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REU Symposium

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.

Current projects (Summer 2018)

Jane Moffatt
Mentor: Davar Khoshnevisan
Intro to Research: Exploration and Simulation of Gaussian Processes

Audrey Brown
Mentor: Alla Borisyuk
Intro to Research: Analysis of Mice Olfactory Response Data

Dylan Johnson
Mentor: Karl Schwede, Daniel Smolkin, Marcus Robinson
Searching for Rings with Uniform Symbolic Topology Property

Faith Pearson, Dylan Soller
Mentor: Anna Romanova, Peter Trapa
Cracking Points of Finite Gelfand Pairs

Jack Garzella
Mentor: Fernando Guevara-Vasquez
Understanding Spring Netowrk Approximations for Continuous Elastic Bodies

Adam Lee
Mentor: Daniel Zavitz, Alla Borisyuk
Relationship between the connectivity of directed networks with discrete dynamics and their attractors.

How to get involved

The Mathematics department provides the following research opportunities for undergraduate students. Note: You do not need to be a Math major/minor to take advantage of these research opportunities!

NEW! Summer Program

Are you interested in learning about deeper mathematical concepts, but don't have the background to take more advanced classes?
Are you interested in learning more about mathematical research, but think there is a lot more you need to learn for now?
This program is intended for enthusiastic students who are looking for an intensive summer of mathematics, even though they do not have the mathematical experience to be ready to do a research project. Our subject is ELEMENTARY NUMBER THEORY, the study of the integers, whose basic questions have stimulated mathematics research for thousands of years. Participants will work closely throughout the day with one another and with the program staff, exploring a series of challenging problem sets that gradually develop many of the great ideas of classical number theory.
Rather than having material presented to them in lectures, students will be asked to experiment with the subject, formulating conjectures about what they believe to be true, and then to justify their claims rigorously. They will discover the excitement of being the origin rather than the receptacle of mathematical ideas; and they will prepare themselves to take advantage of the extensive possibilities open to mathematics majors at the U.
while building closer relationships with like-minded peers, getting to know some of the faculty and graduate students, and taking a closer look at everything the mathematics department has to offer.

The 2018 program is on its way. Please, come back next year!

Projects looking for students

1. Statistical estimation in the presence of highly unbalanced cross sectional data is challenging as traditional estimators perform poorly under those circumstances. Bootstrap based estimators are an option to deal with the problem. Simulation exercises to understand the behavior of bootstrapped estimators are a current topic of research. Undergrads who are excited about programing in R and learning about a simulation involving bootstrap are welcome to apply for this project. This project is offered during this summer.

With questions or to apply please contact Jyothsna Sainath (

Math 4800 Undergraduate Research Topics

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 usually by permission of the instructor only.

Compensation: $500 (Notice that this is a class, so regular tuition policies apply)

Fall 2018: Elliptic curves
Instructor: Gil Moss
When and Where: Tuesday and Thursday, 2:00-3:20, location TBD
The study of diophantine equations forms an ancient branch of number theory whose goal is to count solutions of polynomial equations in the integers or rational numbers. Fermat's last theorem is a famous example. Whereas linear and quadratic equations are well understood, much is unknown when the equations have degree 3. What little is known was proven using elegant combinations of algebra, number theory, and algebraic geometry. This course will focus in depth on cubic equations in two variables, that is, elliptic curves. We will begin by briefly covering some concepts in algebraic geometry, we will then shift to exploring the interplay of geometry and number theory in the setting of elliptic curves. In the first portion of the course, we will explore the interplay of geometry and number theory in the setting of elliptic curves. Examples of topics include finding rational points of finite order, counting points over finite fields, and the group properties of the set of rational points. The second portion of the course will shift to a broader discussion of some major developments that have taken place in the subject over the last century.
For more details, please consult the syllabus.

Prerequisites: Permission of the instructor.
There are no formal prerequisites, besides having experience writing proofs. However, the course will focus on the interplay of algebra, geometry, analysis, and number theory, so it is recommended that students have some familiarity with the basic notions in these areas (e.g. linear algebra, groups, rings, fields, polynomials, infinite series, complex numbers, factorization and primes in the integers). As one example, Math 4400 would provide a good background; or taking Math 5310 concurrently.

Interested students should email the instructor at

Math 4800 class archive

Introduction to Research projects

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 REU student produces a final expository paper on aspects of their research.

Students are strongly encouraged to take Intro to Research first, before doing an individual project. If you would like an exception, please ask your mentor to comment on your previous experience relevant for your project, in the letter of support.

You may take Intro to Research as a class, up to 3 credit hours. Please specify that in your application
(The course number may be: Math 5910, 5960, 4999, depending on your case. If you register, this would be a course, so normal tuition policies apply. You can count this course towards university upper course 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!).
Compensation: 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.

Deadline: Usually Tuesday on the second week of classes (first week of classes in the Summer).

See application instructions below

Independent REU projects

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.

Time Commitment: 10 hours per week, on average
Compensation: 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, and generate an evaluation and a report. Your work, presentation and report will be evaluated by faculty members and 1-2 best projects will be featured on our department website.

Deadline: Usually Tuesday on the second week of classes (first week of classes in the Summer).

See application instructions below

Application for Intro to Research or Independent REU project

Complete the online application form. You also need to submit before the deadline to ugrad_director(AT) math (DOT) utah [DOT] edu the following supplementary material:
  • A letter of support from your mentor (usually sent to the email above directly by your mentor).
  • A current unofficial transcript (generated on CIS). If you have a considerable amount of transfer credits (especially for Math classes), please include an unofficial transcript from your previous institution(s). (If sent by email, please use the PDF format.)
  • A project proposal prepared with your mentor. (If sent by email, please use the PDF format.)
  • If this is a continuing award: your report from previous semester, approved by your mentor.

Other funding sources

The Undergraduate Research Opportunity Program (UROP) which is sponsored by the University of Utah Office of Undergraduate Studies 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. Current department wide grants that provide support for undergraduate research are:

Undergraduate Research Scholar Designation

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 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.

For more information about research opportunities: consult with a faculty member you would be interested in working with, or the Undergraduate Research Coordinator/Director of Undergraduate Studies:

Alla Borisyuk
LCB 303

Research Related Links