Division of Mathematics and Computer Science
Division of Mathematics and Computer Science
Division of Mathematics and Computer Science
Nothing is Mpox-ible: Students delve into real-world problems using math
UOG launches new data science and library science master's programs
UOG alum becomes physician assistant and begins certification in life-saving surgeries
Summer REU teaches undergrads, high schoolers to solve real-world problems using math
Students gain exposure to new math concepts from visiting Boston professor
CNAS Math Day engages more than 100 teens
Math Day returns at UOG with a special visiting speaker
Math students present their research at NREUP Student Showcase
Graduate William Sablan to begin Ph.D. in mathematics
Engineering students go to Chicago for advanced computing challenge
MAA National Research Experience for Undergraduates Program (NREUP)
The Mathematical Association of America supports the participation of mathematics undergraduates from underrepresented groups in focused and challenging research experiences to increase their interest in advanced degrees and careers in mathematics.
Each year, mathematical sciences faculty are invited to apply for a grant to host the National Research Experiences for Undergraduates Program at their campus over the summer. NREUP is structured both to increase undergraduate completion rates and encourage more students to pursue graduate study by exposing them to research experiences after they complete their sophomore year (at this point in their studies, students typically have a strong background in calculus and a course such as linear algebra or differential equations with some degree of exposure to the proof-based mathematics needed prior to undertaking a research project).
NREUP is designed to reach minority students at a critical point in their career path
-- midway through their undergraduate programs. As coursework becomes more abstract
and students are required to work independently, many promising students are not able
to adjust to the demands of a major in mathematics, but with a strong connection to
a faculty mentor established through the NREUP, students are given the tools they
need to succeed.
About the MAA
The Mathematical Association of America (MAA) is the world’s largest community of mathematicians, students, and enthusiasts. MAA furthers the understanding of our world through mathematics because mathematics drives society and shapes our lives.
The mission of the MAA is to advance the understanding of mathematics and its impact on our world. MAA envisions a society that values the power and beauty of mathematics and fully realizes its potential to promote human flourishing.
From 2018-2019 and 2021-2022, the University of Guam hosted the National Research Experience for Undergraduates Program providing valuable research experience and skills to UOG students.
2018: Game Theory and Applications
Students were introduced to the fundamental game-theoretical concepts such as Nash equilibria and evolutionarily stable strategy and taught 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. The students were trained in all aspects of research, starting with the ethics code, going through the workshops on using the library and online resources, and ending with training in delivering oral presentations, as well as in using LaTeX to write mathematical papers.
2018 Faculty Mentor:
- Dr. Hyunju Oh
2019: Summer Undergraduate Research Experiences (SURE) at UOG
Students were 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 to correct and detect 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 had a choice of two projects during the program. Both groups of students were trained in all aspects of research, starting with the ethics code, going through the workshops on using the library and online resources, and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers.
2019 Faculty Mentor:
- Dr. Hyunju Oh
2021: Summer Undergraduate Research Experiences (SURE) at UOG
Students were introduced to fundamental game-theoretical concepts, such as Nash equilibria and evolutionarily stable strategy. Students were taught how to use computational tools (Rstudio 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 were trained in all aspects of research, starting with the ethics code, going through the workshops on using the library and online resources, and ending with training in delivering oral presentations as well as in using LaTeX to write mathematical papers. Students have submitted at least one research paper and presented their findings at two 2 colloquia/conferences (including UOG).
2021 Faculty Mentors:
- Dr. Hyunju Oh
- Dr. Leslie Aquino
- Dr. Aubrey Moore (Ecology & Biological Information)
- Dr. G. Curt Fiedler (Ecology & Biological Information)
A Model of the Dynamics of CRB-G with a Game Theoretical Analysis of the Effectiveness of Control Measures
Student Researchers: Jovic Aaron S. Caasi, Alex Leon Guerrero, Kangsan Yoon
The coconut rhinoceros beetle (Oryctes rhinoceros), or CRB, is an invasive species in Guam that has greatly affected the island's coconut tree population. Native to South and Southeast Asia, it first arrived in Guam in 2007. Various control measures have been used to combat the spread of CRB, but many have been proved ineffective. Strategies used to control the spread of CRB include the removal of coconut tree breeding grounds. We present a mathematical model to understand the dynamics between CRB and coconut trees. Also, we construct a game-theoretical analysis of the effectiveness of removing moribund and coconut tree breeding grounds that individuals can choose to minimize the CRB damage to coconut trees. We find the maximum relative cost to remove a moribund tree is significantly higher than the maximum relative cost to remove a breeding ground.
Population Dynamics of the Mariana Eight-Spot Butterfly and Parasitoid Wasps: A Compartment Model Approach
Student Researchers: Cabrini Aguon and Andrew Lu
This research theoretically modeled the population dynamics between Guam's endangered Mariana Eight-Spot butterfly {Hypolimnas octocula marianensis} with two species of parasitoid wasps (Telenomus remus) and (Echthromorpha intricatoria). We constructed a compartment model to analyze the influence of the number of host plants available and the number of all other parasitoid targets and computed the basic reproduction number to determine the proliferation of the respective wasp species in the system. We found control measures directly targeting the infection compartment rates eventually became ideal in controlling as host plants increased, while control measures targeting non-infection parameters eventually became ideal as other targets increased. In {T. remus}, the most sensitive non-infection parameters were the host plant count and the number of other targets, whereas in {E. intricatoria}, the rate at which larvae matured just slightly surpassed other pupa targets and host plants in sensitivity.
A Game Theoretical to Modeling Population Dynamics Between the H. o. marianensis, H. and H.bolina
Student Researchers: Andrea Gutierrez, Sean Hipolito, Yuan-Jen Kuo, Shaun Wu
The Hypolimnas octocula marianensis, also known as the Mariana Eight Spot Butterfly, is endemic to the island of Guam and was classified as endangered by the U.S. Fish and Wildlife Services in October 2015. Despite sharing many traits with two other butterflies in the same genus, the Hypolimnas anomala and Hypolimnas bolina, the H. o. marianensis is the only endangered species. However, the butterflies’ host plant availability differs remarkably. This project aims to use evolutionary game theory to model the three butterfly species’ populations over time and determine host plant proportions that will sustain the H. o. marianensis and allow it to coexist with the H. anomala and H. bolina. The game theory model analyzes the strategies a population of butterflies can take when laying eggs and determines which is the best. The results show that host plant availability significantly affects all butterfly species’ proportions over time and must fall within certain ranges. These findings also suggest a specific order of host plant proportions needed to sustain the H. o. marianensis. Notably, the model demonstrates that the repopulation of the H. o. marianensis is highly dependent on the only variable within human control: the host plant proportions.
Modeling and Analysis of Oryctes Rhinoceros Behavior
Student Researchers: Gabriel Florencio, Ashley Yang, Michael Cajigal
In Guam, the increase of Oryctes rhinoceros, or rhinoceros beetles, — a species of beetles that prioritizes coconut trees as its source of nourishment — has led to a massive ecological problem since its first appearance in 2007. The rhinoceros beetle problem became exacerbated when the super typhoon Dolphin struck in 2015. Since then, the rhinoceros beetle population has increased dramatically causing many more coconut trees on the island to become damaged. This research aims to focus on the behavioral patterns of rhinoceros beetles as it interacts with coconut trees and to model these patterns. The goal of conducting this is to analyze the results collected from modeling these patterns, from which we can discern the best course of action to take in order to help suppress the population enough to either create an equilibrium between the beetles and the coconut trees, or so that the trees reach a sort of herd immunity, where there are no more coconut trees being affected by rhinoceros beetles. When this has been achieved, the solutions can then be applied in the same fashion, modeled, and the data collected in order to provide evidence of the solutions’ efficacy. Link to Video Presentations: https://www.maa.org/programs-and-communities/outreach-initiatives/nreup/nreup-2021-student-showcase
2022: Summer Undergraduate Research Experiences (SURE) at UOG
Students were introduced to the fundamental game-theoretical concepts such as Nash equilibria and evolutionarily stable strategy and teach them how to use computational tools (Matlab), as well as analytical tools (optimization, differential equations, 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 encountered various examples of codes such as Hamming, BCH, and Reed-Solomon codes. Students will learn the fundamental concepts of coding theory such as correcting and detecting errors, information rate and distance of codes. Cryptography is the study of techniques for secure communication between a sender and receiver, in the presence of an adversary. Students had a choice of two topics during the program. The students of both groups 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. Students will submit at least one research paper and present their findings at least 2 seminar/conferences (including UOG).
2021 Faculty Mentors:
- Dr. Hyunju Oh
- Dr. Raymond Paulino
- Dr. Hideo Nagahashi
- Mr. Vince Campo