# Undergraduate Research

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

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**Title:**Projects on applied and computational discrete mathematics

**Prof. Jesus DeLoera**

**Principal Investigator (PI):**

**Description:**Seeking diligent hardworking students with strong interests and background in at least two of the following topics:

**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

**Prof. Tim Lewis**

**Investigator (PI):****Principal****Description:**Topics include:

**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.

**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.

**Requirements:**Programming in MATLAB.

**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.

**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.

### APPLY ONLINE

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.