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2019 NREUP Projects

 

  • Project Title: The Summer Program in Research and Learning (SPIRAL) at American University
  • Project Directors: Monica Jackson
  • Project Summary: The Summer Program in Research and Learning (SPIRAL) at American University is a research experience for undergraduates (REU) aimed at providing a mentoring structure for women and underrepresented minorities that promotes active learning and engagement in problems in statistics and mathematics. SPIRAL is an awarding winning REU in existence for over 16 years. The seven-week program will be three-pronged: (1) Students will participate in research seminars in mathematics and statistics, in which research projects will be investigated in teams. Each team will write a final paper discussing their results and give an oral presentation. (2) There will be an intensive four week course – emphasizing computer skills, with problem workshops and daily homework. (3) One day a week will be devoted to professional development and career awareness, enhancing the students’ view of the mathematical world. Development activities include learning to write in mathematical software packages, learning to analyze data using statistical packages, training for the GRE, and visits from researchers in industry, academia, and government to share career opportunities. Finally, all students will attend the 25th Conference for African American Researchers in the Mathematical Sciences (CAARMS25) and present preliminary findings of their research project. In previous years, SPIRAL students won first place in the student poster competition at CAARMS.
  • Project Title: Central Convergence REU
  • Project Director: Brandy Wiegers
  • Project Summary:Central Convergence REU provides early-career undergraduate students who have at least a year and a half remaining in their degree program at the time of their REU application a unique summer research experience that encourages them to more fully immerse in the mathematical professional community. The summer project begins with a growth mindset-focused training in problem-solving to prepare them to approach research problems. Then students engage in the research for seven weeks while also receiving professional development mentorship to provide these students the tools and knowledge to engage more in the mathematics profession. By the end of the REU, students have contributed to authentic mathematical research, worked with computational mathematical tools, and practiced multiple forms of mathematical communication. After the students leave the experience they are prepared, encouraged, and supported to find future experiences (research, conferences, courses) to further participate in the professional field with coordinated post-REU activities. The 2018 Central Convergence REU was a success with five-MAA funded students engaging in research that they presented at SACNAS with the support of MAA NREUP and SACNAS traveling funding.
  • Project Title:Computing Change Using Partial Differential Equations
  • Project Director: Nessy Tania
  • Project Summary:Our summer research program will be focused on analysis and computations of partial differential equation (PDE) models. We will begin by introducing students to common PDEs and how to solve them using Fourier series or numerical approximations. There will be two research subgroups: one studying instability in the Euler equation in fluid dynamics and another focusing on pattern formation in a spatial population model. Students will use and develop tools from theoretical mathematics (functional analysis and dynamical systems) to applied mathematics (modeling and numerical approximations). In addition to learning mathematics outside our standard available courses, our undergraduate researchers will build their capacities for mathematical exposition, both in writing and in oral presentations. To complement the mathematical content, students will interview minority professional mathematicians and lead discussions on issues surrounding their URM status. The summer program will end with attendance at MathFest, where students will present their work and engage with the broader mathematical community. We will measure the effectiveness of our program by tracking whether students (particularly those in their first/second years) take further mathematics courses and by measuring their retention within the mathematical sciences post graduation.
  • Project Title: CMAT - Computational Mathematics at Tarleton
  • Project Director: Tom Faulkenberry
  • Project Summary: The proposed NREUP project is called Computational Mathematics at Tarleton (CMAT). With this collaborative, cross-disciplinary project, we aim to stimulate intellectual curiosity and develop transferrable mathematics research skills in a group of 4 underrepresented minority students from the north central Texas region. The project co-directors will engage the students in a fully immersive 8-week research experience, where students will complete collaborative research in computational mathematics, with specific projects in mathematical modeling of cognition and the dynamics of billiard systems. The results of this research will not only contribute to the body of scientific knowledge in these fields, but also contribute to the development of these students' knowledge and research skills related to mathematics and computational science, inspiring these students to persist to graduation, pursue further STEM-related educational opportunities, and ultimately seek careers in the mathematical sciences.
  • Project Title: Summer Undergraduate Reasearch Experiences at UOG (SURE@UOG)
  • Project Director: Hyunju Oh
  • Project Summary:Students will be introduced to the fundamental concepts of Game theory and Coding theory. In game theory and applications, students will learn Nash equilibria and evolutionarily stable strategy and teach them how to use computational tools (NetLogo), as well as analytical tools (optimization and linear algebra) to identify such strategies in real game theoretical models with applications in medicine - “vaccination games” where individuals have to make decisions whether to protect themselves from infectious diseases by taking costly actions such as taking a vaccine. In coding Theory, students will learn correcting and detecting errors, information rate, and distance of codes. Then we will show some examples of codes such as linear and cyclic codes, Hamming codes and BCH codes. While learning coding theory, students will review the basic concepts of linear algebra and will learn some concepts of abstract algebra such as finite fields and polynomials which are the basis for understanding the cyclic codes. Participants will have a choice of two projects during the program. The students of both groups will be trained in all aspects of research, starting with the ethics code, going through the workshops on using library and online resources and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers.
  • Project Title: Long-time Behavior and Allee Effects in Predator-Prey Models
  • Project Directors: Huiqing Zhu
  • Project Summary: The Allee effect was shown to bring essential changes to population dynamics and it has drawn considerable attention in almost every aspect of ecology. In our previous MAA-NREUP project that have been completed in summer 2018, the influences of hunting cooperations and Allee effects in several predator-prey models have been investigated. We plan to lead our undergraduate researchers to continue our research program in summer 2019 since our students were well motivated and they made some significant progress in those topics. One of our main motivations is to study the synergistic effects of Allee effects in prey for predator-prey models since there is not much work having been done in this area. We will also investigate the impact of Allee effects to the Turing pattern formations due to the spatial interactions in the three species predator-prey diffusive model. The proposed research project will have a positive impact on participants’ future academic achievements.
  • Project Title: Stochastic Partial Differential Equations
  • Project Directors: Tamer Oraby
  • Project Summary: Building up on the successful summer 2018 MAA NREUP at UTRGV, we will continue working with our students on stochastic partial differential equations. In particular, we will study exact and numerical solutions of stochastic Schrodinger equations with variable coefficients. We will also study the existence of solutions of systems of stochastic Burgers equations using graph theory. Students will receive extensive training on partial differential equations, probability theory, stochastic processes and analysis and their numerical solutions/simulation using matlab. Students are expected to write up a manuscript of the results coming out of their work during the event and submit it to a peer-reviewed journal. They are also expected to present their research orally and through posters in national conferences.

 

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MAA Programs Department