UCLA Mathematics Department 1999 VIGRE Proposal

摘要数学在科学和技术领域的广泛渗透，极大地扩展了数学家在传统的纯研究和应用研究领域以及新兴的跨学科领域的机会。加州大学洛杉矶分校维格尔项目将努力创造一个环境，让学生和博士后能够探索和参与这些重要的数学发展。在加州大学洛杉矶分校现有项目的基础上，我们将引入新的举措，这些举措将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纯数学和应用数学之间业已密切的合作；(3)促进数学与其他科学之间的互动。为了实现这一目标，数学系将充分利用其作为主要研究中心的地位，优秀的师资队伍，以及广泛的研究生和本科课程。位于加州大学洛杉矶分校校园附近的新国家纯数学与应用数学研究所（IPAM）也将为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纵向整合和扩大：*通过参加研讨会和小组项目，在传统和新兴领域进行研究集群，以实现纵向整合，并使研究生和高级本科生尽早参与研究。*教员研究研讨会：由资深教员定期举办，概述其研究专长。*加强我们在工业和政府实验室的实习机会。*教师、博士后和高级研究生参加的年度静修会议。加州大学洛杉矶分校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博士后将在我们的整合工作中发挥关键作用。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联系。Vigre博士后将受益于：*减少教学。*由资深教师在研究和教学方面提供正式指导，包括在制定研究计划和准备拨款申请方面的指导。*夏季研究支持和旅行/设备津贴。研究生：在研究生阶段，以下课程将帮助研究生更快地从课堂学习进步到积极参与研究，并成为更有效的教师：*研究生开始研究生学习之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。*精简一年级研究生课程及资格考试程序，让学生尽早展开研究，并为跨学科研究创造更多机会。*第一年和论文年不授课。*教师培训和指导。这些项目预计将确保攻读博士学位的平均时间为五年或更短。将通过与南加州的学院和大学建立联系和对潜在新兵的访问日，加强研究生一级的征聘。本科：在本科阶段，我们的目标是吸引更多的学生进入广义的数学科学。以下项目将加强本科生的招生，丰富他们的教育经验，并使他们在大三和大四接触数学研究：*数学学者计划，吸引初学本科生进入数学科学，提高他们的数学教育经验。它包括大一和大二之前的一个密集的暑期课程，学年期间的合作学习小组，以及与教师的特殊项目。*专门的预研究课程，为本科生参与研究项目做准备。*本科生的研究经历，包括暑期研究实习。这些新方案将与现有的部门活动密切结合。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和早期进入各种各样的研究领域。这项活动的经费由数学科学司和MPS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.