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

REU 网站：本科生数学分析及其相关领域应用研究培训

基本信息

批准号：
1852288
负责人：
Andrew Ledoan
金额：
$ 28.27万
依托单位：
University of Tennessee Chattanooga
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-05-01 至 2023-04-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1852288&HistoricalAwards=false
关键词：
REU Site Research Training Undergraduates

项目摘要

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.

REU计划“研究培训本科生在数学分析与应用在盟军领域”，由教师的数学系在田纳西大学查塔努加运行，提供了一个为期八周的夏季研究经验，为十名本科生在每年的运作。该计划采用研究方法培训，实践研究项目和小组活动，将引导参与者进行有效的独立研究。该计划旨在通过招募和鼓励女性，代表性不足的少数群体，第一代大学生以及研究机会有限的机构的学生来增加数学科学的参与。为了促进数学本科研究的兴奋和发展，我们将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。该计划旨在向学生介绍数学的力量和适用性，并鼓励他们追求数学科学的职业生涯。它的成功将为区域性大都市大学的数学本科生研究提供一个全国性的模式。该计划将包括一个海报会议和学生的演讲，一个座谈会系列，由世界一流的研究人员领导的数学的跨学科使用，以及数学写作研讨会，申请研究生院，以及学术界和工业界的就业机会。学生将被分成小组，由教师导师单独监督。每个学生将属于两个不同的团队，这样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都是当前感兴趣的，而且本身就是多学科的。导师将介绍主题，并提供必要的背景和初步练习。目标是将重点转移到学生身上，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，并确保研究活动的质量和进展。这些项目的成功完成将推动数学知识和数学本科生研究的现状。该奖项反映了NSF的法定使命，并被认为是值得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的支持。

项目成果

期刊论文数量（5）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Explicit Krein resolvent identities for singular Sturm-Liouville operators with applications to Bessel operators

奇异 Sturm-Liouville 算子的显式 Kerin 解析恒等式以及 Bessel 算子的应用

DOI：
10.7153/oam-2020-14-65
发表时间：
2007
期刊：
Operators and Matrices
影响因子：
0.5
作者：
Allan, S. Blake;in Kim, Justin Han;Michajlyszyn, Gregory;Nichols, Roger;Rung, Don
通讯作者：
Rung, Don

Linnik's large sieve and the L1$L^{1}$ norm of exponential sums

Linnik 的大筛子和指数和的 L1$L^{1}$ 范数