Mathematics Research and Education at the University of Illinois at Urbana-Champaign

摘要：美国伊利诺伊大学厄巴纳-香槟分校（UIUC） VIGRE项目的主要目标是通过创新的、综合的教学和研究活动来推进数学事业。数学系是世界上规模最大、最活跃的数学系之一。牛津大学的优势，特别是在工程和科学方面，对数学课程的需求很大；数学系每年向大约10,000名本科生教授数学，并有200名学生参加其研究生课程。UIUC的VIGRE项目有三个组成部分：通过课程改革和教学创新来加强研究生项目，通过在研讨会和课程中引入新的研究和教学机会来改善本科项目，扩大与教师研究兴趣相关的博士后项目，并为博士后提供教学和研究培训。此外，研究生、本科生和博士后研究员与不同类型的同侪小组的教师联系，以促进交流，促进专业发展，并垂直整合我们的活动。在研究生教育中，创新的新课程将研究生引入教师和博士后的研究。研究生将开办自己的研讨会，在数学研究方面给予他们自主权。VIGRE奖学金给研究生独立学习的时间，让他们在自己选择的数学专业上更快成熟。其中一些研究金是专门为促进跨学科研究活动而设立的。与此同时，教职员工为研究生提供指导教学经验，为他们进入课堂环境做好准备。在本科生的经历中，特殊的调查课程为数学在UIUC校园的许多学科中所扮演的角色提供了新的见解。本科生的研究经历使本科生对数学研究的性质及其在跨学科研究中的作用有了一个清晰的认识。与教师导师的特殊教师培训经验帮助本科生发展他们的课堂教学技能。VIGRE支持的博士后职位将使UIUC能够将最近的博士学位纳入数学系的研究和教学活动中。该系为VIGRE博士后提供研究生和本科水平的教学机会。教师也指导VIGRE博士后在自己的研究领域。在所有三个专业级别中，都有一个指导结构，包括研究生、本科生和博士后的正规教师。形成了两种类型的指导对等组，跨级别对等组（ALPs）和对等组之间的研究（rap）。项目由本科生、研究生、博士后和教职员工组成；ALPs独立运行，并制定自己的小组研讨会和讨论议程。RAPs包括高级研究生、博士后助理和有共同数学兴趣的教员；rap还自主运行，并计划自己的研讨会和研究活动。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。

AbstractRosenblattThe main goal of the VIGRE program at the University of Illinois at Urbana-Champaign (UIUC) is to advance the mathematics enterprise through innovative, integrated activities in teaching and research. The Department of Mathematics is one of the largest and most active mathematics departments in the world. The University's strength, particularly in engineering and the sciences, creates a huge demand for mathematics courses; the Department of Mathematics teaches mathematics to about 10,000 undergraduate students each year, and has 200 students enrolled in its graduate programs.The VIGRE program at UIUC has three components:strengthening the graduate program through curricular reform and instructional innovation improving the undergraduate program through the introduction of new research and teaching opportunities in seminars and courses expanding the postdoctoral program in correlation with the faculty's research interests, and providing the postdoctoral associates with training in teaching and research. Moreover, graduate students, undergraduate students, and postdoctoral associates are linked with faculty in different types of peer groups to facilitate communication, to promote professional development, and to vertically integrate our activities.In graduate education, innovative new courses introduce the graduate students to the research of the faculty and postdoctoral associates. Graduate students will run their own seminars, giving them autonomy in their mathematical studies. VIGRE fellowships give the graduate students independent study time and allow them to mature more rapidly in their chosen mathematical specialties. Some of these fellowships are specifically designed to foster interdisciplinary research activities. At the same time, the faculty members give graduate students supervised teaching experiences that prepare them for the classroom environment.In undergraduate experiences, special survey courses provide new insights into the role of mathematics in the many disciplines represented at the UIUC campus. Research experiences for undergraduates give the undergraduate students a clear picture of the nature of mathematical research and of its role in interdisciplinary studies. Special teacher training experiences with faculty mentors help undergraduate students to develop their classroom instructional skills.The postdoctoral positions supported by VIGRE will enable UIUC to integrate recent Ph.D.s into the research and instructional activities of the Department of Mathematics. The Department provides the VIGRE postdoctoral associates teaching opportunities at both the graduate and the undergraduate level. Faculty members also mentor the VIGRE postdoctoral associates in their own research areas. Over all of the three professional levels, there is a mentoring structure that involves the regular faculty with graduate students, undergraduate students, and postdoctoral students. There are two types of mentoring peer groups formed, Across Level Peers groups (ALPs) and Research Among Peers groups (RAPs). The ALPs consist of undergraduate students, graduate students, postdoctoral students and faculty members; ALPs run independently and develop their own group seminar and discussion agendas. The RAPs include advanced graduate students, postdoctoral associates and faculty members with specific mathematical interests in common; RAPs also run autonomously and plan their own seminar and research activities. Funding for this activity was provided by the Division of Mathematical Sciences and the MPS Office for Multidisciplinary Activity.