VIGRE: Integration of Research and Education in Mathematics and Applied Mathematics

摘要布朗大学数学系和应用数学系将在美国国家科学基金会VIGRE项目的资助下开展一项研究与教育相结合的项目。我们将开展本科生、研究生和博士后水平的活动，以加强和更好地协调两个系的数学科学项目。通过数学和应用数学系成员的参与和支持，特别是VIGRE博士后导师，VIGRE研究生学员和布朗大学本科生，我们的项目将在所有数学经验和资历的参与者之间建立科学交流和研究互动。VIGRE计划是数学系和应用数学系审查和重塑其研究生和本科课程的机会，以应对学科，研究重点和具有研究经验的数学学位持有人职业机会的不断变化。我们计划重新考虑我们的项目，扩大它们的范围，深化它们对研究生教育的贡献，而不扩大布朗大学数学科学项目的规模。我们的主要目标是在我们的项目中开展创新活动，这些活动将服务于(1)提供实践研究数学家和各级数学学生之间的科学互动模式，(2)让我们的研究生和本科生更深入地接触当前研究兴趣的领域和材料，(3)培养更具科学素养和更善于表达的研究生。并且他们在完成学位后拥有更广泛的职业可能性的基本技能。该计划将同时支持12名研究生作为VIGRE研究生培训生（gt）， 3名VIGRE博士后（vp）和最多12个本科生研究项目（utra）。这些资源将在两个数学系之间平均分配，如下所述。布朗大学的VIGRE项目将由以下部分组成：(1)研究生培训计划（GTs）(2)本科生辅导和研究计划（UTRAs）(3)博士后奖学金计划（VPs）(4)支持科学领域的女性指导计划（WiSE）和科学领域代表性不足的少数民族指导计划（ExSEL）(5)本科生数学研究生和同伴辅导资源中心（MRC）(6)向当地高中的资优高中生提供外展计划(7)向弱势群体提供外展计划(8)由VIGRE赞助的工业实习项目和国家实验室研究生培训项目（GTs）为学生提供了在一个激励和富有研究成果的环境中完成数学研究生教育的机会，研究和教学学期数量平衡，并有足够的夏季支持。博士后将有机会在研究小组中密切合作，减少教学负担，并与高级教师和研究生密切接触。研究生、本科生和博士后项目的主要特点包括：(1)一系列VIGRE研究生研讨会，以实验科学中常见的“文学研讨会”和/或“实验室会议”为例。(2)额外的高级研究生/研究水平研讨会，讨论数学和应用数学的广泛当前主题。(3)研究生课程中以科学传播和有效数学教学为重点的系列研讨课程。(4)关注由教师和VIGRE博士后指导的个人本科生研究活动（UTRAs）。这些活动的资源将来自VIGRE项目拨款以及数学系和应用数学系之间更高水平的协调与合作。VIGRE支持的研究生实习生将获得五年的学习支持，并在布朗大学任职期间教授两到四个学期。他们还将参与VIGRE日常课程之外的活动，并直接参与协调。涉及本科生的活动包括(1)UTRA研究研讨会，(2)与科学本科支持小组中的WiSE女性以及与ExSEL少数民族科学支持小组的指导活动，以及(3)组织和参与本科生数学资源中心MRC。涉及当地社区的活动包括(4)参与普罗维登斯地区学校的拓展项目，针对有天赋的和弱势的学生和教师，以及社区继续教育中心的项目。研究生受训者将被鼓励拓宽他们的科学背景，超越他们特定研究专业的限制和跨部门的界限。特别是VIGRE计划打算使布朗大学数学和应用数学之间的界面更具渗透性。此外，还将定期在工业和国家实验室进行暑期实习。VIGRE博士后将受益于数学和应用数学项目的强大研究环境，他们将被期望为VIGRE研究生研讨会做出贡献。他们将被要求在校期间每学期教一门课程。他们也将有机会与国家实验室和工业界的研究人员合作，并且他们有望从与布朗大学化学系、计算机科学系、工程系、物理系以及以校园为基础的认知小组（计算机和自然视觉、人工和自然智能）的交流中受益。目标：我们打算为我们的博士学位提供一个更广泛的数学和科学的观点，在其中的特定学科的关系的观点。他们应该意识到并为学术界内外的许多可能的职业做好准备，这些职业对具有数学研究经验的学位持有者开放。研究生将接受科学交流和数学教学方面的培训。我们打算通过重点识别和招聘项目，提高即将入学的研究生班级的质量，并增加女性和代表性不足的少数民族学生在我们项目中的比例。布朗大学VIGRE项目将特别关注这些学生的留用问题。VIGRE资源将为参与者增加研究支持学期的数量，因此我们期望降低获得学位的平均时间。我们打算培养准备更充分的数学专业本科生，他们已经有了一些研究经验，其中许多人有望继续读研究生，并随后在数学科学领域从事职业。我们希望VIGRE的博士后在学术就业市场上有额外的竞争优势，从他们在布朗大学的研究经验的广度，从更多的合作研究机会，从与行业和国家实验室的联系的可用性，从对数学教学和交流的关注，以及他们在高质量本科院校的教学经验。影响：我们预计我们将能够增加主修数学的美国本科生的数量，并增加进入数学研究生院的人数。我们希望增加Am的比例

AbstractBrown The Mathematics Department and the Division of Applied Mathematics at Brown University will undertake a program of integration of research and education, supported by a grant from the NSF VIGRE Program. We will develop activities on the undergraduate, graduate and postdoctoral level which will strengthen and provide better coordination for the mathematical sciences program of the two departments. Through the participation and support of the members of the Mathematics and Applied Mathematics departments, in particular VIGRE Postdoctoral Instructors, VIGRE Graduate Trainees and Brown undergraduates, our program will forge scientific communication and research interaction between participants at all levels of mathematical experience and seniority. The VIGRE program is an opportunity for the Mathematics Department and the Division of Applied Mathematics to review and reshape their graduate and undergraduate programs, responding to changes in the discipline, research priorities and the evolving landscape of career opportunities for Mathematics degree holders with experience in research. We plan to rethink our programs, broaden their scope and deepen their contributions to graduate education, without enlarging the size of the mathematical sciences program at Brown. Our main objectives are to develop innovative activities in our programs which will serve (1) to provide modes of scientific interaction between practicing research mathematicians and students of mathematics at all levels, (2) to give our graduate and undergraduate students more in-depth contact with areas and material of current research interest, and (3) to produce graduate students who are more scientifically literate and more articulate, and who possess the basic skills for a wider range of career possibilities after completing their degree. This program will support 12 graduate students as VIGRE graduate trainees (GTs), 3 VIGRE postdoctoral fellows (VPs) and up to 12 undergraduate research projects (UTRAs) at a time. These resources will be shared equally between the two mathematics departments as described below. The VIGRE program at Brown will consist of the following components: (1) a graduate traineeship program (GTs) (2) an undergraduate tutoring and research program (UTRAs) (3) a postdoctoral fellowship program (VPs) (4) support for a mentoring program for women in sciences (WiSE) and under-represented minorities in sciences (ExSEL) (5) a graduate and peer tutoring resource center in mathematics for undergraduates (MRC) (6) a program of outreach to gifted high school students at local area high schools (7) a program of outreach for disadvantaged high school students, resumed education students and their teachers (8) a program of internships with industry and with the National Laboratories Graduate Traineeships (GTs) sponsored by VIGRE are opportunities for students to complete a graduate education in mathematics in a stimulating and research productive environment, with a balanced number of research and teaching semesters, and with adequate summer support. Postdoctoral Fellows (VPs) will have the opportunity to work closely in research groups, with reduced teaching load and with close contact with both senior faculty and graduate students.Principal features of the graduate, undergraduate and postdoctoral programs include: (1) A series of VIGRE graduate seminars, modeled on the example of a 'literature seminar' and/or a 'lab meeting' that is common in experimental sciences. (2) Additional advanced graduate/research level seminars, on a broad set of current topics in mathematics and applied mathematics. (3) A seminar course series in the graduate program focusing on scientific communication and effective mathematics instruction. (4) A focus on individual undergraduate research activities (UTRAs), directed by faculty and VIGRE Postdoctoral fellows.Resources for these activities will come both from the VIGRE program grant and from an increased level of coordination and cooperation between the Mathematics Department and the Division of Applied Mathematics. Graduate Trainees supported by VIGRE will expect support for five years of study, and teach between two and four semesters during their tenure at Brown. They will also participate in the VIGRE activities outside of their usual course work, which they will be directly involved in coordinating. Activities involving undergraduates include (1) UTRA research seminars, (2) mentoring activities with the WiSE women in sciences undergraduate support group, and with the ExSEL minority sciences support group, and (3) organization and participation in the MRC, mathematics drop-in resource centers for undergraduates. Activities which involve the local community include (4) participation in outreach programs to Providence area schools, aimed both for gifted and for disadvantaged students and for teachers, and programs in community continuing education centers.Graduate Trainees will be encouraged to broaden their scientific background, past the confines of their particular research specialization and across department boundaries. In particular the VIGRE program intends to make the interface at Brown between Mathematics and Applied Mathematics substantially more permeable. Furthermore, there will be regular programs of summer internships with industry and national labs.VIGRE Postdoctoral Fellows will benefit from the strong research environment in both the programs in mathematics and applied mathematics, and they will be expected to contribute to the VIGRE graduate seminars. They will be required to teach one course each semester that they are on campus. They will also have opportunities to collaborate with research staff at national labs and in industry, and they are expected to benefit from communication with the Brown departments of Chemistry, Computer Science, Engineering, Physics, and the campus-based group in cognition (computer and natural vision, artificial and natural intelligence).Objectives: We intend to provide our finishing PhDs with a broader view of mathematics and science, with perspective on the relationship of their particular discipline within it. They should be aware and prepared for the many possible careers both in and outside of academia that are open to degree holders with mathematics research experience. Graduate students will receive training in scientific communication and in mathematics instruction. We intend to increase the quality of our incoming graduate classes, through a focussed identification and recruitment program, and to increase the proportion of women and under represented minority students in our program. The Brown VIGRE program will pay particular attention to the problem of retention of these students. VIGRE resources will increase the number of research support semesters for participants, and as a result we expect to lower the average time to degree. We intend to produce better prepared undergraduate mathematics concentrators, who already have some research experience, many of whom are expected to go on to graduate school and subsequently a career in the mathematical sciences. We expect our VIGRE Postdoctoral Fellows to have an additional competitive advantage in the academic job market, from the breadth of their research experience at Brown, from the increased opportunity for collaborative research, from the availability of contacts with industry and national labs, and from the focus on instruction and communication of mathematics, and their experience teaching at a high quality undergraduate institution.Impact: We expect that we will be able to increase the numbers of American undergraduate majors in mathematics, and to increase the subset of the pool which goes on to graduate school in mathematics. We expect to increase the proportion of Am