UNDERGRADUATE RESEARCH

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.

OPPORTUNITIES FOR 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 2025:	Introduction to Optimal Design
Instructor:	Andrej Cherkaev, [email protected]
Day(s)/Time:	Tu/Th 3:40-5:00 PM
Location:	WEB 2470
Course Credit:	3 credits
Compensation:	$500 (Notice that this is a class, so regular tuition policies apply.)
Description:	Optimization of the performance of physical systems means choosing parameters and positions of their elements to maximize the desired outcome. Examples: In an optimal frame loaded with known forces, one chooses the thickness of the rods or their locations to maximize the stiffness if the total weight of available material is given. If the load is unknown a priori, one may play the game load vs. design, finding the best response to the worst load position. In biological structures perfected by evolution, one may ask what the optimality of a specific organ means. In what sense are they optimal? Examples include a tree trunk, jellyfish shape, bone structure, etc. Generally, optimal design asks for the best layout of several conducting or elastic materials in a domain to minimize a functional, something like the temperature in a chosen point or a stress in a part of the boundary. The optimal layout is often a composite with unique microstructures or a metamaterial with properties not typically found in nature. In Math 4800, we will outline optimal design ideas and challenges and work on several projects. Interested students should contact the instructor for admission to the course.
Prerequisites:	Linear Algebra Ordinary Differential Equations Familiarity with computing, either MATLAB or Maple, is preferred

Math 4800 class archive

*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.

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, 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.

*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, 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.

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.

OTHER FUNDING SOURCES

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.

RESEARCH RELATED LINKS

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 (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.

Questions?

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

Aaron Bertram

Undergraduate Research Coordinator/Director of Undergraduate Studies
JWB 325
801-585-1628