An Integrated Program of Training in Mathematics

9819728加州大学伯克利分校数学系VIGRE计划旨在改善该系对各级数学学者和教育工作者的培训计划。该项目将努力创建一个学者社区，让他们都觉得自己和自己的工作是一个相互联系的整体的组成部分。在过去几年中，该部一直在加紧审查和修订整个课程。迄今为止，最广泛的修订工作发生在低年级，数学系的教师和研究生组成的团队，经常与其他系的教师和研究生一起，设计工作表和计算机模块，用于我们微积分课程的讨论部分。这些课程的学生将体验到更积极的学习环境。在高年级，我们计划引入新的课程来丰富课程，并将我们的专业引入数学的应用。一个这样的课程已经成功地到位是小波和信号处理课程。其他人也会效仿。摩尔教授和吴教授获得了斯图尔特基金会的资助，为即将进入中学教学的数学专业学生开发一门新课程的材料，并作为一门面向现任中学教师的专业发展课程。课程的概念是“从高等（即大学）的角度来看高中数学”。其基本思想来自于菲利克斯·克莱因著名的小书《高等观点下的初等数学》。VIGRE基金将帮助我们将这门课程用于当前高中教师的专业发展。本系亦启动了一项名为“数学老师”的新计划，以培养中学数学教师领袖。数学专业的学生可以在大四的时候报名参加这个项目，同时完成专业和开始教育课程和实践教学。在第五年，他们完成了教师培训，并选修了两门额外的数学课程。我们为参加这个项目的学生提供津贴。研究生课程的修订正在进行中，但仅处于初始阶段。本系在试验性的基础上开始了本科生研究研讨会计划。一名资深教师将带领研讨会，平均约有7或8名我们最有才华的本科专业的学生参加，作为本科生研究经验，并将获得津贴。在教师的几次初步讲座奠定基础之后，学生将在教师的指导下阅读期刊文章并呈现论文或论文中的结果，并在此过程中填写一些细节。这种经历将帮助学生学习如何获取和使用数学文献，并将提高他们的沟通技巧。一个研究生，通常是一个和老师一起写论文的学生，将协助研讨会，从而导致从研究到研究生教育再到本科教育的垂直整合。VIGRE需要通过提供研究津贴来继续和增加这个项目。我们还将启动一个夏季研究项目计划，在许多情况下，这些研究项目将从这些研究研讨会中流出，这样学生就可以加深和扩展他们的研究经验，并获得夏季工作津贴。在研究生阶段，VIGRE项目的目标首先是减少获得学位的平均时间，利用我们应用数学项目的优势以及我们与劳伦斯伯克利国家实验室（LBNL）的联系，以鼓励更多的学生利用应用领域的机会。我们将强烈鼓励所有的研究生在工业或国家实验室进行暑期实习。11个VIGRE培训生将致力于支持一年级学生，目标是为每个一年级学生提供奖学金或实习支持。我们认为，确保没有一年级学生担任研究生导师（GSI）是VIGRE基金的最佳用途，可以减少研究生获得学位的平均时间。在随后的几年中，VIGRE学员将担任gsi，接受教学培训和指导，并将在高级教员的适当指导下，在夏季会议中独立负责课程的丰富教学经验。这五个半学期的VIGRE博士后奖学金将与由大学资助的教学任命相结合。所有博士后都将被分配一名导师，导师将是学院的资深成员，其职责不仅包括指导研究员的研究项目，还包括他们的教学。教学任务将包括高年级和研究生课程。鼓励博士后通过与校园其他部门和LBNL的联系来扩大他们的经验。该部门将系统地收集有关VIGRE计划的一些关键指标的绩效的定量和定性数据，我们将任命一个访问委员会，每年访问该部门，并向我们提供我们实现目标进展的外部评估。该奖项的资金由数学科学司、MPS理事会多学科活动和初等、中等和非正式教育办公室（ESIE）提供。

9819728The University of California Berkeley Mathematics Department VIGRE program is designed to improve the Department's training programs for mathematics scholars and educators at all levels. The program will try to create a community of scholars who all feel that they and their work are an integral part of a connected whole.During the last few years the Department has been engaged intensively in review and revision of the entire curriculum. The most extensive revision effort to date has been in the lower-division where teams of faculty and graduate students from the Mathematics Department, often joined by faculty and graduate students from other departments, have been designing worksheets and computer modules to be used in the discussion sections of our calculus courses. Students in these courses will experience a more active learning environment. At the upper-division level, we plan to introduce new courses to enrich the curriculum and that will introduce our majors to applications of mathematics. One such course already successfully in place is a course on Wavelets and Signal Processing. Others will follow. Professors Moore and Wu have been awarded a grant by the Stuart Foundation to develop materials for a new course for math majors going into secondary school teaching and as a course open to current secondary school teachers for professional development. The concept of the course would be "High School Mathematics from an Advanced (i.e. College) Point of View". The underlying idea flows from Felix Klein's famous little book "Elementary Mathematics from an Advanced Standpoint". The VIGRE grant will help us to employ this course for professional development of current high school teachers. The Department has also initiated a new program TeachMath to prepare secondary school mathematics teacher leaders. Mathematics majors can enroll in this program in their senior year and simultaneously complete the major and begin education courses and practice teaching. In a fifth year they complete their teacher training and take two additional mathematics course. We provide a stipend to students who are enrolled in the program. Graduate curriculum revision is underway but is only in its initial phase.The Department has started on an experimental basis a program of undergraduate research seminars. A senior faculty member will lead the seminar in which an average of about 7 or 8 of our most talented undergraduate majors will participate as an Undergraduate Research Experience and will receive a stipend. After a few initial lectures by the faculty member to set the stage, students will read journal articles and present, under the guidance of the faculty member, the results in the paper or papers, and in the process filling in some details. This experience will help students learn how to access and use the mathematics literature, and will enhance their communications skills. A graduate student, usually a student working on a dissertation with the faculty member, will assist in the seminar, thus leading to a vertical integration from research to graduate education to undergraduate education. VIGRE funding is needed to continue and increase this program by providing research stipends. We will also initiate a program of summer research projects that will in many cases flow out of these research seminars so students can deepen and extend their research experience and receive a stipend for work in the summer.At the graduate level, our goal in the VIGRE program is first to decrease average time to degree, to build on the strengths of our applied mathematics program and our connections with the Lawrence Berkeley National Laboratory (LBNL) in order to encourage more of our students to take advantage of the opportunities in applied areas that are available. We will strongly encourage all graduate students to take a summer internship in industry or a National Laboratory. The eleven VIGRE traineeships will be dedicated to support first year students with the goal of providing every first year student with fellowship or traineeship support. We believe that ensuring that no first year student serves as a Graduate Student Instructor (GSI) is the best use of the VIGRE funds to reduce average time to degree for our graduate students. During subsequent years the VIGRE trainees will serve as GSIs, will receive training and mentoring for their teaching, and will have a substantial teaching experience of having independent responsibility for a course in Summer Session, with appropriate mentoring by a senior faculty member.The five half-time VIGRE postdoctoral fellowships will be coupled with teaching appointments funded by the University. All postdoctoral fellows will be assigned a mentor who will be a senior member of the faculty whose duties will include not only mentoring the research program of the fellow, but also their teaching. Teaching assignments will consist of upper division and graduate courses. Postdoctoral fellows will be encouraged to broaden their experience through contacts with other Departments on campus and through contacts at LBNL.The Department will systematically collect quantitative and qualitative data concerning performance on a number of key indicators of the VIGRE program, and we will appoint a Visiting Committee which will visit the Department yearly and provide us with an external evaluation of our progress toward our goals.Funding for this award is provided by the Division of Mathematical Sciences, the MPS Directorate's Office of Multidisciplinary Activities and Elementary, Secondary and Informal Education (ESIE).