The Department of Mathematics at Texas State University will host an 8 week summer REU (Research Experience for Undergraduates) program for carefully selected undergraduate students in the summers of 2011 and 2012. The research areas include graph theory, algebra, additive number theory, game theory, and algorithm design. The objectives of the program are to directly involve students in research, allow the students to interact with each other as a team of researchers, and to form close mentoring relationships with faculty members. The program will guide the students to develop independence as mathematical researchers, introduce the students to the mathematical community, encourage the students to consider graduate school and a career in mathematics, help the students develop their skills in orally presenting mathematics, and help them write a mathematical research paper.

The program will support nine undergraduate students per year by providing lodging, meals, transportation, and a stipend. The faculty mentors of the program compose a diverse group of mathematicians including a female, an American American, Caucasians, and Asians. Significant efforts will be made to recruit and select students of mathematically underrepresented groups including minority students and women, as well as from institutions with limited resources available to support faculty-sponsored scholarly activity for undergraduates. The students will work in teams of three under the supervision of a faculty mentor. The students will present their research work at local, regional, and national STEM meetings during the following academic year. By focusing on important open problems we anticipate that our research will lead to faculty and student co-authored peer-reviewed manuscripts, make significant contributions to mathematics, and create a long-term and lasting impact on the careers of a diverse group of students.

Project Report

This is a two-year grant for Texas State University Mathematics Department to run an REU program in Discrete Mathematics and Algebra during the summers of 2011 and 2012. The grant supports nine students per year to spend eight weeks on site working in groups with a supervising faculty mentor on an open problem in Mathematics. In addition two more students are financially supported by fundings not from NSF. All participating students are provided with opportunities to present their research at national conferences in the year following the summer program. Faculty mentors introduce the students to a network of researchers in the field, and guide the students in the process of applying to graduate programs and fellowships. Our first year REU program ran from Monday June 13 to Friday August 5, 2011, and the second-year REU program ran from Monday June 11 to Friday August 3, 2012. In order to increase the visibility of the program to underrepresented groups, Dr. Nathaniel Dean (President of National Association of Mathematicians) has utilized his personal contacts with colleagues at Minority Serving Institutions and Historically Black Colleges and Universities. We have sent program flyers to a variety of over 200 mathematics departments across the country. All five faculty members have contacted people in their disciplines with a request to have the flyers posted and to encourage their students to apply. This has targeted the professors who teach the relevant background courses. We received over 160 applications. We read each application very carefully. Faculty mentors met a number of times in discussing and selecting a diversified group of participating students. We are very glad to report that each participating group had at least one female student. Two of the 18 NSF supported students are minority students. During this 8-week REU program all participating students were invited to attend weekly seminar talks organized by Mathworks (a Texas State University summer math camp program). After each Friday afternoon talk all students were invited to a catered BBQ along the beautiful San Marcos river. Social events were organized for the REU students. Students particularly enjoyed tubing down the San Marcos river during weekends. The first week of the program consisted mainly of studying the background material necessary to begin work on the problems. By the beginning of the second week, all students were engaged in original research under close supervision of a faculty member. The students continued working in small groups on the research topics throughout the summer. The faculty met with the students daily to provide guidance. In addition, there were presentation days once a week where each group shared the results of their research with the other participants. All faculty members in the Mathematics Department were invited to students' final presentation. Below is the list of all six projects mentored by faculty of the REU site: 1. (2011 Program) Charles Berahas (Georgetown University), Matthew Jacobson (University of Colorado-Boulder), Qingqing Wu (City College of New York), and Nathaniel Dean (Mentor), Screen Size of Crossing Minimal Drawings of Graphs. 2. (2011 Program) Daniel Campos (Texas State University), Ryan Gunderson (University of Nebraska- Lincoln), Chelsey Paulsen (North Dakota State University), Thomas Polstra (Georgia State University), and Susan Morey (Mentor), Depths of Power of Monomial Ideals. 3. (2011 Program) Nina Freeman (Southwestern University), Hunter Merrill (Mississippi State University), Ian Philipp (University of Louisville), and Jian Shen (Mentor), On the CSS Conjecture on Cycles in Triangle-free Digraphs. 4. (2012 Program) Jordan Blocher (University of Nevada-Reno), Samantha Hampton (University of Arkansas-Fayetteville), Christopher Linden (University of California at Los Angeles), and Xingde Jia (Mentor), Extremal Functions on Cayley Digraphs of Finite Cyclic Groups. 5. (2012 Program) Alexander Gruber (University of Cincinnati), Daniel Lenders (California State University-Fullerton), Keeley Naughton (Syracuse University), Ben Strasser (Carleton College), and Thomas Keller (Mentor), Prime Graphs of Groups. 6. (2012 Program) Toby Boas (University of Central Florida), Emily Dayton (Vanderbilt University), Lidong Zhou (Carnegie Mellon University), and Jian Shen (Mentor), On the Chudnovsky-Seymour-Sullivan Conjecture and Related Problems. All six REU groups obtained publishable research results. All groups have submited or expect to submit their papers to refereed journals very soon. The following paper by Dr. Morey’s group has been accepted for publication: D. Campos, R. Gunderson, S. Morey, C. Paulsen, T. Polstra, Depth and Cohen-Macaulay Properties of Path Ideals, to appear in Journal of Pure and Applied Algebra. The following paper by Dr. Jia’s group has been published in a reprefeed conference proceeding: Jordan Blocher, Samantha Hampton, Christopher Linden, and Xingde Jia Extremal Functions on Cayley Digraphs of Finite Cyclic Groups, Proceedings of the 2012 International Symposium on Pervasive Systems, Algorithms and Networks (I-SPAN), Pages 53-57, 2012.

National Science Foundation (NSF)
Division of Mathematical Sciences (DMS)
Standard Grant (Standard)
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Program Officer
Jennifer Slimowitz Pearl
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Texas State University - San Marcos
San Marcos
United States
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