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 

Mathematics education with a focus on teaching K12; Mathematics education with a focus on student learning K12; Mathematics education with a focus on inservice teacher professional development; Mathematics education with a focus on preservice teacher preparation; 
Interest in mathematics education research and/or preparing to be a teacher; MATH 112 & MATH 302A & MATH 302B (elementary teaching major) OR MATH 122A/B/MATH 125 & MATH 129 (math major, secondary teaching)  Yes  Yes  Maybe  9/17/2012  
Numerical Simulation of Waves in Optics, fluids and solids; 
introductory numerical analysis, basic physics/optics and computer programming. 
Yes 
Yes 
Yes 
6/13/2013 

Ildar Gabitov  mathematical modeling in material science, nanophotonics, optical fiber communications, wave theory  Differential equations, Calculus I and II  Yes  Yes  Maybe  9/24/2012 
Andrew Gillette  Computational geometry, especially using graphics software to generate visualizations of certain polygons and polyhedra.  Vector calculus (223), linear algebra (215), general mathematical sophistication. An interest in computational geometry and visualization. Some experience with computer science / programming.  Yes  Yes  Maybe 
9/15/2014* unable to take more students for spring 2015 
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 

Robert Indik  Computation and⁄or Numerical Linear Algebra  Programing experience, linear algebra at the level of 215 (including eigenvalues/eigenvectors) and differential equations (preferably 355, but 254 might be OK). Two out of three may work if the students is willing to work and learn.  Yes  Yes 
Maybe 
9/17/2013 

Monte Carlo methods; neural network dynamics; other problems involving dynamical processes on complex networks.  Probability at the level of 464; one of 454 or 485; some programming experience (for example Matlab, Python, R, C, ...). 456 and/or 468 a definite plus.  Yes  Yes  Maybe  9/24/2012 
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.