Duke University Program for Vertically Integrated, Interdisciplinary Reseasrch

摘要：杜克大学数学系VIGRE项目的设计符合美国国家科学基金会的既定目标，即在保持现有学科优势的同时，“增加（增加）涉及数学的跨学科活动”和“鼓励（鼓励）旨在扩大本科和研究生课程的活动”。跨学科研究是垂直整合的完美环境，杜克大学数学系在代数几何、分析、微分方程、微分几何、数值分析、概率和拓扑等方面都有现有的学科优势。我们将使用团队研究模式来加强我们的研究生培养计划和我们的本科和博士后项目。研究生和本科生将在职业生涯的早期面临研究问题，并将通过各自的项目不断接触这些问题。高级研究生和博士后将在垂直整合研究研讨会课程和团队研究小组中担任项目负责人的新角色。作为数学训练的一部分，所有学生和博士后都将发展计算、沟通和协作技能，从而拓宽他们作为数学科学家的机会范围。该计划的目标是让学生和博士后完成他们的项目，具有广泛的科学知识和对科学团队内部运作的清晰理解，以及学术研究和教学组合，这将提高他们的职业发展潜力。在本科课程中，我们的目标是提高学生对数学的热情，以及在杜克大学各级训练中数学在研究中的作用。我们将增加第一年和主要研讨会的数量，旨在让学生接触当前的研究课题。目前的研讨会课程主题包括密码学、生理学和医学、几何学和最优化。新的主题包括心脏动力学、引力透镜和人工智能。一个针对对数学、统计学和计算机科学感兴趣的一年级女生的科学新视角研讨会将让年轻学生了解高级科学家、博士后和研究生的最新研究。本科VIGRE项目的基石是一个新的为期两年的强化研究项目，名为“VIGRE本科生实践研究”（PRUV，发音为“prove”），针对高等数学专业，包括课程作业、垂直整合环境中的暑期实习和高级论文。本科课程的这些改进旨在让更多的学生参与研究活动。我们预计，结果之一将是更多关于研究问题的高级荣誉论文，以及更多的学生选择申请数学科学研究生院。对于研究生项目，VIGRE补助金将与杜克大学的资源相结合，以支持所有没有教学职责的一年级学生。第一年之后，最优秀的vigre合格学生将获得每年一个学期的教学释放，以便将更多的精力投入到研究中。所有研究生将有机会在垂直整合的研究团队中工作，包括博士后，研究生PRUV学生和至少一名数学教授。那些研究跨学科问题的人还将与至少一位来自其他学科的教授合作。目前的跨学科活动包括森林砍伐和气溶胶动力学、几何计算、颗粒流、心脏动力学、液体膜、光子带隙、生理学和医学、弦理论和多孔流动的不确定性，与杜克大学环境学院、计算机科学、物理学、生物医学工程、细胞生物学、土木与环境工程和统计与决策科学研究所的合作者合作。研究生教师培训目前从第一年开始，由学生监督微积分实验室。为了缩短取得学位的时间和增加留校率，我们将把所有研究生的教学责任和教师培训推迟一年。这将使所有第一年的研究生能够在第二年开始之前专注于通过资格考试所需的基础课程。目前的教师培训计划将扩大到包括学生和博士后的替代教学经验，包括与高中教师的联系，以及对本科生和研究生的指导。一项新的计算要求将成为他们第一年课程的一部分。目前，研究生每周举办一次研讨会，由研究生和博士后主持，针对一年级和二年级的研究生。我们将鼓励PRUV本科生参加本次研讨会。VIGRE博士后将在整个项目中发挥领导作用。每年，前三年，VIGRE将聘用两名博士后，任期三年。这些职位将与杜克大学资助的助理研究教授（ARP）平行。VIGRE博士后将有机会在团队研究小组中发挥强大的领导作用，包括指导研究生和本科生，并制定明确的独立研究计划。他们还将有机会在以下至少一项活动中发挥重要的支持作用：(1)协调研究研讨会和讲习班，(2)共同指导暑期PRUV学生和研究生实习，(3)在写作研讨会上帮助本科生和研究生。博士后和学生将在CHISEL项目“卡罗莱纳高中教育领导项目”中与高中教师合作。他们将设计课堂使用的模块，向高中生介绍数学在当前研究中的应用。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。

AbstractBertozziThe Duke Mathematics Department's VIGRE program was designed with NSF's stated objectivesof "increas(ing) interdisciplinary activities involving mathematics" and "encourag(ing) activities aimed at broadening undergraduate and graduate curricula" in mind while maintaining existing disciplinary strengths. Interdisciplinary research is a perfect setting for vertical integration andthe Duke Mathematics Department has existing disciplinary strengths in algebraic geometry, analysis, differential equations, differential geometry, numerical analysis, probability, and topology.We will use the team research model to enhance our graduate training program and our undergraduate and postdoctoral programs. Graduate and undergraduate students will confront research problems early in their careers and will have ongoing exposure to them through their respective programs. Advanced graduate students and postdocs will take on new roles as project leaders in vertically integrated research seminar courses and in team research groups.All students and postdocs will develop skills in computation, communication and collaboration as part of their mathematical training, thereby broadening the range of opportunities availableto them as mathematical scientists. The goal of the program is to have students and postdocs completing their programs with a broad scientific knowledge and clear understanding of the inner workings of a scientific team, as well as an academic research and teaching portfolio that will enhance their career advancement potential.In the undergraduate program our goal is to increase students' enthusiasm for mathematics and its role in research at all levels of their training at Duke. We will increase the number of first-year and major seminars aimed at exposing students to current topics of research. Current seminar course topics include cryptography, physiology and medicine, geometry, and optimization. New topics include heart dynamics, gravitational lensing, and artificial intelligence. A new Perspectives on Science seminar aimed at first-year women interested in mathematics, statistics and computer science will expose young students to current research of senior scientists, postdocs, and graduate students.The cornerstone of the undergraduate VIGRE program is a new two-year intensive research program, entitled `Practical Research for Undergraduates with VIGRE' (PRUV, pronounced "prove"), for advanced mathematics majors, which integrates course work, summer internships in a vertically integrated environment, and senior theses. These improvements in the undergraduate program are targeted to involve more students in research activities. We expectthat one outcome will be more senior honors theses on research problems and more students choosing to apply to graduate school in the mathematical sciences.For the graduate program, the VIGRE grant will be combined with Duke resources to support all first year students without teaching duties. After the first year, the strongest VIGRE-eligible students will receive a one semester-per-year teaching release in order to direct more of their energy towards research. All graduate students in the graduate program will have the opportunity to work in vertically integrated research teams, including postdocs, graduate students PRUV students, and at least one mathematics professor. Those working on interdisciplinary problems will also collaborate with at least one professor from another discipline. Current interdisciplinary activities include deforestation and aerosol dynamics, geometric computing, granular flow, heart dynamics, liquid films, photonic band gaps, physiology and medicine, string theory, and uncertainty in porous flow, with Duke collaborators in the School of the Environment, Computer Science, Physics, Biomedical Engineering, Cell Biology, Civil and Environmental Engineering, and the Institute for Statistics and Decision Sciences. Graduate teacher training currently begins in the first-year with students supervisingcalculus laboratories. In order to shorten time to degree and increase retention, we will postpone teaching responsibilities and teacher training by one year for all graduate students.This will enable all first year graduate students to focus on fundamental course work required to pass the qualifying exam before the beginning of year two. The current teacher-training program will be expanded to include alternative teaching experiences for students and postdocsincluding outreach to high school teachers, and mentoring of undergraduate and graduate students. A new computational requirement will be part of their first-year curriculum. The graduate students currently run a weekly seminar with talks aimed at first and second year graduate students given by graduate students and postdocs. PRUV undergraduates will be encouraged to attend this seminar.VIGRE postdocs will play a leadership role in the overall program. Each year, for the first three years, two VIGRE postdocs will be hired for three year terms. These positions will parallel existing Duke funded Assistant Research Professors (ARP). VIGRE Postdocs will have the opportunity to play a strong leadership role in the team research groups including mentoring graduate students and undergraduates and developing a well-defined independent research program. They will also have the opportunity to take on a significant supporting role in at least one of the following activities: (1) coordinating research seminars and workshops, (2) co-supervising summer PRUV students and graduate student internships, (3) helping undergraduates and graduate students in a writing workshop.Postdocs and students will collaborate with high school teachers in Project CHISEL `Carolina High School Educational Leadership project'. They will design modules for classroom usethat will introduce high school students to the use of mathematics in current research.Funding for this activity was provided by the Division of Mathematical Sciences and the MPS Office for Multidisciplinary Activity.