# 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: FALL 2018

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**Title:**Detecting percolation in random environments

**Principal Investigator (PI):**Prof. Javier Arsuaga

**Description:**Certain morphogenesis processes in molecular biology seem to be subject to percolation. In previous work we have developed algorithms to detect percolation in planar lattices and have done some preliminary work on detecting percolation in random environments (see reference below). In this project, one or two, student(s) will work together to develop algorithms to detect percolation in random environments in the plane and in spheres. The applications of these models include kinetoplast DNA and the formation of some viral capsids.

**Reference:**

**Requirements:**GPA at least 3.6, MAT128A and B or C. Interested in applications of mathematical physics to molecular biology. Excellent programming skills, excitement for interdisciplinary work. At least 10 hour/week commitment.

**Application Code:**arsuaga

**Title:**Tau functions of Drinfeld-Sokolov hierarchies

**Principal Investigator (PI):**Prof. Martin Luu

**Description:**Drinfeld and Sokolov constructed in the 1980’s interesting dynamical systems attached to suitable Lie algebras (such as square matrices with vanishing trace). For each point in the phase space one expects to have a special function, the so-called tau function, encoding important and subtle information. Only recently a general definition of this function has emerged. In this project the student will write computer code that can (with suitable initial data) actually calculate these functions.

**Requirements:**Most important is a good grasp of linear algebra as covered in MAT 67 as well as a strong background in programming.

**Application Code:**luu

**Title:**Renewable Energy Stochastics

**Principal Investigator (PI):**Prof. David L. Woodruff (Graduate School of Management)

**Description:**Paid internship: Help develop, test, document and experiment with software for characterizing uncertain energy production from renewable energy sources.

**Requirements:**Coursework in probably and statistics, demonstrated skill as a Python programmer.

**Application Code:**woodruff

**Title:**Mathematical modeling projects in neurobiology and cardiac electrophysiology [Note: Not looking for new students until Spring 2019]

**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:**will be available closer to Spring 2019

### APPLY ONLINE

The application for Fall 2018 research opportunities is available online. Please note that you will need the Application Code (from the section above) for the position(s) you are interested in. **For full consideration, please apply before October 15.**