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.
Looking for examples of undergraduate research? The Honors College maintains a repository of past honors thesis submissions; use the Advanced Filters to search by discipline (Mathematics or Statistics & Data Science). It may also be helpful to look at past MathFest Student Papers, as well as SUnMaRC abstracts.
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 list is not exhaustive - there are additional faculty who are interested in working with undergraduates that have not provided information to us.
If a project has not been updated in a long time, check the professor's homepage to see what they have been working on most recently. Research areas tend not to change drastically.
| Name | Research Area(s) | Prerequisites | Honors Thesis?* | URA for Credit? | URA for Pay?** | Last Updated |
|---|---|---|---|---|---|---|
|
Mathematics education; teacher noticing; equitable teaching practices; community learning; the teaching and learning of linear algebra; socio-politics of mathematics education in Indonesia |
Interest and awareness of diversity, equity, and inclusivity; Interest in issues related to the teaching and learning of mathematics; Math 313, specific for the linear algebra project; Proficiency in Indonesian (Bahasa Indonesia), specific for the Indonesian narrative project. | Yes | Yes | Ask | 10/3/2023 | |
|
Numerical Simulation of Waves in Optics, fluids and solids. |
introductory numerical analysis, basic physics/optics and computer programming. |
Yes |
Yes |
No |
9/7/2021 |
|
|
Multiagent systems |
Math 254, Math 335, Math 454, | Yes | Yes | No | 10/3/2023 | |
|
statistical mechanics, artificial intelligence, computer graphics |
ability to program | Yes | Yes | No | 8/16/2022 | |
| 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 |
1/17/2017 |
| 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 |
1/17/2017 |
|
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 |
|
| Computational Biology; Population Genetics; Bioinformatics | Some programming experience is essential, as is an interest in biological questions. | Yes | Yes | Ask | 12/4/2023 | |
| Mainly number theory, although I have worked with undergrads on a variety of topics outside of number theory. | None | Yes | Yes | No | 8/25/2022 | |
| Analysis of partial differential equations (PDE) and/or ordinary differential equations related to PDE | Math 313, Math 355, perhaps a bit of coding, Math 425 is a plus | Yes | Yes | Ask | 8/16/2022 | |
|
Geometry: Study the space of three and four point configurations on the (projective) plane.
|
good command of Linear Algebra |
Yes |
Yes |
Ask |
1/3/2017 |
|
| Tom Kennedy | Self-avoiding random walks. More detail at : math.arizona.edu/~tgk/undergrad_research_s19 | Math 464. Some programming experience would be helpful, but not required. | Yes | Yes | Yes | 12/2/2018 |
|
Nonlinear dynamics; Monte Carlo methods; machine learning.
|
Minimum prerequisites are the calculus sequence, linear algebra (313), and differential equations (254 or 355). Some probability (363 or higher) a bonus, and 464 and/or 454 would be great but not required. Programming ability or willingness to learn by doing a must. | Yes | Yes | Maybe | 9/2/2021 | |
|
Computational Group Theory; |
413 Linear Algebra or |
Yes |
Yes |
Maybe |
9/18/2012 |
|
| evolutionary theory; bioinformatic studies of protein evolution or molecular error rates | Some programming experience required (C and/or Python preferred). Knowledge of probability & statistics, and/or biology preferred but not required. | Yes | Yes | Ask | 10/3/2023 | |
| Random matrix theory (general theory, modeling applications) | Undergrad probability sequence, measure theory (intro level), basic coding (e.g., MATLAB, python, Julia) | Yes | Yes | No | 8/25/2022 | |
| Douglas Pickrell | Power series identities; conformal mappings; random self-avoiding loops and random surfaces | Linear algebra, complex variables, and basic probability, respectively | Yes | Yes | No | 10/3/2023 |
| Walter Piegorsch | Statistical inference; Quantitative risk analysis | MATH 466; DATA 467 | Yes | Yes | No | 9/2/2021 |
| Henry Scharf | Bayesian hierarchical models; ecological applications of statistics; data visualization | DATA 375 or strong experience with R; MATH 464 and 466; DATA 467 is helpful | Yes | Yes | Yes | 12/4/2023 |
| Patrick Shipman | topological data analysis; applied modeling and differential equations in (bio)chemistry and physics with the option to do experimental laboratory work with plant pigments; complex variables and differential geometry; continued fraction expansions and projective geometry; pattern formation | Varied requirements depending on the project, so please contact me if interested in a topic. | Yes | Yes | No | 10/3/2023 |
| Robert Sims | (sabbatical 2023-24 - not available) Mathematical Physics; also see Dr. Sims' website | Linear Algebra and Differential Equations | Yes | Yes | No | 8/16/2022 |
| Doug Ulmer | Number theory, algebraic geometry, possibly cryptography. | Abstract algebra required. Some geometry and/or complex analysis would be helpful. | Yes | Yes | Yes | 9/2/2021 |
| Aparna Upadhyay | Group Theory; Representation Theory, Combinatorics | Math 313, Math 323, Math 415A | Yes | Yes | No | 9/9/2022 |
| 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 |
| Pan Yan | Number Theory; Representation Theory | linear algebra (Math 413) and abstract algebra (Math 415A) | Yes | Yes | Ask | 10/3/2023 |
| Hang Xue | Number Theory, Representation Theory | solid background in linear algebra and abstract algebra | Yes | Yes | No | 8/16/2022 |
| Helen Zhang | Statistics, Machine Learning | MATH 466, DATA 467 | Yes | Yes | No | 11/30/2023 |
*Honors Thesis MATH 498H credit available to students in the Honors College.
**Restrictions may apply. Ask the individual faculty member for details.