Mathematics research by undergraduates in the United States has gone from rare in the mid-1980s to commonplace now. Undergraduate contributions range from introductory to cutting edge, with occasional publications in prestigious professional journals. Now there are several undergraduate journals, Involve, Rose-Hulman, Minnesota, SIAM and Pi Mu Epsilon among them, containing significant results in all mathematical specialties.
These days undergraduate research experience is critical to being competitive for entrance into top graduate programs. Numerous summer programs are funded by the National Science Foundation and the Mathematics Association of America, among others. VCU also offers summer support through the Undergraduate Research Opportunities Program and Honors Summer Undergraduate Research Program, the latter available to Honors students only. These experiences are also highly valuable for employment at the plethora of national labs and federal agencies (including the National Security Agency, the largest employer of mathematicians in the world), as well as the huge array of technical companies in STEM industries like communications, biotech, information, finance, internet, pharmaceuticals, entertainment and more.
But there are other, more fundamental reasons to engage in mathematical research. Students often gain a greater understanding of how mathematics works in the modern world, a heightened facility with generating and analyzing data in any realm of life, an exuberance for group and solo problem solving that welcomes hard challenges, a stronger ability to communicate technical information and a deepened connection with fellow students and professors in the project.
Sponsored by the National Security Agency and the National Science Foundation
8-10 undergraduates will have a hands-on introduction to computational research endeavors and improve their problem-solving, communication and computer programming skills through our REU (Research Experience for Undergraduates) Program. Selected students will receive a $4,800 stipend and will be funded to present their work at conferences.
Visit the REU page for full details and application information.
RAMS Conference at VCU
Sponsored by the National Science Foundation
This free conference promotes education and research in the fields of mathematics, applied mathematics, statistics and operation research. It is tailored for undergraduate and graduate students to present results of their research.
Students have a number of opportunities to participate in cutting edge research. Many of these opportunities, see below, are offered in the summer. Though if you are interested please feel free to seek out a faculty member to ask if they have any opportunities beyond these listed or whether they might be interested in participating in these.
Undergraduate Research Opportunities Program: This is a summer VCU program that involves an application process that you complete with a faculty mentor. The application is typically due in early to mid-spring semester.
Honors Summer Undergraduate Research Program: This is a summer VCU program for honors students. The descriptions for the projects usually come up in early spring. You must be an honors student.
VCU Office of the Vice President For Research and Innovation: The VCU Strategic Research Priorities Plan seeks to enrich the human experience and advance human health and well-being through exceptionally creative, collaborative and community-engaged research.
This project studies a network model for the transportation of consumable resources. As in most models, a supply of the resource (in this case, "pebbles") is placed on various vertices of the graph, and a demand of pebbles is identified at certain other vertices. In this model, the movement of a pebble across an edge requires the loss or payment of a partner pebble; that is, while two pebbles leave a vertex together, only one arrives at the other end of the edge, as the other pebble vanishes. The central question asks whether a given supply can satisfy a fixed demand, but many other significant questions exist. We study this paradigm on an array of special graph classes, seeking to discover when one can be successful in achieving assorted goals. This field is new enough to have numerous interesting problems within reach of talented undergraduate students, and there have been many strong contributions from students over the years. Students with some background in graph theory, discrete math, combinatorics, and/or computer programming are particularly well suited, but the essential concepts can be learned as needed.
Chronic disease resulting from a diet high in fat and cholesterol affects over 50% of adults. Although the relationship between atherosclerosis and inflammation is not fully understood, it is known that macrophages and foam cells promote inflammation by secreting pro-inflammatory cytokines following accumulation of cholesterol. We are developing a computational model that accounts for the conversion of macrophages to foam cells and the formation of arterial plaques in atherosclerosis. Understanding the progression of size/shape/density and markers of disease progression are all important to examine with regard to the diagnosis and long term prognosis of individuals with atherosclerosis. Students with some background in MATLAB or other coding platforms will be most successful. Some knowledge of odes and/or pdes is also useful but the essential concepts can be learned as needed.
This is a funded project through the Jeffress Memorial Trust involving analyzing the biodiversity in a forest. In this project we create a mathematical model of a forest to simulate different types of disturbances (e.g. hurricane, fire, etc.) to examine their effect on biodiversity assuming different types of conspecific and heterospecific interactions within and between different species of trees. There are funds to pay a student $10/hour to work on this project. The requirements for the position include the ability to program in Matlab, being able to work with a team, and to available to work on the project through at least June 2019.
This research position involves mathematically modeling barrier island evolution. Students will work with, modify and run Matlab code that simulates how barrier islands are transformed based on physical, environmental, and biological processes. Experience with Matlab is not required but helpful. This is a paid position $12/hour. During the semester the expectation is about 10 hours/week and during the summer 29 hours/week.
The convex body isoperimetric conjecture in the plane states that the least perimeter to enclose given volume inside an open disk in the plane is greater than the least perimeter needed to enclose the same volume within any other convex body of the same volume. This conjecture has been proved for several special cases, and multiple sharp lower bounds have been obtained. The goal of this project is to investigate the convex body isoperimetric conjecture using weighted perimeter and areas, for example, when the length and the area of a shape are calculated with respect to a metric induced by p-norms. A strong background in single and multivariable calculus is the only requirement to be successful in this project.
Efficient Algorithms for the Quantum Satisfiability Problem
In quantum computers the fundamental bits of information are states of a quantum system known as qubits. In analogy with classical algorithms, quantum algorithms can be thought of as recipes to transform information stored in qubits. Some algorithms are faster than others and classifying problem based on how fast they can be solved by a quantum computer is of great importance for both theoretical and practical applications, including cryptography and on-line security. This project aims at developing efficient algorithms to efficiently solve specific instances of the quantum satisfiability problem (QSAT), which is expected to be in general intractable even on a quantum computer. Basic knowledge of linear algebra is recommended, some experience with coding (in any language) is desirable but not required.
Lie algebras provide an algebraic framework for encoding infinitesimal symmetries. Besides their many applications in geometry and in the theory of differential equations, Lie algebras are of fundamental importance in high energy physics as they are required in order to formulate the Standard Model of particle physics. The goal of this project is to study a class of geometric symmetries of Lie algebras known as generalized CRF structures, which have applications to the mathematical study of string theory. No prior knowledge of physics or Lie algebras is required. Familiarity with linear algebra is recommended.
Model of Breathing in Extremely Premature (EP) Infants
This project studies a model of breathing in extremely premature (EP) infants as it relates to the naturally compliant (floppy) chest wall typical of this population. EP infants that present with respiratory distress are currently treated with surfactant replacement therapy which aids in lung development but mechanical ventilation is almost always required as well. However, invasive ventilation is a source of trauma leading to irregular lung development in 1/3 of infants, and noninvasive ventilation has been observed to ineffective in this population. It is hypothesized that this is due to the highly compliant (floppy) chest wall leading to insufficient inhalation and progressive lung collapse. Our short term goal is to develop a full model with which to investigate this hypothesis and potentially uncover biomarkers that can distinguish infants at risk for ventilation failure, with a long term goal of developing a supportive treatment to stiffen the chest wall and facilitate ventilation. We are currently working with a base model parameterized for an idealized preterm infant, and several potential directions exist for further model development and analysis. Experience coding in MATLAB or related languages, familiarity with differential equations, and interest in human physiology are desired.
Knots and links are embeddings of closed loops in three-dimensional space. Knot and link invariants are mathematical objects that capture topological and geometric information about the link and its three-dimensional complement. This project seeks to advance our mathematical understanding of basic operations on knots and links, to explore the relationships between invariants of knots and three-manifolds, and to leverage these developments toward knot-theoretic models of DNA recombination mediated by enzymes. The central hypothesis of the proposal is that knot theory provides a rigorous mathematical framework with which to investigate molecular knotting and entanglement in DNA.
Students with a genuine interest in topology and geometry or some background in linear algebra or coding will be most successful. Prior knowledge of knot theory is not required, and essential skills can be learned along the way. There are funds to pay students an hourly wage. Students from underrepresented groups are especially encouraged to apply.
