The Department of Mathematics at the California State University, Fresno (CSU Fresno) will host an eight week long REU for eight students during the summers of 2012 and 2013. During both years, two faculty mentors will be working with 4 students each. The research topics for each summer will be selected from the following: the location of zeros of analytic functions, stability preserving operators, and multiplier sequences; knot and link labelings; embeddings of graphs in finite planes; and survival analysis and modeling survival data. To equip the students with the necessary tools, they will be given a series of introductory lectures related to their research topic. Students will then work on the assigned research problems individually, as well as in groups. Participants will be required to write a summary research report suitable for publication, and will give weekly oral presentations while maintaining increasingly strict professional standards. Research activities will be complemented by guest lectures, excursions and informal gatherings.
Students will be working on open research problems in mathematics. The mentoring faculty is actively involved in research in the proposed areas and has extensive experience in mentoring undergraduate research projects. Many of the past projects have led to conference presentations and publications in research journals. The REU aims to have at least half of the participants be underrepresented minority students, as two of the faculty are also mentors for the National Alliance for Doctoral Studies in the Mathematical Sciences, which promotes minority participation in doctoral programs in mathematics. By providing all participants with a research environment cognizant of different cultural backgrounds, students will have a meaningful and encouraging experience to supplement their undergraduate education. In addition, the REU will provide all students with computer and research skills, which are widely applicable in the scientific workplace.
The Fresno State Research Experiences in Mathematics was an eight week long resident research program for undergraduate students which ran during the summers of 2012, 2013 and 2014. The program was aimed at students from primarily undergaduate institutions and from minority serving institutions. An expressed goal of our program was to have half of our participants come from an underrepresented group in the STEM fields. We attracted 50 complete applications in the first year, 271 complete applications in the second year, and 228 complete applications in the third year. We admitted a total of 20 students (8, 8 and 4 in 2012, 2013 and 2014 respectively). Of these 20 students, 11 were male, 9 were female, 15 were white, 5 were hispanic. Overall we had 25% of our participants come from ethnic minority groups, and 50% form underrepresented groups in the STEM fields. Our four mentors also formed a diverse group with 3 males (one asian, one hispanic and one white) and one female (white). Intellectual Merit Participants of the program carried out original research in statistics, combinatorics, finite geometry, knot theory and complex analysis. More specifically, students studied various graph families and their well-covered dimensions, embeddings of graphs in finite projective spaces, survival analytic techniques and their applications, (virtual) link invariants and their extensions, and the family of polynomials which interpolate Legendre multiplier sequences. In addition to advancing the theory, students often used computer programs to run experiments, to carry out computations and to formulate conjectures. The research efforts of the participants resulted in five faculty co-authored publications (Contributions to Discrete Geometry (2), Involve - a Journal of Mathematics (2), and the Journal of Geometry), and one student authored publication (Rose-Hulman Undergradaute Journal of Mathematics). There are two additional papers resulting from this program which are currently under review (Involve - a Journal of Mathematics, Rocky Mountain Journal of Mathematics). Program participants also gave numerous talks and poster presentations at the AMS-MAA Joint Mathematics Meetings, at Sectional Meetings of the MAA, at the Nebraska Conference for Women in Mathematics, at the Pacific Coast Undergraduate Mathematics Conference, and at seminars and symposia at local institutions. Broader Impact We were successful in recruiting a rather diverse gorup of participants, from a healty mix of institutions (Auburn University, Davidson College, City College of New York, SUNY Geneseo, SUNY Stony Brook, Utah Valley University, CSU Monterey Bay, CSU Fullerton, CSU Fresno, Humboldt State, Kansas Wesleyan University, Harvey Mudd College, Carnegie Mellon University, University of Rochester, University of North Carolina Asheville, Wheaton College, Rice University, and the College of William and Mary). The program provided professional development workshops for its participants, aimed at improving oral and written communications skills, navigating the pitfalls of research, and at streamlining the process of appying to graduate programs in the mathematical sciences. Fifteen of our participants are now either in graduate school (masters or PhD) in the mathematical sciences, or are applying to such programs. One student is in a graduate program in accounting, two are working, and one is still a junior in college.Our program also provided an opportunity for students in the McNair and LSAMP programs to conduct their summer resarch along the REU students, enhancing the quality of the research experience of all students involved. During the 2014 year we applied for, and were granted a supplement to the original grant. This supplement provided support for the pilot year of the Faculty and Undergraduate Research Student Teams (FURST) program. FURST aims to involve faculty in (i) undergraduate research mentoring and (ii) faculty collaborative research. The inaugural year of the program supported four students and two faculty mentors, whose research activities resulted in five conference presentations, and three four research papers. FURST participants spent one month during the summer of 2014 at the Fresno State REU site, where they immersed themselves in the ongoing REU activities. This immersion helped broaden the impact of both the REU and the FURST program, by providing the arena for an extended exchange of academic ideas, research results, and professinoal networking for students and facutly alike.
