REU Site at Lamar University

拉马尔大学的本科生研究经验（REU）计划在2018-2020年的夏天为8名学生提供了在数学系为期10周的真实研究经验。 参与者在PI的监督下以四人一组的方式工作。一位经验丰富的研究导师和一位初级教员领导每个团队。LU的REU网站旨在为本科研究机会有限或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的学生，学生有权攻读STEM学位，并过渡到STEM的高级学习或职业。参加结构化研究计划的好处超出了学生获得的技术知识。学生提高写作和口头沟通能力，并在参加会议，介绍他们的工作接触到专业发展的机会。此外，教师顾问继续担任导师为学生超过十周的计划。每年，许多学生在当地社区学院完成两年制学位后转学到LU。LU的REU网站为当地社区学院的参与者创造了一个机会，以满足其他成功过渡到四年制大学的STEM学生。最后，在每个研究项目上，将经验丰富的研究导师与经验不足的共同导师配对，为共同导师提供了建立或扩大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十字路口进行跨学科研究。在许多应用中，降维对于有效处理大量高维数据是必不可少的。使用矩阵分解和图论的降维可以用于确定数据的底层结构，并找到数据属性之间的相关性。由于图论、奇异值分解（SVD）和非负矩阵分解（NMF）在数学和计算机科学的各个研究领域中的应用，人们对它们的研究兴趣越来越大。SVD和NMF都是目前用于大数据分析的无监督学习工具。 REU参与者将接触到与大数据相关的挑战和机遇。学生将被介绍到大数据的三个V：卷，品种，速度。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。 学生有机会参与（1）理论研究，学生调查图论，SVD和NMF的属性，以生成图表，证明定理，并研究现有的算法;和（2）编程相关的研究，学生进行矩阵分解和图论的实验，并编写算法来处理大型数据集。

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.