REU Site at Lamar University

拉马尔大学本科生研究体验项目（REU）为8名学生提供了2018-2020年夏季在数学系为期10周的真实研究体验。参与者在pi的监督下以四人一组的方式工作。每个小组由一位经验丰富的研究导师和一位初级教员领导。鲁大的REU网站旨在为那些本科生研究机会有限或根本不存在的机构的学生增加研究机会。通过招募代表性不足的少数民族、退伍军人和社区大学生，学生们有权攻读STEM学位，并过渡到STEM领域的高级学习或职业生涯。参加一个结构化的研究项目的好处超出了学生获得的技术知识。学生可以提高写作和口头沟通能力，并通过参加会议来展示他们的工作，获得专业发展的机会。此外，在为期十周的项目结束后，教师顾问将继续担任学生的导师。每年都有许多学生在当地社区大学完成两年制学位后转到LU。LU的REU网站为来自当地社区学院的参与者创造了一个机会，可以与其他成功过渡到四年制大学的STEM学生见面。最后，在每个研究项目中将经验丰富的研究导师与经验不足的共同导师配对，为共同导师提供建立或扩展本科研究项目所需的工具。该计划的智力重点是在数学，统计学和计算机科学的交叉学科研究。在许多应用程序中，为了有效地处理大量高维数据，降维是必不可少的。使用矩阵分解和图论的降维可以用来确定数据的底层结构，并找到数据属性之间的相关性。由于在数学和计算机科学的各个研究领域的应用，人们对图论、奇异值分解（SVD）和非负矩阵分解（NMF）的研究兴趣日益增加。SVD和NMF都是目前在大数据分析中使用的无监督学习工具。REU参与者将接触到与大数据相关的挑战和机遇。向学生介绍大数据的三个v：体积（Volume）、种类（Variety）、速度（Velocity）。Volume指的是数据的绝对数量，Variety指的是不同类型的数据，Velocity指的是处理数据的速度。学生将有机会参与(1)理论研究，学生将研究图论、奇异值分解和NMF的性质，以产生猜想、证明定理和研究现有算法；(2)与编程相关的研究，让学生进行矩阵分解和图论的实验，并编写处理大型数据集的算法。

The Research Experience for Undergraduates (REU) program at Lamar University provides 8 students a 10-week authentic research experience in the Department of Mathematics during the summers of 2018-2020. Participants work in teams of four under the supervision of the PIs. An experienced research mentor and a junior faculty member lead each team. The REU site at LU aims to increase research opportunities for students at institutions where undergraduate research opportunities are limited or nonexistent. By recruiting underrepresented minorities, veterans and community college students, students are empowered to pursue degrees in STEM and to transition to advanced study or careers in STEM. The benefits of participating in a structured research program extend beyond the technical knowledge that students gain. Students increase writing and oral communication skills and are exposed to professional development opportunities in attending conferences to present their work. Furthermore, the faculty advisors continue to serve as mentors for the students beyond the ten weeks of the program. Each year, many students transfer to LU after having completed two-year degrees at local community colleges. The REU site at LU creates an opportunity for participants from local community colleges to meet other STEM students who successfully made the transition to a four-year university. Finally, pairing experienced research mentors with less experienced co-mentors on each research project gives the co-mentors the tools necessary to establish or expand undergraduate research programs. The intellectual focus of this program is on interdisciplinary research at the crossroads of mathematics, statistics and computer science. In many applications, dimension reduction is imperative for efficient manipulation of massive quantities of high-dimensional data. Dimension reduction using matrix factorizations and graph theory can be used to ascertain the underlying structure of the data and to find correlations among the data attributes. Interest is increasing in the study of graph theory, singular value decomposition (SVD) and nonnegative matrix factorization (NMF) due to applications in various research areas of mathematics and computer science. SVD and NMF are both unsupervised learning tools currently used in big data analytics. REU participants will gain exposure to the challenges and opportunities associated with big data. Students are introduced to the three Vs of big data: Volume, Variety, Velocity. Volume refers to the sheer quantity of the data, Variety refers to the different types of data, and Velocity refers to the speed of processing the data. Students are allotted the opportunity to participate in (1) theoretical research, with students investigating properties of graph theory, SVD and NMF to generate conjectures, prove theorems, and investigate existing algorithms; and (2) programming related research, with students performing experiments on matrix factorizations and graph theory and writing algorithms to process large data sets.