Research Experience for Undergraduates, Math REU

Mathematics REU: TBA

We have an application in at the NSF to restart the program in Summer 2026. We will update this page as soon as we have more information. You may direct all inquiries to Dr. Maddie Dawsey (mdawsey@uttyler.edu).

Mentors and Subject Areas

Dr. Maddie Dawsey – Integer Partitions

In number theory, an integer partition is a way of writing an integer as a weakly decreasing sum of positive integers, and the partition function counts the number of partitions of each integer. For example, one partition of 5 is 3+2, and there are 7 different partitions of 5. The partition function has lots of interesting size, divisibility, and asymptotic properties and is applicable to many other areas of mathematics, including combinatorics, algebra, and representation theory. We will explore various properties of partition functions for partitions whose summands are restricted in certain ways.

Past REU projects include: REU 2022.

Dr. Pamela Delgado – Summability Theory

For this project, we will explore Summability Theory, which extends the concept of classical convergence to assign meaningful values to sequences that may be divergent in the usual sense. A key example is Cesàro averaging, where a bounded sequence is replaced by the sequence of arithmetic means of its initial segments; this agrees with ordinary limits when they exist, but can also “sum” sequences such as (1,0,1,0,…), which do not converge in the classical sense. Building on recent work generalizing the Cesàro operator to function spaces and studying fractional powers of this operator, we will pursue open questions such as: generalize other summability operators to function-space settings, define fractional powers for these operators for both sequences and functions, and investigate when such operators commute, enabling the construction of Banach limits invariant under their compositions.

Dr. Joseph Vandehey – Continued Fractions

Continued fractions are an alternative to decimal expansions that encode additional information about how best to approximate the number by rationals. While the study of continued fractions over the reals is centuries old, far less is known about continued fractions of higher-dimensional spaces, like complex numbers, the quaternions, or — dare we even mention it — the octonions. In this project, we will investigate a well-known property of real continued fractions that is known to break for complex numbers.

Program Benefits

• A stipend of $5,600 for the eight-week program.
• Some travel funding to Tyler and partial funding to attend a national conference.
• Free on-campus housing at the Patriot Village or Eagle's Landing apartments, only a short walk from the mathematics department facilities in Ratliff Building North.
• Work daily with faculty during the research experience.
• Learn how to write and typeset a professional mathematics article using LaTeX.
• Learn how to prepare and deliver an excellent talk on mathematics.
• Participate in fun team-building social activities. Past activities have included:
  • Outdoor activities (disc golf, soccer, and a picnic at Tyler State Park).
  • A swamp boat tour of Caddo Lake.
  • A trip to Dallas to visit the arts district and watch a baseball game.