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2021 NREUP Projects

Due to the COVID-19 pandemic, 2020 awardees were given the option to defer their funding until 2021. Those awardees are indicated with a *.​

  • Project Title: The Summer Program In Research and Learning (SPIRAL at American)
  • Project Directors: Monica Jackson
  • Project Summary: Building upon the success of the past 17 years, the Summer Program in Research and Learning (SPIRAL) at American University aims to provide a mentoring structure for underrepresented minorities and women that promotes active engagement in mathematics through a Research Experience for Undergraduates (REU) program. The main goal is to support and encourage intercultural understanding and educational excellence. Students are being prepared to excel in the difficult field of mathematics and statistics with the goal of being capable of taking on challenging problems in the future. In addition, we are focusing on diversifying the mathematical sciences to allow for different views and experiences to help solve world problems. The 8-week onsite program will run full-time from June 1, 2020 to August 1, 2020. The research goal will be accomplished first by providing students with an intensive 3-week lecture in the field of statistics and mathematics. The students will then spend the remaining weeks actively engaged in research. Students will also participate in field fields trips to local research agencies to discover applications of mathematical and statistical research. Finally, the students will submit their work for publication in a peer-reviewed journal. By participating in SPIRAL, students in the program will interact with other students with different racial/ethnic backgrounds to understand how excellence and diversity in STEM matters.
  • Project Title: Effects of Strong Fusion on Links
  • Project Director: Anthony Bosman,Yun Myung
  • Project Summary: Band fusion modifies a link by fusing together two link components with a band. T. Kanenobu, D. Buck, and others have studied the effects of fusion on links and tabulated the fusion pathways between links. We extend their work with an original analysis of the effects of strong fusion. Strong fusion a modified form of fusion that preserves the number of components of a link by introducing an unknotted component around the fusion band. In particular, we link invariants--including work from U. Kaiser on dichromatic invariants--to classify which links are the result of strong fusion, tabulating all such links with up to 10 crossings. We study when various necessary conditions are sufficient to determine if a link is the result of strong fusion as well as if strong fusions occur within various families of links. Fusion and strong fusion, and more generally band surgery, are important to the study of knot and link concordance.
  • Project Title: NREUP - DSU EAGER -- Enhancing Advancement to Graduate Education through Research
  • Project Director: Vinodh Chellamuthu
  • Project Summary: In this proposed NREUP – DSU EAGER program, students will work on research problems in the area of mathematical epidemiology. Students will learn how to develop mathematical models by identifying the problem, determining the necessary assumptions, finding the interrelationships among the variables, constructing a model, developing a numerical scheme, implementing a numerical scheme in MATLAB, and interpreting the results given by their models. They will be taught LaTeX so that they can prepare papers for publication. While working on their projects, students will investigate ways to modify and incorporate environmental factors into the model. This will make the models more robust by allowing students to analyze disease transmission in more realistic settings and establish stability properties of equilibria. Students will learn advanced mathematical concepts during the research process such as modeling, ODEs, matrix analysis, and numerical analysis. They will be expected to both present their work at professional meetings and publish their findings. Students will experience an increase in awareness of the broad array of mathematical research disciplines and will leave the NREUP – DSU EAGER program being encouraged, supported and geared up to pursue graduate studies and careers in mathematics.
  • Project Title:NREUP at Fairfield University
  • Project Directors: Zhanar Berikkyzy & Liyang Zhang
  • Project Summary: NREUP at Fairfield University is a multi-faceted seven-week program focusing on graph theory and its current applications in mathematics and other scientific disciplines. The program will prepare four undergraduate students for a career in mathematics research and offer unique opportunities for them to fully immerse in the mathematical professional and academic communities. The program will first introduce fundamental concepts in graph theory and the programming tool SAGE, following which students will be divided into smaller groups to investigate two research problems: one group will work on a random forest building process, in particular, computing the probability of obtaining given number of components in this process for various families of graphs, and the second group will work on enumerating Hamiltonian paths and cycles in various lattice graphs. The program will include professional development mentorship, including seminars talks from invited speakers, weekly discussions on career in mathematics, guidance on graduate school and financial aid applications, and conferences and travel grants. Students will write a manuscript and submit it to a journal for publication and will present their research results at national and local conferences, including a colloquium at Fairfield University. Program effectivness will be measured by tracking the trajectories of student participants as they grow in confidence and ability and monitoring REU participation, conference presentations, and graduate school applications beyond the duration of the program.
  • Project Title:Modeling the Spread of Infectious Diseases with Dynamical Systems
  • Project Directors: Matthew Johnston & Bruce E. Pell
  • Project Summary: The NREUP at Lawrence Technological University will introduce underrepresented minority students from the diverse Metro Detroit region to the multifaceted techniques of mathematically modeling the spread of infectious diseases. During the first two weeks of the project, students will learn the mathematical tools researchers use to estimate key epidemiological parameters, such as R_0 (R-naught), and to project the spread of diseases under a variety of public policy interventions. From the third week on, the students will independently build and analyze mathematical models for the spread of disease which account for a variety of different factors, such as demographic variations, face mask utilization, changes in social behavior, and different vaccination distribution priorities. The primary focus of the project will be model building and rigorously showing how these models behave using dynamical systems theory. A secondary focus will be on simulating the systems numerically, performing parameter estimations, and validating with real-world data.
  • Project Title: The evolution of zombies and cost-effective ways to prevent the end of the world.
  • Project Directors:Scott Greenhalgh & Kursad Tosun
  • Project Summary: Our summer research program focuses on applying tools from mathematical biology to predict pertinent information on the evolution and control of the undead. In particular, the program will provide insight as to whether zombies can naturally arise, and identify cost-effective strategies to control the (potentially inevitable) zombie apocalypse. Given these goals, this research program will feature two research subgroups. The first subgroup will investigate the potential for zombies to evolve from the dead through the application of an evolutionary invasion analysis on a population growth model. The second subgroup will apply cost-effectiveness analyze to a zombie outbreak model to identify economical ways to control (and potentially prevent) a zombie uprising. Students in both subgroup will be trained in all aspects of the research, starting with common techniques from applied mathematics used in the development and analysis of compartmental models, including differential equations theory, stability analysis, and probability theory. In addition, students will also enhance their computational skill sets from practical experience in coding mathematical models, and gain valuable experience both in scientific writing and in oral presentations.
  • Project Title: Introduction to Mathematical Modeling of Infectious Diseases
  • Project Directors:Enahoro Iboi & Naiomi T. Cameron
  • Project Summary: As a continuation of the development of the Math RaMP summer research program, we propose a seven-week summer research experience for four students in summer 2021 on the topic of modeling population-level impacts of the novel Coronavirus outbreak in the U.S. Dr. Enahoro Iboi will serve as faculty research mentor. The focus of this research experience is to encourage African American women who are mathematics majors at Spelman College to pursue graduate studies in Applied Mathematics. This NREUP will benefit students by exposing them to an area of applied mathematics (mathematical biology) not commonly presented on an undergraduate level by exposing them to modeling techniques, analysis, and simulations used for gaining insight into the transmission and control of some emerging and re-emerging diseases that are of public health concern. By the end of the program, students will be expected to be skilled in developing infectious disease models, perform basic analysis, collect, analyze, and visualize data, estimate unknown model parameters, and perform numerical simulations. The research projects will be accessible to students who have completed at least the calculus sequence and linear algebra. Thus, this program is appropriate for students who have completed their sophomore year or for students who are advanced first-year students. Students who participate in this NREUP will be expected to present at the annual Spelman College Research Day, MAA MathFest, NAM MATHFest, JMM 2022, or at a regional MAA conference and submit the results to appropriate professional journals for publication.
  • Project Title: CMAT: Computational Mathematics at Tarleton
  • Project Directors:Thomas Faulkenberry, Scott A. Cook & Christopher D. Mitchell
  • 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 an online 8-week research experience, where students will complete collaborative research in computational mathematics, with specific projects in mathematical modeling of cognition, billiard dynamics, and disease modeling. 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: Game Theory and Applications
  • Project Directors: Jan Rychtar, & Hyunju Oh
  • Project Summary: Our students will be introduced to the fundamental game-theoretical concepts (Nash equilibrium and evolutionarily stable strategy) and taught how to use computational and analytical tools to identify such strategies in models with applications in biology and/or medicine (cat vaccination to prevent Toxoplasmosis infection or bed-net use to prevent malaria). The students will be trained in all aspects of research, starting with the ethics code, going through 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:Summer Undergraduate Research Experiences at UOG (SURE@UOG)
  • Project Directors: Hyunju Oh & Leslie Aquino
  • Project Summary: For a 7 week period, from June 1, 2020 to July 17, 2020, we will engage 6 Pacific Islander undergraduate students from the University of Guam (UOG) in research projects. The students will work under the supervision of project directors Hyunju Oh and Leslie Aquino. Aubrey Moore and G. Curt Fiedler will provide ecology and biology background to our research groups. We will first introduce students to fundamental game-theoretical concepts, such as Nash equilibria and evolutionarily stable strategy. Then, we will teach them how to use computational tools (NetLogo and Matlab), as well as analytical tools (optimization, differential equations, and linear algebra) to identify such strategies in real game theoretical models, with applications for biology and ecology. The students 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. We expect that each student will submit at least one research paper and present their findings at least 2 colloquia/conferences (including UOG).
  • Project Title: Deep Learning for solving Differential Equations
  • Project Directors: Huiqing Zhu
  • Project Summary: In the past decade, deep learning has become a core component of artificial intelligence and a computational technology that can be trained to automate human skills. It has a potential to transform many traditional research approaches used in science and engineering. Recently, solving differential equations via deep learning has emerged as a potentially new sub-field under the name of Scientific Machine Learning. The 2020 NREUP summer undergraduate program will provide participants (1) an introduction to machine learning and deep learning; (2) an introduction to Python; (3) hands-on practice using deep learning as a numerical tool to solve differential equations; (4) an application to predator-prey models.
  • Project Title:Summer Undergraduate Research Experience in Statistics at Wofford
  • Project Directors: Deidra Coleman
  • Project Summary: Students who participate in a Summer Undergraduate Research Experience in Statistics at Wofford College will receive a broad overview of the research process in the discipline of Statistics. While pursuing original research on one of the two problems presented to them for study, students will be encouraged to recognize the stage of the research process they are currently engaged in. Students will learn the stages of the research process as identifying an open problem and conducting a literature review; choosing or developing methodology towards solving the problem; implementing methodology that leads to either solving the problem or making progress towards its solution; generating tables, graphs, or figures from findings; summarizing results; considering future work; and disseminating the new knowledge. Students will perform miniature literature reviews; learn relevant programming languages; prepare tables, figures, and data to adequately represent results; prepare discussions about graphics; write abstracts for submission to relevant conferences; and enhance their oral presentation skills by giving routine presentations. When students master these skills, it helps them prepare to pursue other REUs in future summers as well as to consider earnestly graduate study.

 

Program Contacts

MAA Programs Department