VIGRE: Vertical Integration of Research and Education in the Mathematical Sciences at the University of Wisconsin-Madison

brualdi威斯康星大学麦迪逊分校数学系在研究生教育方面有着卓越的传统，可以追溯到100多年前，成功培养了900多名数学博士，他们现在在美国乃至世界各地的大学和行业中担任重要职位。在超过25年的时间里，它有一个成功的博士后项目（Van Vleck项目），有80多名数学博士在知名研究人员和教育工作者的指导下继续他们的研究和教学培训。我们的建议旨在维持，加强，增强，修改和整合威斯康星大学麦迪逊分校数学教育的五个领域：(1)数学本科教育，(2)应用数学，工程和物理本科课程（AMEP），(3)数学系内的数学博士课程，(4)数学科学中心内的应用数学科学跨学科课程（GPAMS），以及(5)纯数学和应用数学博士后培训。我们的主要目标是(1)扩大对本科生、研究生和博士后的数学教育，使他们能够(a)与科学家和工程师进行有效的互动和沟通(b)在很高的水平上进行数学研究，以及(c)理解计算在数学科学中的作用，并在适当的时候进行计算；(2)加强传统的核心数学本科、研究生和博士后的培养；(3)将获得博士学位的时间缩短到平均5年或更短。我们提案的组成部分整合了纯数学和应用数学的研究和教育，在本科，研究生和研究生阶段，以培养能够处理上述任务的数学科学家。我们新措施的重点包括：1。本科课程的实验组成部分在一门或多门课程中，将开发一个实验组成部分，它将清楚地说明应用数学建模物理问题的成功和局限性。实验将是为了清楚地说明要点而进行的演示，而不是为了训练学生进行实验。可能的课程有：应用动力系统与混沌，偏微分方程，应用数学导论，以及本科生和研究生流体力学。学生将以个人或小组的形式，从组合和概率的角度研究各种空间系统（主要是在格子上），并使用一些计算机模拟。在教师和博士后研究中出现的研究问题将被描述给研究这些问题和其他在研究过程中出现的问题的学生。这个实验室将在下午晚些时候开会，我们将寻找一两个聪明的高中生作为可能的参与者，例如来自当地高中的学生，他们是威斯康星州数学竞赛的获胜者。,是女士。2、科学人才搜索；数学博士课程和GPAMS。有效利用VIGRE基金，我们将：(a)招收优质的美国研究生，提供实习机会（VIGRE奖学金和助教奖学金）；(b)向研究生提供高质量的研究生课程，包括提供解决实际数学问题经验的跨学科培训；(c)减少获得学位的时间，将大量奖学金集中在一小群有潜力成为顶尖大学和实验室的研究数学家的学生身上。认识到许多毕业生没有在学术机构工作的事实，我们计划扩大数学系目前数学博士课程的范围，为我们的研究生提供解决实际数学问题的必要经验。为此，我们计划开办应用数学咨询公司。这将采取为数学研究生开设非标准研究生课程的形式，其主要目标是在大学数学研究生和其他领域的研究人员之间建立研究层面的跨学科合作。学生将在第二年学习这门两个学期的课程，由数学系的一名教员指导，并得到VIGRE资助的博士后研究员的帮助。该项目的目标是在数学和其他学科的研究人员之间建立新的联系，并鼓励数学研究生和其他学科的教师之间的互动。4. 我们的博士后项目——Van Vleck （V^2）项目吸引了一些最近最好的博士：每个V^2博士后都有一个教师导师，负责研究和教学，每学期教两门课程。他们与教师合作，与博士生一起工作，参加研讨会，教授初级和高级本科课程，以及至少一次研究生课程。V^2项目是我们研究生项目的延伸，为新博士提供持续（合作）研究和教师培训。我们将扩大和加强我们的博士后计划，包括维格尔·范·弗莱克的组成部分，V^3-计划。我们建议奖励几个V^3——博士后。博士后将为研究生提供必要的指导，跨学科的博士后将在GPAMS指导学生。跨学科的博士后研究员也将参与应用数学咨询项目。V^3——博士后将由常规教学职责（每学期一门课程）部分支持。他们将：(1)接受当地教师的指导，制定独立的研究计划，提高教学技能；(2)通过研究研讨会的展示，包括一次面向普通观众的学术讨论会，培养沟通技巧；(3)准备在专业期刊上发表论文；(4)在聘任结束时，拟备一份研究计划提交资助机构。此外，作为VIGRE项目的一部分，我们还将开发一些新的本科和研究生课程，包括数学学院教学课程（如何在大学水平教授数学）。该奖项的资金由数学科学部和MPS理事会的多学科活动办公室提供。

9819788BrualdiThe Department of Mathematics of the University of Wisconsin-Madison has a tradition of excellence in graduate education that goes back more than 100 years, successfully training more than 900 PhDs in Mathematics who now occupy important positions in universities and industries throughout the USA and indeed the world. For more than 25 years it has had a successful postdoctoral program (the Van Vleck program), with more than 80 Mathematics PhDs continuing their training in research and instruction under the mentorship of established researchers and educators. Our proposal seeks to sustain, strengthen, enhance, revise, and integrate the five areas of mathematics education at UW-Madison: (1) Mathematics Undergraduate Education, (2) Applied Mathematics, Engineering, and Physics Undergraduate Program (AMEP), (3) Mathematics PhD Program within the Department of Mathematics, (4) Applied Mathematical Sciences Interdisciplinary Program within the Center for Mathematical Sciences (GPAMS), and (5) Postdoctoral Training in Pure and Applied Mathematics. Our primary goals are (1) to broaden the mathematics education of undergraduate and graduate students, and postdoctoral fellows so that they will be able to (a) interact and communicate effectively with scientists and engineers (b) carry out mathematical research at a very high level, and (c) appreciate the role of computing in the mathematical sciences and, when appropriate, perform computations; (2) strengthen our traditional undergraduate, graduate, and postdoctoral programs in core mathematics, and (3) decrease the time to PhD degree to an average of 5 years or less. The components of our proposal integrate research and education in pure and applied mathematics, at the undergraduate, graduate, and post-graduate level in order to train mathematical scientists capable of handling the above noted tasks.Highlights of our new initiatives include: 1. Laboratory Components of Undergraduate Courses A laboratory component in one or more courses will be developed that will clearly illustrate the successes and limitations of Applied Mathematics Modeling of physical problems. The experiments would be demonstrations carried out to clearly illustrate points and not to train students for experimentation. Potential courses for such a component are: Applied Dynamical Systems and Chaos, PDEs, Introduction to Applied Mathematics, and undergraduate and graduate Fluid Mechanics. 2. Integrated Undergraduate, Graduate, and Faculty Research Lab in Spatial Systems\noindent Individually and in groups, students will study various spatial systems (mostly on lattices) from combinatorial and probabilistic perspectives, with some use of computer simulation. Research questions that arise in faculty and postdoctoral fellowsresearch will be described to students who investigate these and other questions that surface in their course of investigation. This Lab will meet in late afternoon, and we shall seek out one or two bright high school students as possible participants, e.g. students from local high schools who are among the winners of the Wisconsin Math., Engin., & Science Talent Search. 3. Mathematics PhD Program and GPAMS. With the effective use of VIGRE funds, we will: (a) Recruit quality American graduate students with offers of traineeships (VIGRE fellowships and Teaching Assistantships);(b) Provide graduate students with a quality graduate program, including interdisciplinary training that giving experience in solving practical mathematical problems; (c) Reduce the time-to-degree by targeting substantial fellowship money on a small group of students who have the potential of becoming research mathematicians at top universities and labs.Cognizant of the fact that many graduates do not work in academic settings, we plan to widen the scope of the current Mathematics PhD program in the Department of Mathematics, supplying our graduate students with the necessary experience in solving practical mathematical problems. To these ends, we are planning to start an Applied Mathematics Consulting . This would take the form of nonstandard graduate courses for mathematics graduate students whose main goal is to set up interdisciplinary cooperation, at a research level, between mathematics graduate students and researchers in other fields at the University. Students would take this two-semester course in their second year, supervised by a faculty member in the Department of Mathematics, with the help of post--doctoral fellows funded through VIGRE. The goals of this project are to foster new connections between researchers in mathematics and other disciplines and to encourage interaction between mathematics graduate students and faculty in other disciplines. 4. Post-Doctoral Training ProgramOur post-doctoral program - the Van Vleck (V^2) program has attracted some of the best recent PhDs: each V^2-postdoc has a faculty mentor for both research and teaching, and teaches two courses a semester. They collaborate with faculty, work with PhD students, participate in seminars, and teach elementary and advanced undergraduate courses and, at least once, a graduate course. The V^2--program is an extension of our graduate program providing continuing (collaborative) research and teacher training for new PhDs.We will extend and strengthen our postdoctoral program, to include a Vigre Van Vleck component, the V^3--program. We propose to award several V^3--postdocs. The post--doctoral fellows will provide essential mentoring to the graduate students with interdisciplinary postdocs mentoring students in GPAMS. The interdisciplinary post--doctoral fellows will also participate in the Applied Mathematics Consulting Program previously described. V^3--postdocs will be supported in part by regular teaching duties (one course each semester). They will be: (1) mentored by local faculty, develop an independent research program, and improve teaching skills; (2) develop communication skills through presentation of research seminars, including one colloquium talk for a general audience; (3) prepare papers for publication in professional journals; (4) prepare a research proposal for submission to a funding agency at the conclusion of her or his appointment.As part of our VIGRE program, we will, in addition, develop several new undergraduate and graduate courses, including a Mathematics College Teaching Course (How to teach Math at the College level). Funding for this award is provided by the Division of Mathematical Sciencesand the MPS Directorate's Office of Multidisciplinary Activities.