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The Department of Mathematics research experiences allow students to better understand published works, learn to collaborate, explore new interests, develop independent critical thinking skills with oral/written communication skills, discover their passion for research and continue on to graduate studies. Below are opportunities to engage in research. 


(NOTE: You do not need to be a Math major/minor to take advantage of these research opportunities): 

These courses provide a research experience in a familiar course setting. Topics vary every semester, but there is usually a Pure Mathematics and an Applied Mathematics oriented course every academic year. Enrollment in this class is by permission of the instructor only.

MATH 4800 - Undergraduate Research Topics

Spring 2024: Exploring Field Pattern Materials
Instructor: Graeme Milton (
Day(s)/Time: TuTh/03:40PM-05:00PM
Location: WEB 2460
Course Credit: 3 credits
Compensation: $500 (Notice that this is a class, so regular tuition policies apply.)

Composite materials sometimes have properties unlike those of their constituents and in this context they are known as metamaterials.  A famous example is the Roman Lysurgis glass cup in the British museum which may appear either green or red depending on whether the light source is inside or outside the glass.  Regular arrays of spheres of silica give opals their color.  Wave propagation in static but inhomogeneous media has been well studied.  Now there is great interest in exploring wave propagation in dynamic media, i.e. "space-time materials," where the material properties vary with both time and space.  This class will explore space-time materials for which waves propagate in ordered patterns in space-time.  These are known as field pattern materials.  Previous research has only scratched the surface and there is much to investigate here.  More examples of field pattern materials are needed.  This is just ray tracing, but one needs to position the interfaces so the rays form patterns.  What relations are possible between the periodicity of the material and the periodicity of the field pattern?  (The field pattern can break symmetry just as symmetry is broken in "time crystals.")  If there is no field pattern, but rather just a complicate cascade of wave scattering, can one find something analogous to an ergodic hypothesis to make predictions?  After reviewing the literature, the class will start with easy problems then move on to more challenging problems.  It is anticipated that all students making significant contributions will be coauthors of a publication resulting from the work.  Writing up the paper will be part of the class.  For further background see the SIAM news article, "New Horizons in the Study of Waves in Space-Time Microstructures" and references therein.  Please email the instructor ( if you are interested in taking this class.


Linear Algebra (MATH 2270 or MATH 2250) and Partial Differential Equations (MATH 3150 or MATH 5440).

Applications are due the first Friday of each semester.  Applications will be considered on a rolling basis as they come in.

See below for instructions.


The student works with a faculty mentor on exploring an area of mathematics not usually taught in standard classes. Mentor and advisor meet weekly throughout the semester to discuss topics from relevant text or journal article readings. These projects may sometimes be appropriate as preludes to independent projects, in cases where the ultimate research area requires a lot of prerequisite knowledge. At the end of the semester, the student produces a final expository paper on aspects of their research.


Up to $1000 in Fall or Spring.

Up to $750 in the Summer.

Expectations: During the semester meet regularly with mentor (at least weekly), and generate an expository paper summarizing what you learned. You are also encouraged to give a presentation in our symposium, which is usually held on the Reading Day before final exams begin.
Course Credit: You may take Introduction to Research as a class (up to 3 credit hours). Please specify that in your application(The course number will be 5910. Normal tuition policies apply. You can count this course towards university Upper Division Hour requirements, but not as an elective for your math/applied math major. Note that a section needs to be created for you and your mentor, so please apply early!).

Application Instructions:

See this file for instructions.

Applications are due the first Friday of each semester.  Applications will be considered on a rolling basis as they come in.

See below for instructions.

Work on a research project in Mathematics under the mentorship of a faculty member. You must have a member of the Mathematics faculty who is willing to serve as your mentor. Discuss with the prospective mentor the scope and design of your project and prepare a project description.


Up to $1,500 for Fall and Spring semesters. For the Summer, the amounts are multiplied by 3/4. Continued funding depends on the student's performance in the previously funded REU activities.

Expectations: Meet regularly with mentor, give a talk with slides, write a report, and submit an evaluation. Your work, presentation, and report will be evaluated by Mathematics faculty.
Time Commitment: 10 hours per week, on average

Application Instructions:

See this file for instructions.


Science Research Initiative (SRI)

Within the College of Science

The SRI is a program for first- and second-year students that enables them to start working in an SRI stream, or research experience, at the beginning of their journey at the University of Utah. This program assumes incoming students will not have any college-level research experience; instead, you will learn alongside your fellow students to gain research skills, technical experience, and the unique opportunity to learn from faculty.

Click Here for More Information


The Department of Mathematics offers travel support for undergraduates who are presenting their research.  Each award is for up to $500 and there will be a max of three awards per year.  Apply now.


These meetings are held at the end of semester and showcase the research that is being done by undergraduates in our department.

Archive of the symposium from Fall 2013 and here for pre-Fall 2013.


The Undergraduate Research Opportunity Program (UROP) which is sponsored by the University of Utah Office of Undergraduate Research also supports undergraduate research. The support you get is $1200 for the first semester and $600 for a renewal (as of Fall 2015). The deadlines are usually mid July (for Fall support) and mid November (for Spring support), so plan accordingly.

Individual faculty members or research groups may also sponsor undergraduate research through grants.




Students fulfilling certain qualifications may have the designation of "Undergraduate Research Scholar" appear in the awards section of their transcript. For more information visit the Undergraduate Research Scholar Designation (URSD) webpage.

Why? An independent research project is excellent preparation for graduate school, teaching, research, or a job in industry. It is also fun and challenging. You will learn things in a completely new way when you work independently, but with the help of a faculty mentor.

How? Choose an undergraduate research advisor (a faculty member) and a problem or topic to work on. If you desire, you may apply for funding, either through the Mathematics department REU program (see above) or the Office of Undergraduate Studies' UROP program.

What? Whatever you do --- solve a problem, prove a theorem, develop a computer model, find a new way of teaching or explaining a topic -- you will write up the results in a paper accessible to other undergraduate students.

When? Usually during the junior or senior year.





Consult with a faculty member you would be interested in working with...


Aaron Bertram

Undergraduate Research Coordinator/Director of Undergraduate Studies
JWB 325
Last Updated: 1/26/24