UCLA Mathematics Department 1999 VIGRE Proposal

数学广泛渗透到几乎每一个科学和技术领域，极大地增加了数学家在传统的理论研究和应用研究领域以及新兴的交叉学科领域的机会。加州大学洛杉矶分校的Vigre计划将寻求创造一个环境，让学生和博士后能够探索和参与这些重要的数学发展。在现有加州大学洛杉矶分校课程的基础上，我们将推出新的举措，在结构和文化层面上广泛影响该部门。总体目标是(1)鼓励教师、博士后、研究生和本科生之间的互动，(2)加强加州大学洛杉矶分校(UCLA)纯数学和应用数学之间本已密切的合作，以及(3)促进数学与其他科学之间的互动。为了实现这一目标，数学系将利用其作为主要研究中心的地位、其优秀的教师队伍以及其庞大而广泛的研究生和本科生课程。位于加州大学洛杉矶分校附近的新的国家理论和应用数学研究所(IPAM)也将为与Vigre相关的跨学科活动提供令人兴奋的焦点。将通过以下举措加强垂直整合和拓宽：*传统和新兴领域的研究集群，通过参与研讨会和小组项目，实现垂直整合，并尽早让研究生和高级本科生参与研究。*学院研究研讨会：由高级教员定期举办，概述他们的研究专业。*加强我们与行业和政府实验室正在进行的实习。*与教师举行年度务虚会，博士后和高级研究生。加州大学洛杉矶分校的Vigre项目有三个主要组成部分：博士后、研究生和本科生。博士后：Vigre博士后研究员将在我们的整合努力中发挥关键作用。他们将通过参与研究集群，在教师和学生之间的研究互动中形成纽带。Vigre博士后研究员将受益于：*减少教学。*由高级教员在研究和教学方面进行正式指导，包括指导制定研究计划和准备拨款提案。*暑期研究支持和旅行/设备津贴。GRADUATE：在研究生层面，以下计划将帮助研究生更快地从课堂学习提高到积极参与研究，并成为更有效的教师：*研究生开始学习前的新暑期预备课程，为第一年的资格考试课程提供坚实的基础。*精简第一年研究生课程和资格考试程序，使研究早日开始，为跨学科研究创造更多机会。*第一年和论文期间不授课。*教师培训和指导。这些计划预计将确保获得博士学位的平均时间为五年或更短时间。将通过与南加州的学院和大学建立联系以及未来应聘者的探视日来加强研究生一级的招聘。本科生：在本科生层面，我们的目标是吸引更多的学生进入广义的数学科学。以下计划将加强招收本科生，丰富他们的教育经验，并让他们在初中和高中接触数学研究：*数学学者计划，以吸引初学本科生进入数学科学，并提高他们在数学方面的教育经验。它包括一年级和二年级之前的密集暑期计划，学年期间的协作学习小组，以及与教职员工的特殊项目。*为本科生准备参与研究项目的特别预科课程。*本科生的研究经验，包括暑期研究实习。这些新计划将与现有的部门活动紧密结合。他们将共同创造一个令人兴奋和丰富的教育和科学环境，这将提供广泛的数学文化，并尽早进入广泛的研究领域。这项活动的经费由数学科学处和重大计划署多学科活动办公室提供。

ABSTRACTThe widespread penetration of mathematics into almost every area of science and technology has vastly expanded the opportunities available to mathematicians, both in traditional areas of pure and applied research and in emerging interdisciplinary areas. The UCLA Vigre Program will seek to create an environment in which students and post-docs can explore and participate in these important mathematical developments. Building on the strength of existing UCLA programs, we will introduce new initiatives that will broadly impact the department at both structural and cultural levels. The overall goals are to (1) encourage interaction between faculty, postdocs, graduate students and undergraduates, (2) enhance the already close cooperation at UCLA between pure and applied mathematics, and (3) facilitate interaction between mathematics and other sciences. To accomplish this, the Department of Mathematics will take advantage of its position as a major research center, its excellent faculty, and its large and wide-ranging graduate and undergraduate programs. The new national Institute for Pure and Applied Mathematics (IPAM), located nearby on the UCLA campus will also provide an exciting focus for VIGRE-related interdisciplinary activities.Vertical integration and broadening will be enhanced through the following initiatives: * Research clusters, in both traditional and emerging areas, via participating seminars and group projects to achieve vertical integration and to involve graduate students and advanced undergraduates in research as early as possible.* Faculty Research Seminars: to be given regularly by senior faculty to provide overviews of their research specialties.* Strengthening of our on-going internships with industry and government laboratories.* An annual retreat conference with faculty, postdocs and senior graduate students.The UCLA VIGRE Program has three major components: postdoctoral, graduate, and undergraduate. POSTDOCTORAL: VIGRE Post-doctoral Fellows will play a pivotal role in our integration efforts. They will form a link in the research interaction between faculty and students via participation in research clusters. Vigre Postdoctoral Fellows will benefit from:* Reduced teaching.* Formal mentoring by senior faculty in both research and teaching, including guidance in formulating a research program and grant proposal preparation.* Summer research support and travel/equipment allowance.GRADUATE: At the graduate level, the following programs will help graduate students to progress more rapidly from classroom learning to active participation in research and to become more effective teachers:* New summer program of preparatory courses for graduate students prior to beginning graduate study to provide a solid foundation for the first year qualifying exam courses.* Streamlined first-year graduate curriculum and qualifying exam process, to enable an early start on research and create more opportunities for interdisciplinary research. * No teaching in the first and dissertation years.* Teacher training and mentoring.These programs are expected to ensure that the average time to PhD is five years or less. Recruitment at the graduate level will be enhanced through contacts established with colleges and universities in Southern California and visitation days for prospective recruits. UNDERGRADUATE: At the undergraduate level, our goal is to attract more students into the mathematical sciences broadly construed. The following programs will enhance recruitment of undergraduates, enrich their educational experience, and allow them to make contact with mathematical research in the junior and senior years:* The Mathematics Scholars Program to attract beginning undergraduates into the mathematical sciences and to enhance their educational experiences in mathematics. It consists of an intensive summer program prior to the Freshman and Sophomore years, collaborative learning groups during the academic year, and special projects with faculty. * Special Pre-research Courses to prepare undergraduates to participate in research projects.* Research experiences for undergraduates, including summer research internships.These new programs will be closely integrated with existing departmental activities. Together, they will create an exciting and enriching educational and scientific environment which will provide a broad mathematical culture and an early entrance into a wide variety of research areas. Funding for this activity was provided by the Division of Mathematical Sciences and the MPS Office for Multidisciplinary Activity.