URA Research Project Ideas
What follows is a list of some of the project topics that faculty members in the department of mathematics have suggested as suitable for undergraduate research projects. Students who wish to participate can register and receive credit for an independent study or may be able to obtain URA funding to get paid to work on these projects.
Details of the project requirements will be worked out between the faculty supervisor and the student. Some of these projects require little background and are suitable for freshmen or sophomores, while others require knowledge of linear algebra, ordinary differential equations, or group theory. This list is by no means exclusive: any student with a particular interest in some area of research is encouraged to seek out a faculty supervisor. Students are encouraged to contact the URA Program Coordinator for help finding a suitable faculty research mentor.
Students participating in undergraduate research for credit must submit a proposal form through the math academic office. Stop by the window at Math 108 once you have lined up your project advisor and topic.
Project ideas under construction; this list is not exhaustive  there are additional faculty who are interested in working with undergraduates.
Name  Research Area(s)  Prerequisites  Honors Thesis?^{*}  URA for Credit?  URA for Pay?**  Last Updated 

Numerical Simulation of Waves in Optics, fluids and solids; 
introductory numerical analysis, basic physics/optics and computer programming. 
Yes 
Yes 
Yes 
6/13/2013 

Andrew Gillette  Derive formulas that will be used in "maximally efficient" code for the numerical simulation of physical phenomena. The specifics of the project will be determined later but may rely on computational geometry, combinatorics, and numerical analysis.  Vector calculus (223) and linear algebra (313 or higher). Computer science and programming background is preferred. Interested students should contact me in Spring 2017 to start research in Summer or Fall 2017.  Yes  Yes  Maybe 
9/21/16 
Developing computer software to visualize abstract geometries and polyhedral geometries (like the dodecahedron). Study of differential equations that deform arbitrary embeddings of graphs into "nice" embeddings for graphs. 
Basic linear algebra, differential equations. Topology can be a plus, but not necessary. General mathematical sophistication. Some computer science/programming background is a plus. 
Yes 
Yes 
Yes 
9/17/2012 

Create a dynamic map of mosquito abundance across Arizona hat evolves with current and future weather predictions though 2090. Current climate data will be acquired and future daily weather predictions (temperature and precipitation) generated across the entire state and used to estimate daily abundance for multiple species of mosquitoes. Interested students are also encouraged to enroll in ISTA 420/520 for Fall 2016. 
Programming is not essential, but encouraged (you will learn command line proficiency and basic programming) 
Ask 
Ask 
Ask 
5/17/16 


Evolution of gene circuits controlling segmentation;Description: A basic question in evolutionary developmental ("evodevo") biology is how the genetic circuitry controlling development have evolved to produce more and more complex organisms. Motivated by this question, Eric Siggia and collaborators have proposed a highly idealized model that tries to capture some of the basic features of the evolution of segmented bodies. Though extremely simplified, their models have yielded some insights into the origin and structure of gene circuits controlling development, and also leads to some interesting mathematical questions involving e.g. bifurcations. This project proposes to implement and study the model. Potential directions include bifurcation analysis and modifying the model to address features other than segmentation. 
Probability (464); programming (Python, Matlab, Java, or C/C++); stochastic processes (468) and/or nonlinear dynamics (454) helpful.  Yes  Yes  Maybe  3/1/2016 
Computational Group Theory; 
413 Linear Algebra or 
Yes 
Yes 
Maybe 
9/18/2012 

Douglas Pickrell  power series identities; conformal mappings  linear algebra, complex variables.  Yes  Yes  Maybe  9/23/2012 
Shankar Venkataramani  Differential equations and modeling physical phenomena; Geometry and applications; Problems in Complex analysis 
Math 254/Math 355 (for Differential equations); Math 323 (for all the problems); MATH 425 (for Complex analysis). 
Yes  Yes  Yes  9/12/2014 
*Honors Thesis MATH 498H credit available to students in the Honors College.
**Restrictions may apply. Ask the individual faculty member for details.