Undergraduate Research is an great opportunity to get more involved in the Math Department while working directly with faculty to expand the bounds of existing knowledge. There are many benefits to conducting undergraduate research, including the opportunity to:
- Explore an area of interest more deeply
- Learn first-hand about research to determine if you would like to pursue advanced study after your bachelor's degree
- Gain experience that is often highly valued by graduate school admissions committees
- Present your findings at the UC Davis Undergraduate Research Conference or other symposia, and possibly co-author a published paper
- Build relationships with faculty, which can lead to personalized letters of recommendation
MAT 099/199: RESEARCH CREDIT
Students completing undergraduate research (MAT 99/199) will receive lower/upper division credit toward graduation requirements (180 unit requirement) but will not receive credit toward their major. Every 1 unit of credit corresponds to 3 hours of work a week, or 30 hours of work per quarter.
MAT 099: Undergraduates students who have 83 units or less completed (lower division credit)
MAT 199: Undergraduate students who have 84 units or more completed (upper division credit)
RESEARCH PROJECTS AVAILABLE: SPRING 2018
Title: Projects on applied and computational discrete mathematics
Principal Investigator (PI): Prof. Jesus DeLoera
Description: Seeking diligent hardworking students with strong interests and background in at least two of the following topics:
Discrete Math, Algorithms, Optimization, Computational Geometry/topology, Operations Research and Data Sciences,
Machine learning. One or two projects in the intersection of these mathematical areas open starting Spring 2018.
Requirements: GPA 3.6 or higher. Very strong programming experience (e.g., at least ECS 60 with an A), A or higher grade in at least two of the following courses: Math 145, 146, 148, 168, 160, 167, 128, 150, or 135. Preferably junior level as the projects could be extended to last for a year. Honors senior thesis possible.
Application Code: deloera
Title: Mathematical modeling projects in neurobiology and cardiac electrophysiology
Principal Investigator (PI): Prof. Tim Lewis
Description: Topics include:
- neural and mechanical mechanisms of locomotion in "model" systems
- autonomic (neural) regulation of cardiac activity
- effects of pharmacological drugs on electrical activity in the heart.
Requirements: MAT 22AB necessary; MAT 119A and/or MAT 124 highly preferred. Some experience in computer programming is required, and a willingness to learn mathematical modeling and biology is essential.
Application Code: lewis
Title: Forest Fire Simulator
Principal Investigator (PI): Prof. David L. Woodruff
Description: The research project involves a new cells-based fire spread simulator that captures stochastics. It includes a wide range of options that gives flexibility to the user when performing simulations such as statistical analysis, graphical outputs, GIS interaction, etc. In addition, a parallel implementation for high performance computers is included, allowing the users to take advantage of this approach when performing large-scale simulations. Its outputs are already integrated with optimization software like AMPL or PYOMO. It has been completely programmed in Python.
1a. For serious Python programmers: make existing code pep-8 compliant (with google-style docstrings), improve unit tests, prepare for git-hub release. Perhaps add new features.
1b. Verify code works on real forests as well as synthetic test forests. Try to validate on real forests.
1c. Improve documentation.
1d. Improve animations.
1e. Improve user interface.
1f. Improve stats output.
Only 1a requires extensive knowledge of Python, but some knowledge will be helpful for 1d and 1e.
Requirements: Students must have previously taken a college-level course (preferably at UC Davis) in probability or statistics and a college-level (preferably from ECS) programming course.
Application Code: woodruff1a, woodruff 1b, woodruff 1c, etc. (based on which project or projects you are interested in)
Title: Investigating computational methods for viscoelastic fluids
Principle Investigators (PI): Prof. Bob Guy and Prof. Becca Thomases
Description: This project involves investigating computational methods for viscoelastic fluids. We are seeking one or two students to participate in this project. We are interested in working with students to (1) investigate GPU acceleration of an existing code, (2) investigate the stability/accuracy of different time integrators applied to this system, (3) use the codes to explore applications in biology.
Backgroud: Viscoelastic fluids are typically mixtures of solvent (e.g. water) and macromolecules (e.g. polymers) which give the fluid memory of past deformations. Consider egg white or mucus as examples. These kinds of fluids present different numerical challenges beyond those of traditional computational fluid dynamics. Our group has been investigating numerical methods for solving the equations, as well as applications of viscoelastic fluids including microscale mixing and locomotion of micro-organisisms.
Requirements: Programming in MATLAB.
Math courses that would be helpful, but not required:
- Numerical Analysis Sequence 128ABC, particularly 128C
- Ordinary Differential Equations 119A
- Partial Differential Equations 118A
- Fourier Analysis 129
Application Code: guy
Title: The light-cone in non-relativistic lattice systems: Estimating Lieb-Robinson velocities [positions filled]
Principal Investigator (PI): Prof. Bruno Nachtergaele
Description: The intriguing consequences of quantum entanglement are often described as "spooky action at a distance" but, in reality, signals in quantum many-body lattice systems of interacting spins, particles, or phonons, propagate with a finite speed. Lieb-Robinson bounds are mathematical estimates that provide an upper bound for this speed.
The established approach, which is well-documented in the literature, gives estimates that apply very genearlly but that are far from optimal. The goal of this project is to obtain accurate upper and lower bounds for the propagation speed in specific model systems. For some models, experiments in optical lattices and other systems have produced data on observed speeds.
Requirements: basics of linear algebra and ODE (MAT 22A or MAT 67, and MAT 22B). Familiarity with the principles of quantum physics would be helpful but is not required.
Application Code: positions are currently filled, so we are no longer accepting applications for this project.
The application for Spring 2018 research opportunities is online here. Please note that you will need the Application Code (from the section above) for the position(s) you are interested in.
The deadline to apply for Spring 2018 research opportunities is the first week of Spring Quarter. Applications submitted before the deadline may be reviewed on a rolling basis.