The University of Arizona

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

Moysey Brio

Numerical Simulation of Waves in Optics, fluids and solids;
molecular and quantum dynamics simulations of laser ablation.

introductory numerical analysis, basic physics/optics and computer programming.





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


Karl Glasner Pattern formation on graphs; view description. ODEs, Linear Algebra, experience with MATLAB. Ideally one or more of: Graph Theory (math 443), Dynamical Systems (math454), PDEs (math456), Numerical Methods (math475) Yes Yes Ask


Karl Glasner Dynamics of self assembly at the nanoscale; view description. ODEs, some experience with MATLAB. Ideally one or more of: Dynamical Systems (math454), PDEs (math456), Numerical Methods (math475). Yes Yes Ask


David Glickenstein

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.





Yi Hu

Geometry:  Study the space of three and four point configurations on the (projective) plane.

good command of Linear Algebra





Joceline Lega

Unifying principles for vector-borne disease spread
Join our team working on the spread of mosquito-borne diseases. This undergraduate research assistantship, provided through support from the UA’s Improving Health/BIO5 Institute Graduate/Undergraduate Interdisciplinary “Link” Program, will allow you to work closely with an interdisciplinary, vertically-integrated team of professors and students (graduate and undergraduate) from Geography, Mathematics and Public Health on a current hot topic in the news: developing unifying principles for vector-borne disease spread. As a member of this team, you will work with a PhD student in Geography and three professors (in Mathematics, Geography, and Public Health) on collecting, maintaining, cleaning and analyzing data on mosquito presence, network information, and models of disease spread.
Please submit a letter of interest, transcript (unofficial is fine), and your CV to Dr. Joceline Lega ( by September 1st, 2016. The up-to 20 hr/week position (at $10 per hour or more depending on experience) begins this fall and can go through the spring 2017.

Preferred experience: math major core courses and some programming experience.





Kevin Lin


Evolution of gene circuits controlling segmentation;Description: A basic question in evolutionary developmental ("evo-devo") 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 

Klaus Lux

Computational Group Theory;
Computer Algebra

413 Linear Algebra or
415A Abstract Algebra





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
Calvin Zhang Research in Mathematical Biology: use methods from mathematics and computing to study operating mechanisms of living systems. In particular, I am interested in synaptic transmission and sensorimotor system. Topics of recent interest are stochastic synaptic vesicle release and rhythmic motor pattern generation in crustacean swimming. Familiarity with differential equations and probability as used in applications. Yes Yes Ask 9/29/2016

*Honors Thesis MATH 498H credit available to students in the Honors College.

**Restrictions may apply. Ask the individual faculty member for details.

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