Welcome to the 2021 Rose-Hulman Undergraduate Mathematics
Conference. This is our 37^{th} conference
and the first year we have held our conference *completely online*. The vision for the
Rose-Hulman Undergraduate Mathematics Conference
is to provide a venue to highlight and celebrate the accomplishments and work
of undergraduate mathematicians and statisticians. The conference is put on
largely by undergraduates for undergraduates. The contributed student talks and posters will
cover an array of topics including pure mathematical
theory, applied modeling, statistics, and data science.

** Due to the current uncertain conditions related to COVID, we regret that we have to cancel the 2022
Rose-Hulman Undergraduate Mathematics Conference.
We anticipate holding a conference in the spring of 2023 and look forward to seeing you then!
**

*Studying the shape of data through topology and geometry*

Big data is everywhere, and many techniques are being developed across math and computer science to analyze and study data sets. For example, one fundamental concept is how to compare such datasets; this requires new types of distance measurements to study how similar they are. In a related vein, techniques are needed to look for underlying patterns or shapes in the data. Many of these methods pull from fundamentals tools in topology and geometry, which have a rich history for studying such problems. In this talk, we will introduce and discuss the growing field of topological data analysis, which leverages key concepts from topology and geometry to simplify, compare, and analyze a wide range of data sets.

Dr. Erin Wolf Chambers is a Professor and the Associate Chair at Saint Louis University in the Department of Computer Science, with a secondary appointment in the Department of Mathematics. Her research focus is on computational topology and geometry, with a more general interest in combinatorics and combinatorial algorithms. Complementing this work, she is also active in research projects to support and improve the culture and climate in computer science and mathematics, as well as to try to improve broader STEM educational experiences at all levels. She serves as a trustee for the Society of Computational Geometry and on the SafeTOC organizing committee, as well as being an editor for Journal of Computational Geometry and for the Journal of Applied and Computational Topology. She received her PhD in Computer Science from the University of Illinois at Urbana-Champaign in 2008, and was a Visiting Research Professor at Saarland University in summer 2011.

*All Tangled Up*

Toys have inspired a lot of interesting mathematics. The Spirograph^{TM} helps children create lovely curves by rolling a small circle around the inside or the outside of a larger circle. These curves are called hypotrochoids and epitrochoids and are special cases of mathematical curves called roulettes. A roulette is created by following a point attached to one curve as that curve "rolls" along another curve. Another children's toy, the Tangle^{TM}, inspired some students and me to investigate roulettes that we get by rolling a circle around the inside of a "tangle curve," which is made up of quarter circles. The resulting roulettes we named "tangloids." In this talk, we will look at many pretty pictures and animations of these curves and discuss some of their interesting properties. As a bonus, I will discuss the nature of generalization, which is very important in mathematics.

Carol Schumacher is Professor of Mathematics at Kenyon College and is currently serving her fourth term as department chair. She received her Ph.D. in mathematics from The University of Texas at Austin. Schumacher is the recipient of Kenyon's Trustee Teaching Award and of the Ohio Section MAA's Distinguished Teaching Award. She is the author of *Closer and Closer: Introducing Real Analysis* and *Chapter Zero: Fundamental Notions of Abstract Mathematics, 2E*. Schumacher is active in the Mathematical Association of America. She was co-chair of the 2015 CUPM Curriculum Guide to Majors in the Mathematical Sciences and recently completed a term as MAA VP.