为期一年的课程中，有很大的重叠，相同的想法以不同的形式反复出现。 除了讲座，课程还包括由该计划支持的高级研究生和博士后研究员主持的圆桌讨论。该项目侧重于数学科学的三个领域，其中哥伦比亚具有特殊优势：1）核心数学，重点是几何; 2）理论物理数学; 3）概率，重点是金融数学。 在每个领域，我们提供（a）重组课程和研究活动，反映该主题的前沿发展。 (b)联合博士后里特助理教授职位的结构，以提供更好的支持年轻的数学家开始他们的职业生涯作为教师和研究人员。 这些职位将有一半的教学工作量的普通里特助理教授职位的部门。 (c)在其他部门或金融或工业公司等相关机构的实习职位。 (d)在数学教学问题上，各级教育更加重视，这在很大程度上是通过与师范学院数学系的合作。 (e)改善研究生的资金，以缩短获得学位的时间。 (f)改善数学本科生的研究活动和资金。 这将通过哥伦比亚大学的I.I.拉比奖学金计划，该计划已经建立了促进科学和数学本科生研究的良好记录，特别是通过暑期实习计划，让拉比学者加入活跃的研究小组，并参与数学和科学调查和发现的实际过程。 (g)研讨会和其他活动，旨在增加不同层次的学生和教师在不同阶段的职业生涯之间的互动量。纽约城市环境中的数学将是我们努力的一个重要方面。它将包括对纽约市的高中数学教师和高中学生进行外联，重点是处境不利的学生和在处境不利学生比例高的学校工作的教师。在这里，我们将与两个完善的和国家认可的哥伦比亚大学计划合作：一）双重发现中心（DDC），成立于1965年在哥伦比亚大学，青年服务机构服务超过1,000名在纽约市的高风险学生。 由该提案支持的本科生和研究生将与DDC合作，为这些年轻人提供数学课程和辅导。 B）哥伦比亚星期六科学荣誉计划（SHP），这是一个长期的、高度选择性的计划，面向在数学和科学方面有特殊天赋的高中生。 这项建议将允许SHP聘请高中数学教师作为SHP提供的数学课程的“教学伙伴”，目的是使他们能够在自己的学校提供类似的课程。 该项目还将允许学生和博士后参与创新数学课程的设计和教学。该项目由数学科学部、MPS多学科活动办公室和小学、中学和非正规教育部资助。