The Department of Mathematics at Missouri State University will offer summer research opportunities in 2012, 2013 and 2014 in the fields of algebra, combinatorics, analysis, differential equations and numerical analysis. Junior and senior undergraduate students from across the country are invited to apply, but we are especially targeting students from nearby institutions where undergraduate research is limited. This program will involve undergraduate students in active research, help them reach a higher level of independence in mathematical reasoning, and encourage them to pursue graduate studies. The students will learn to assimilate the latest research through reading, discussions and constant interaction with their cohort and experienced faculty mentors. Participants will learn how to effectively communicate their results by writing and presenting them to the mathematical community, and in some cases by publishing in refereed journals. This program is designed in order to achieve the goal of improving participants' understanding of mathematics, leading to the discovery of original results through high-quality research. We are fully committed to substantially increase the participation of women, minorities, persons with disabilities, and first generation students.
An NSF-sponsored program such as this is one of the best ways to attract and retain talented undergraduate students, and to help them realize their full potential for research, by involving them in direct interaction with a diverse group of students and experienced faculty mentors. Every effort will be made to foster a sense of community among the REU team of faculty mentors and students, with the goal of providing the undergraduate participants with the experience of being part of a well-integrated research team.
http://people.missouristate.edu/lesreid/reu/2014/ PD/PI name: Leslie F Reid, Principal Investigator Jorge L Rebaza, Co-Principal Investigator Recipient Organization: Missouri State University Project/Grant Period: 03/15/2012 - 02/28/2015 Reporting Period: 03/01/2014 - 02/28/2015 Major Activities: • We successfully trained REU participants in the areas of mathematical research, including: group theory, graph theory, real analysis, applied mathematics, and dynamical systems. • Several of our participants are currently applying to graduate school in mathematics and related areas, and some have already been accepted. Those who are not applying are currently underclassmen and intend to apply in the near future. Other Achievements: • Several REU participants have presented their results of their research at conferences for undergraduate research. • We expect a number of the research projects' results to be submitted to peer-refereed journals. • More than 50 percent of our REU participants came from underrepresented groups. The students clearly advanced their knowledge and understanding of mathematics and its applications. Students had one-on-one meetings and discussions with their mentors and attended several seminars where each participant presented his or her progress and findings. The graduate assistants also greatly benefited from their mathematical interactions with the undergraduates and mentors. Conference Papers and Presentations More than half of the participants presented their results at the MAKO undergraduate research conference (http://math.missouristate.edu/MAKOcomp.htm). Some of the research projects will be shortly submitted for publication in peer-refereed journals. Major Findings: 1. The intersection subgroup graph of a group has its proper non-trivial subgroups as vertices and two vertices are connected by an edge exactly when their intersection is non-trivial. Preliminary results were obtained concerning the oriented and nonorientable genera of intersection subgroup graphs. In particular, the groups having genus one (oriented or nonorientable) were almost completely classified (three participants). 2. A networked connectivity model of waterborne epidemics was studied. By constructing an appropriate Lyapunov function and using LaSalle’s invariance principle, previous results on local stability were extended to include rigorous proofs on global stability of the disease-free equilibrium, existence of an endemic equilibrium, and existence of some bifurcations (three participants). 3. We studied the problem of mid-point iteration of a given finite point set. We found that the limiting sets have a certain fractal-type structure, and defy intuitive characterizations. We also found that if the given point set consists of the four vertices of a square, then the limiting set has a boundary that resembles the structure of a Cantor-type curve (three participants). Impact on the development of human resources The main goals of this project are to provide undergraduates (especially under-represented groups) who usually do not have much opportunity to do mathematical research at their home institutions a chance to do so and to encourage participants to pursue careers in the mathematical sciences. This program helped REU participants appreciate team work within a diverse group of students and faculty mentors.
