REU Site: Research Training for Undergraduates in Mathematical Analysis with Applications in Allied Fields

REU项目“数学分析与相关领域应用的本科生研究培训”由田纳西大学查塔努加分校数学系的教职员工运营，每年为10名本科生提供为期8周的暑期研究经历。该计划采用研究方法培训，动手研究项目和小组活动，将导致参与者有效的独立研究。该项目旨在通过招募和鼓励女性、来自弱势群体的少数族裔、第一代大学生以及来自研究机会有限的机构的学生，提高对数学科学的参与。为了促进本科数学研究的兴奋和发展，我们结合了纯数学和应用数学以及计算建模的元素，特别关注数论，概率论和动力系统。该课程旨在向学生介绍数学的力量和适用性，并鼓励他们从事数学科学方面的职业。它的成功将为区域性城市大学的数学本科研究提供一个全国性的模式。该计划将包括海报会议和学生演讲，一系列学术讨论会，由世界级研究人员领导的跨学科数学应用，以及数学写作，申请研究生院以及学术界和工业界的职业机会研讨会。学生将被分成小组，由教师导师单独指导。每个学生将属于两个不同的团队，因此他或她将深入研究两个研究问题。这些项目在其各自的领域具有当前的兴趣，并且本质上是多学科的。导师将介绍主题，并提供必要的背景和初步练习。目标是将注意力转移到学生身上，他们将根据自己的兴趣和能力水平提出和调查问题。导师将在这一过程中发挥催化剂和顾问的作用，确保研究活动的质量和进展。这些项目的成功完成将促进数学知识和数学本科研究的现状。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知识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 REU program "Research Training for Undergraduates in Mathematical Analysis with Applications in Allied Fields," run by faculty members of the Department of Mathematics at the University of Tennessee at Chattanooga, provides an eight-week summer research experience for ten undergraduate students during each year of its operation. This program employs research methods training, hands-on research projects, and group activities that will lead participants to effective independent research. The program aims to increase participation in the mathematical sciences by recruiting and encouraging women, minorities from underrepresented groups, first-generation college students, and students from institutions with limited research opportunities. To contribute to the excitement and development of undergraduate research in mathematics, we incorporate elements of pure and applied mathematics as well as computational modeling, with a special focus on number theory, probability theory, and dynamical systems. This program is designed to introduce students to the power and applicability of mathematics and to encourage them to pursue careers in the mathematical sciences. Its success will provide a national model for undergraduate research in mathematics at a regional metropolitan university. The program will include a poster session and presentations by students, a colloquium series, interdisciplinary use of mathematics led by world-class researchers, and workshops on mathematical writing, applying to graduate school, and career opportunities in academia and industry. The students will be divided into groups supervised individually by the faculty mentors. Each student will belong to two different teams, so that he or she will delve deeply into two research problems. The projects are of current interest in their respective areas and inherently multidisciplinary. The mentors will introduce the topics and provide background and initial exercises as necessary. The goal will be to shift the focus to the students, who will pose and investigate questions according to their levels of interest and abilities. The mentors will serve as catalysts and advisors in the process and ensure the quality and progress of the research activities. Successful completion of these projects will advance the current state of mathematical knowledge and undergraduate research in mathematics.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.