Division of Mathematics and Computer Science
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The Young Scholars Research Experience in Mathematics (YSREM) program works in conjunction with the University of Guam’s Research Experiences for Undergraduates (REU) program on game theory, graph theory, and coding theory, which will run concurrently as a single program. The program is supported by the University of Guam College of Natural & Applied Sciences.
The YSREM program provides students hands-on engagement on theoretical and computational research to improve problem-solving, communication, and computer programming skills.
Game Theoretical Models of Disease Prevention
With Dr. Hyunju Oh, Dr. Leslie Aquino, Dr. Jan Rychtar, and Dr. Dewey Taylor
The students will pick a preventable disease of their interest, do a literature search and build a compartmental ODE (ordinary differential equation) model incorporating the disease prevention. Students will solve for disease-free and endemic equilibria and determine conditions for their stability using the effective reproduction number. They use these results to get an incentive function which quantifies the net benefits of the preventive actions compared to the net benefits of no action at all when the population vaccination coverage (or the average use of the preventive action) is p. The incentive function is typically decreasing and concave down on the interval [0, p0] where p0 is the population level of preventive action needed for disease elimination. The solution of the game, the Nash equilibrium, is given as the (unique) root of the incentive function. Students also typically have to carefully calibrate the ODE model; and they perform sensitivity and uncertainty analysis as well as validate the model and its findings of independent sets of data.
Model of Insect Invasion
With Dr. Hyunju Oh, Dr. Leslie Aquino, Dr. Jan Rychtar, and Dr. Dewey Taylor
Ideally, we would like to create and solve a general “insect invasion prevention game” in which several different entities with different interests interact and potentially try to eliminate the insect or at least curb the negative effects of the invasion. We will build on the [insect] population dynamics (as provided) and incorporate the game and the players to see what the optimal actions are and what kind of central action should be taken to curb negative impacts of the insects on local agriculture and economy as a whole.
With Dr. Hideo Nagahashi
Coding theory, and its application to recreational mathematics–magic tricks–is well suited for students’ first encounter with mathematical research. In coding theory we study the codes used for the error detection and correction of data transmission. When the audience intentionally tells lies replying to the magician’s questions, it can be considered as errors, and the error detection and corrections are interpreted so that magicians figure out the correct response to surprise the audience. The goal of the project is to create original magic tricks using various (existing or new) codes.
Students will encounter various examples of codes such as Hamming, BCH, Reed-Solomon and Golay codes. While learning code theory, students will review linear algebra and learn some concepts of abstract algebra such as the ring of integers modulo n, finite fields, and polynomials. Students will also learn the computational tool (SAGE Math) to understand and test codes. Applying code theory in this manner strongly motivates students to learn advanced algebra, and helps them to improve their creative and independent skill for doing mathematical research.
With Dr. Raymond Paulino
The main objective of this project is to investigate connections between the adjacency and/or Laplacian matrices of graph G , its powers Gk, and the chromatic numbers of G and Gk. Students will study the spectrum of adjacency and Laplacian matrices of Gk for a fixed graph G and increasing k=1,2…,d, where d is the diameter of G, i.e., the maximum distance among all the vertices in G. The students will look for analogues of that sequence for the spectra of AGk and LGk.
In this project, students will draw and visualize graphs using online computer software such as SAGE Math. Students will then look at connections between the matrices and chromatic numbers of the graphs. Students will discover that with certain types of graphs, the spectrum of the adjacency matrix can provide upper and lower bounds for their chromatic number. While learning graph theory with matrices, students will be introduced to selected topics from linear algebra. Graph theory and its applications encourages students to improve their creativity and their interest in mathematics.
Participants must be:
Prerequisite: Calculus I (Grade B or better) or AP Calculus A/B
Applications are especially encouraged from students who identify with populations currently underrepresented in mathematics from schools with limited access to research opportunities and current freshmen and sophomores.
Who: 11th or 12th grade high school students on Guam
When: 9 a.m. - 5 p.m. on weekdays from May 30 - July 22, 2023
Modality: In-Person
Stipend: $1,000
Deadline to Apply: May 5, 2023
Questions? Email mathreu@triton.uog.edu
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