Erin McNicholas
Dr. Erin McNicholas is a full professor of mathematics at Willamette University. Before receiving her Ph.D. from the University of Arizona she worked for the State of Oregon as a Metrologist and for the cryptography group at Sandia National Laboratory. As an algebraist, Professor McNicholas searches for symmetry in a wide variety of settings. In particular, she enjoys analyzing voting methods, cryptosystems, combinatorics, and graph theory through an algebraic lens. She is interested in courses and materials that integrate multiple mathematical perspectives, incorporate technology and applications, and generally humanize the subject. She co-authored the text Explorations in Number Theory - Commuting through the Numberverse and has developed courses on the history of mathematics and the design of escape rooms and mathematical puzzles. She has received teaching awards from the University of Arizona and Willamette University. In addition to her academic pursuits, Professor McNicholas enjoys painting and is a contributing artist for the second deck of EvenQuads playing cards honoring notable women in mathematics.
Professor of Mathematics
Ford Hall 211
900 State St
Salem, Oregon 97301
503-370-6590
Student Hours, Spring '25
Check the calendar below for updates
Tuesday 3:30-4:30, Wednesday 11:30-12:30, and Friday 12:00-1:00
*While these are the default times and you don't need an appointment, please check the calendar below for any changes. Student hours are canceled on University holidays. Additional times are available by appointment. You can also post questions on the course channel of the WU Math discord server.
Looking for something to do?
Attend an upcoming Math Colloquium
Check out other opportunities and fun things to do on my Opportunities & Community page, including opportunities for paid summer math research
Announcements & Recent Publications:
Research Connections: Career and Research Journeys from the SMP Community Editors: Abra Brisbin, Karen Lange, Erin McNicholas, and Emilie Purvine, Spring (2025)
We dedicate this volume to Deanna Haunsperger and Stephen Kennedy, and to the many instructors, teaching assistants, students, and visiting mathematicians who made the Carleton Summer Mathematics Program for Women (SMP) a transformational experience for us the editors, and for so many other participants. By organizing this book to mirror the structure of SMP, integrating personal connections with mathematical inquiry and discovery, we hope to honor the mathematical curiosity, mentorship, and community that Deanna and Steve’s efforts have instilled.
What does math research really look like? Which subfield is right for me? Do people like me go to graduate school, and succeed? This book provides students a “sneak preview” of math research in a variety of subfields. Each chapter features the work of a different mathematician along with enough background material for an advanced undergraduate or early graduate student to understand the key ideas and get a sense for the styles of thinking involved in each subfield. Each chapter is prefaced by a short biography of the mathematician who wrote the chapter (all people connected to the Carleton College Summer Math Program for Women), providing advice and examples of paths from undergraduate education, through graduate school and beyond.
This book provides a source of ideas and starting points for in-class projects, independent studies, and student talks as well as supplementary reading in courses. The profiles of early career mathematicians and statisticians at the beginning of each chapter are valuable as an advising resource for students considering graduate school, or to show students a diverse view of modern mathematicians in a “Math for Liberal Arts”-style course.
Toggling, Rowmotion, and Homomesy on Interval-Closed Sets (J. Elder, N. LaFreniere, E. McNicholas, J. Striker, A. Welch), Journal of Combinatorics, Volume 15, No. 4 (2024)
Partially ordered sets, or posets, are ubiquitous in mathematics and many other fields. They capture the relationships between elements of the set when not every pair of elements is directly comparable. In this paper, we initiate the study of interval-closed sets of finite posets from enumerative and dynamical algebraic perspectives. In particular, we define the action rowmotion on interval-closed sets as a product of toggles from the generalized toggle group. Our main theorem is an intricate global characterization of rowmotion on interval-closed sets, which we show is equivalent to the toggling definition. We also study specific posets; we enumerate interval-closed sets of ordinal sums of antichains, completely describe their rowmotion orbits, and prove a homomesy result involving the signed cardinality statistic. Finally, we study interval-closed sets of product of chains posets, proving further results about enumeration and homomesy.
Approval Gap of Weighted k-Majority Tournaments by J. Coste, B. Flesch, J. Laison, E. McNicholas, and D. Miyata now available from Theory and Applications of Graphs Vol 11, Iss 1 Article 3 (2024)
Lying at the intersection of graph theory and voting theory, a k-majority tournament is a direct graph whose vertices are the set of candidates or choices given to voters. An edge is drawn from candidate u to candidate v if and only if they are preferred by at least k of the voters, where k is some set value greater than half the size of the electorate. In a weighted k-majority tournament, each edge is labeled with the number of voters preferring u to v. In this paper we define a measure (the approval gap) for how strongly a dominating set in such a tournament beats the next most popular candidate. We prove upper and lower bounds on the approval gap, and construct tournaments having a specified approval gap within a given range dependent on k.
I'm excited to announce the publication of Explorations in Number Theory: Commuting through the numberverse, with coauthors Cam McLeman and Colin Starr. Quoting from the Springer website,
This innovative undergraduate textbook approaches number theory through the lens of abstract algebra. Written in an engaging and whimsical style, this text will introduce students to rings, groups, fields, and other algebraic structures as they discover the key concepts of elementary number theory. Inquiry-based learning (IBL) appears throughout the chapters, allowing students to develop insights for upcoming sections while simultaneously strengthening their understanding of previously covered topics.
Last updated: 1/21/2025