REU Site: UCSB Mathematics Summer Research Program for Undergraduates

UCSB面向本科生的数学暑期研究项目旨在为来自不同背景的本科生提供全面的数学研究体验。在为期八周的课程中，学生们将学习调查和解决不同数学领域的公开问题，在协作环境中工作，通过演讲和书面报告交流他们的数学结果，并将他们的发现发表在适当的期刊上，目的是传播他们的研究。该项目将通过与南加州大学伯克利分校数学系的研究生、研究生导师、教职员工和博士后的互动，让参与者接触到研究生的日常生活。此外，通过专业发展工作坊，参与者将了解行业中需要具有良好研究技能的专业人员的不同领域。从历史上看，UCSB REU并不专注于特定的数学领域。然而，该项目打算面向具有不同数学背景的学生。因此，研究项目可能是线性代数、矩阵分析、数值线性代数、组合学和图论，也就是说，在不需要学生广泛数学背景的领域。本程序以前研究过的主题的例子包括：1)原始循环矩阵；2)矩阵多项式和线性化；3)矩阵方程；4)停放函数；5)Alexander和Jones多项式；6)序列动力系统。根据参与该计划的导师活跃的研究领域，主题每年都会改变。最终目标是让学生接触到解决这些领域问题的技术和方法，在被推荐的专业期刊上发表论文，并参加本科生会议并发表演讲。REU以一次海报会议结束，在会议上，在UCSB所有部门进行暑期研究的本科生展示了他们的结果，并使该领域的非专家能够获得这些结果。以前的项目和出版物以及关于该计划的更多信息可以在网站上找到http://math.ucsb.edu/REU.This网站由国防部与美国国家科学基金会REU计划合作支持。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

The UCSB Mathematics Summer Research Program for Undergraduates aims to provide a full research experience to undergraduate students in mathematics from different backgrounds. Over the course of the eight-week program, the students will learn to investigate and solve open problems in diverse areas of mathematics, to work in a collaborative environment, to communicate their mathematical results through talks and written reports, and to publish their findings in appropriate journals with the goal of disseminating their research. The program will expose the participants to daily life in graduate school, through interactions with graduate students, graduate advisors, faculty and postdocs in the UCSB math department. In addition, through professional development workshops, the participants will learn about different areas in industry that demand professionals with good research skills. Historically, the UCSB REU has not focused on a specific area of mathematics. However, the program intends to be accessible to students with a variety of backgrounds in mathematics. Thus, the research projects are likely to be in linear algebra, matrix analysis, numerical linear algebra, combinatorics and graph theory; that is, in areas that do not require extensive mathematical background from students. Examples of topics that have been studied in this program before include 1) primitive circulant matrices; 2) matrix polynomials and linearizations; 3) matrix equations; 4) parking functions; 5) Alexander and Jones polynomials; 6) sequential dynamical systems. The topics will change every year depending on the active research areas of the mentors involved in the program. The final goal is to expose the students to the techniques and methods used to tackle problems in these areas, to publish papers in refereed professional journals, and to participate and give talks in conferences for undergraduates. The REU concludes with a poster conference in which undergraduates doing summer research in all the UCSB departments present their results and make it accessible to non-experts in the area. Previous projects and publications as well as more information about the program can be found on the website http://math.ucsb.edu/REU.This site is supported by the Department of Defense in partnership with the NSF REU program.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.