Math 492 Undergraduate Research in Math
A.J. Hildebrand

About Math 492

Math 492 is a recently introduced course, intended to accommodate undergraduate research projects in mathematics. Here is the official course description:
Work closely with department faculty on a well-defined research project. Topics and nature of assistance vary. Capstone paper or computational project required.

Why take Math 492

Undergraduate research experiences are increasingly valued by employers and graduate schools, A Math 492 project provides an accessible way for UIUC students to gain such a research experience, while at the same time earning advanced course credit, and offering opportunities to gain additional experiences through presentations at conferences and outreach events. It increases your chances of getting into competitive summer research programs and sought-after internships, and it can boost your prospects with graduate schools.

My experience with Math 492

Since Fall 2014 (when the course number was first introduced), I have been running more than a dozen Math 492 projects, involving between one and four students each, and I have enjoyed every one of them! See my Undergraduate Research page for more information on these projects.

Some of these projects were offered under the Illinois Geometry Lab (IGL) framework, while others have been run as independent Math 492 projects that I have arranged directly with the students involved. I typically run one or two IGL projects each semester (one on a theme at the interface of Calculus, Geometry, and Probability, and the other on a theme at the interface of Probability, Number Theory), along with one or more independent projects, typically mini projects with 1 or 2 hours of Math 492 credit.

All of my projects have led to conference presentations by the students involved (another resume booster!), some at local or regional undergraduate conferences such as the annual University of Illinois Undergraduate Research Symposium, others at prestigious national meetings such as the meetings of the Mathematical Association of America and the American Mathematical Society.

How to get involved in a Math 492 project

For IGL projects there is a centralized online application process through the IGL website. Each semester, around a dozen or more projects are offered. Students list up to three choices in their application, and the IGL Management then selects three or four students for each project. The IGL typically receives two or three times as many applications as there are spots available, so acceptance is not guaranteed. Applications open usually in late fall for projects in the spring semester, and in late spring for projects in the fall semester. Check the IGL website for announcements.

Independent Math 492 projects are arranged directly with the faculty member. (If you are interested in one of my projects, contact me!) These projects offer more flexibility in terms of deadlines, the number of students involved, the time commitment (for example, a project can be run at 1 or 2 credit hours instead of 3, with a correspondingly lower time commitment). They can also accommodate topics that would not be a good fit for the Illinois Geometry Lab.

Next steps: If you are interested in doing a Math 492 project with me, first check out my Undergraduate Research Page for descriptions of past projects, general expectations, and prerequisites. In coming semesters, I plan to expand the project offerings in areas such as data analytics, stochastic modeling, and applied probability, while still offering a range of projects in traditional areas of mathematics, such as calculus, geometry, probability, and number theory. If you are interested in any of these projects, I'd be happy to discuss possible options with you. Contact me at, and send me a current cv/resume and a transcript.

Math 492 (Undergraduate Research in Math) versus Math 390 (Individual Study)

These two courses are closely related and targeted at similar audiences: students who have a strong record of math courses (typically including honors courses) and who may be considering graduate school in mathematics or a related field such as mathematical finance, economics, statistics, computer science, etc. In Math 390 the focus is mainly on the reading and studying of advanced material (e.g., research papers). A Math 492 project typically starts out in the same way, by studying relevant articles in the literature, and then moves on to the research aspect. For more about Math 390 opportunities see my Math 390 page.

Links and Resources

Last modified: Wed 08 May 2019 12:10:26 PM CDT A.J. Hildebrand