The mission and goal of the Research Experiences for Undergraduates (REU) at Louisiana State University (LSU) is to mentor undergraduates who show promise in mastering the rigors of mathematical research for the next generation.  Mathematics is quintessentially a language, symbolic in nature and abstract in style, that has amazing applicability to explain phenomena that we perceive and sense in our every day experiences.  To help move forward our technology, our understanding of society and our understanding of the universe in all its myriad complexity, mathematics provides a symbolic tool and language for communicating these understandings, these description and models.

Specifically, we support the  development of that sector of our future workforce that understands clearly mathematical formulaic formalism and who can further develop these descriptions. From an alternative optic, the program supports enhanced development of the workforce necessary to develop and refine the mathematical relationships that are at the core of all algorithms and of computer software. In fact, the quintessential description of the computational heart of the current technology revolution is also logical and mathematical at its central core.

In the spring semester before the REU begins, the mentors refine a set of problems suitable for proposing to the participants. Although the mentors specialize in essentially distinct fields of research (typically, topology, algebra and geometry) we work hard to fashion a set of topics around an overarching theme with intertwining relationships that blossom as the summer develops. During the time period of this grant award, this theme has been the branched coverings of the two-sphere (the geometry of the surface of our earth) with applications to the theory of knotting and linking of circles and the symmetries and the parameter spaces of deformations for these mathematical objects.  The students are introduced to the projects available through lectures in the first week of the program. In the afternoon labs students learn LaTeX, a key tool for writing mathematical formalism and practice by writing assigned lectures, and working exercises based on the daily lectures.

A unique feature of our program, which mirrors the real world of research exploration, is that the students explore different potential projects during the first week with the mentors and other participants and make their final project selection only at the end of the first week. We then create research teams around each mentor and work together on individual and/or group projects. In addition to the training in mathematical research through exploration and development of  the research projects, we also introduce the participants to the larger world of professional mathematics. There are extended presentations by other mathematicians and discussions on graduate school and other opportunities to pursue mathematical interests.  Communication of their endeavors and results is a substantial part of their activity ranging from a short presentation of their problem to the whole REU in the second week to their final oral presentations and a written final report prepared during the final week.

Students are encouraged to present a summary of their research to their peers at their home institution during their next academic semester. Opportunities for presentation of research work at undergraduate research conferences as well as participation in professional meetings are specifically discussed and encouraged during the program and in the continued mentoring after the program as they make their career choices (overwhelmingly graduate school in mathematics).

Inter alia, our students have competed successfully for invitations to the prestigious Young Mathematician Conference at Ohio State University and won prizes at the annual poster session at the Joint AMS meeting. In addition, our success in motivating students toward graduate school is also reflecting in four students from the 2011-2013 REUs who were award NSF Graduate Fellowships and one additional Honorable Mention.  There were also two Goldwater Scholarship recipient and a Marshall scholar.

By mentoring students in the selection of a research problem and its subsequent development, refinement and communication, we strive to develop technologically and mathematically savvy citizens for the national workforce. During the past twenty years, we have developed a traditional REU format that brings undergraduates from the selection of an interesting research problem to a forefront of research in eight weeks. Some students make significant breakthroughs; all gain a thorough understanding of graduate level research in mathematics.

Last Modified: 07/29/2016
Modified by: Neal W Stoltzfus