UNDERGRADUATE RESEARCH
OPPORTUNITIES FOR RESEARCH
MATH 4800 - Undergraduate Research Topics
| Fall 2025: | Category Theory |
| Instructor: |
Sri Iyengar, srikanth.b.iyengar@utah.edu |
| Day(s)/Time: | Tu/Th 12:25-1:45 PM |
| Location: | LCB 323 |
| Course Credit: | 3 credits |
| Compensation: | $500 (Notice that this is a class, so regular tuition policies apply.) |
| Description: |
This is an introductory course in category theory. The plan is to discuss basic concepts like functors, natural transformations, adjoint functors, colimits and limits, etc, that play an important role in many branches of mathematics. The focus will be on learning by doing: I will begin each class with a short introductory lecture and the rest of the time will be spent on worksheets related to the topic of the day. Towards the end of the course, there will be student presentations on various topics. Some relevant texts: Category theory in context by Emily Riehl, A first course in category theory by Ana Agore Interested students should contact the instructor for admission to the course. |
| Prerequisites: |
Nothing more than some mathematical maturity. There will be plenty of examples, to illustrate the concepts we encounter, which may require some prior knowledge of basic mathematical structures like groups, rings, etc. but this can be picked up along the way. |
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?
OR
JWB 325
801-585-1628