Vertical Integration of Research and Education in the Mathematical Sciences at the University of Arizona

亚利桑那大学数学科学研究与教育的垂直整合

• 批准号: 9977116
• 负责人: William McCallum
• 金额: $ 228.83万
• 依托单位: University of Arizona
• 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: 1999-09-01 至 2005-10-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9977116&HistoricalAwards=false
• 关键词: Vertical; Integration; Research; Education; Mathematical

AbstractUniversity of ArizonaThe combined forces of the Mathematics Department and the Applied Mathematics Program at the University of Arizona provide an environment in the mathematical sciences that offers breadth and excellence in both research and innovative teaching activities. The research spectrum spans a wide range of activities from number theory and geometry to biomathematics and scientific computation; and the teaching program was among the first to embrace technological innovation, outreach, and vertical integration. Over the past several years the Department and the Program have introduced many training innovations, including Research Tutorial Groups, a unique experimental modeling laboratory, a variety of options aimed at improving communication and computational skills, an internship program, and vertically integrated outreach activities. Combined with additional activities especially designed for students who will be supported by VIGRE grants, and the rich research and teaching environment, all these initiatives will provide graduate students, undergraduates, and postdoctoral associates with the training they will need to be successful mathematicians in the coming decades. Central to our proposal are distinguished research groups in Algebra/Number Theory, Biomathematics, Dynamical Systems, Fluid Dynamics, Geometry, Mathematical Physics/Applied Probability, Mathematics Education, Nonlinear Optics, and Partial Differential Equations. Each of these groups has not only an outstanding reputation in research but an excellent track record of integrating graduate students, undergraduates, and postdoctoral fellows into their research activities. We note that the Number Theory group was recently recognized by the award of a Group Infrastructure Grant by the NSF Division of Mathematical Sciences, and the Biomathematics activity is part of a larger enterprise that was recently awarded one of the new IGERT (Integrative Graduate Education and Research Training) grants by the NSF.The interdisciplinary graduate Program in Applied Mathematics adds an extra dimension to this spectrum of research. Established twenty years ago to foster campus-wide cross-disciplinary research and training in the mathematical sciences, the Program connects students with faculty across an array of disciplines, drawn from 15 departments in the Colleges of Science, Engineering, and Medicine. Despite the Program's executive independence it maintains a unique working relationship with the Mathematics Department, many of whose faculty are among its most active members; 31 of the 53 PhDs awarded by the Program in the past five years were supervised by faculty from the Department of Mathematics. Graduate Funding: Except for two first-year fellowships VIGRE funds will be used to support students who have passed Qualifying Examinations. To apply for VIGRE support a student will write a short proposal describing a research strategy and chosen elective activities. The proposal should identify a research group that the student will join and explain the student's intended contribution to the group. A small number of summer support awards will be made to students preparing for examinations. We anticipate a steady state of approximately 18 students supported by VIGRE or matching funds in each academic year semester, and slightly larger numbers having at least partial summer research support. Undergraduate Activities: Engaging the interest of undergraduates in mathematics and encouraging them to pursue careers in mathematics - either as teachers, researchers, or in industry - is a major goal of our proposal. The various training components that will fulfill these goals are a comprehensive range of research experiences, an expanded summer internship program, and opportunities for qualified undergraduates to help in teaching. Under the aegis of VIGRE we will coordinate all undergraduate research initiatives carried out by the Department and the Program. Graduate students and postdoctoral fellows will be encouraged to participate in the supervision of selected undergraduate projects. Participating undergraduate students will prepare written reports about their activities, and at least once each semester the students will present their results at a Saturday conference devoted to undergraduate research. The participants whose presentations are judged the best will be provided with travel funds to present their results at regional or national meetings of appropriate professional organizations such as the Mathematical Association of America and the American Mathematical Society. We anticipate supporting 10-12 REU students each academic year, and slightly smaller numbers in the summers. Postdoctoral Fellows: Our recruitment of VIGRE Postdoctoral Fellows will target recent PhDs who anticipate future careers as faculty members in research universities, and whose research interests have significant intersection with at least one of our research groups. To prepare them for such careers we will provide them with exciting research opportunities, innovative teaching experiences at all levels, and a leadership role in a variety of graduate and undergraduate educational experiences outside the classroom. A Postdoctoral Mentoring Committee will ensure, beginning with the postdoctoral recruiting process, that appropriate faculty mentors will be available for all VIGRE postdoctoral fellows. Postdoctoral fellows will teach one course each semester (in residence). To prepare them properly for university careers, these courses will be at all levels. At least one course will be a graduate course in the fellow's area of research, possibly team-taught with a faculty mentor. Postdoctoral fellows will be encouraged to spend a summer or semester internship at a national laboratory, a research institute such as MSRI, or in industry. We will support four VIGRE postdoctoral fellows in each year after the first, with matching support being provided for two each from the Department and the Program. The two fellows supported and selected by the Department will be chosen to ensure continuing strength and growth in existing research groups. The two supported by the Program will be chosen by a committee of Program faculty to create cross-disciplinary ties with other departments.

亚利桑那大学数学系和应用数学项目的联合力量为数学科学提供了一个广泛和卓越的研究和创新教学活动的环境。研究范围广泛，从数论和几何到生物数学和科学计算；该教学项目是首批采用技术创新、拓展和垂直整合的项目之一。在过去的几年里，该部门和项目引进了许多培训创新，包括研究指导小组，一个独特的实验建模实验室，旨在提高沟通和计算技能的各种选择，实习计划，以及垂直整合的外展活动。再加上为VIGRE资助的学生专门设计的额外活动，以及丰富的研究和教学环境，所有这些举措将为研究生、本科生和博士后提供他们在未来几十年成为成功数学家所需的培训。我们提议的核心是代数/数论、生物数学、动力系统、流体动力学、几何、数学物理/应用概率、数学教育、非线性光学和偏微分方程等领域的杰出研究小组。这些小组不仅在研究方面享有盛誉，而且在将研究生、本科生和博士后纳入其研究活动方面也有着良好的记录。我们注意到数论小组最近获得了美国国家科学基金会数学科学部的团体基础设施资助，生物数学活动是一个更大的企业的一部分，该企业最近获得了美国国家科学基金会新的IGERT（综合研究生教育和研究培训）资助之一。应用数学跨学科研究生课程为这一研究领域增加了一个额外的维度。该项目成立于20年前，旨在促进全校范围内的跨学科研究和数学科学培训，该项目将学生与来自理学院、工程学院和医学院15个部门的一系列学科的教师联系起来。尽管该计划的执行独立性，它与数学系保持着独特的工作关系，数学系的许多教师都是其最活跃的成员；该计划在过去五年中授予的53位博士中，有31位由数学系的教师指导。研究生资助：除了两个第一年的奖学金外，VIGRE基金将用于支持通过资格考试的学生。为了申请VIGRE支持，学生将写一份简短的提案，描述研究策略和选择的选修活动。提案应确定学生将加入的研究小组，并解释学生对小组的预期贡献。准备考试的学生将获得少量的夏季支持奖。我们预计每个学年学期大约有18名学生得到VIGRE或匹配基金的支持，而获得至少部分夏季研究支持的人数略多。本科生活动：激发本科生对数学的兴趣，鼓励他们从事数学方面的职业——无论是教师、研究人员还是工业界——是我们提案的主要目标。实现这些目标的各种培训组成部分包括全面的研究经验，扩大的暑期实习计划，以及为合格的本科生提供帮助教学的机会。在VIGRE的支持下，我们将协调所有由部门和项目开展的本科生研究活动。鼓励研究生和博士后参与选定的本科项目的指导。参与的本科生将准备关于他们的活动的书面报告，并且每学期至少一次，学生们将在周六专门用于本科生研究的会议上展示他们的成果。报告被评为最佳的参加者将获得旅费，以便在适当的专业组织如美国数学协会和美国数学学会的区域或国家会议上报告其结果。我们预计每学年支持10-12名REU学生，夏季人数略少。博士后研究员：VIGRE博士后研究员的招聘将针对那些期望未来在研究型大学担任教职的近期博士，并且他们的研究兴趣至少与我们的一个研究小组有重大交集。为了让他们为这样的职业生涯做好准备，我们将为他们提供令人兴奋的研究机会、各级创新的教学经验，以及在课堂外的各种研究生和本科教育经验中发挥领导作用。博士后指导委员会将确保从博士后招聘过程开始，为所有VIGRE博士后提供合适的教师导师。博士后每学期（驻校）讲授一门课程。为了让他们为大学生涯做好准备，这些课程将涵盖各个层次。至少有一门课程将是该研究员研究领域的研究生课程，可能与教师导师共同授课。鼓励博士后在国家实验室、研究机构（如MSRI）或企业进行暑期或学期实习。我们将在第一个博士后之后每年支持四名VIGRE博士后，并由部门和项目各提供两名博士后的配套支持。由该部支持和挑选的两名研究员的选择将确保现有研究小组的持续实力和增长。该计划支持的两名学生将由计划教师委员会选出，以与其他部门建立跨学科联系。