Deborah C. Arangno

Professional Biography

Dr. Deborah Arangno is Professor of Mathematics and the first Father David Tyson Endowed Chair of Natural and Quantitative Sciences, Holy Cross College at Notre Dame, where she also serves as the Director of Mathematics.

A pure mathematician with a diverse background that spans writing, international academia, and defense systems research, Dr. Arangno specializes in graph theory, cosmology, and mathematical philosophy.

Academic Background and Early Career

Dr. Arangno’s academic foundation is rooted in both the sciences and humanities. She earned a Bachelor of Science with a triple major in Mathematics, Physics, and Latin from Mercer University, graduating magna cum laude. She subsequently obtained a Master of Science in Mathematics from Emory University and completed her PhD in Pure Mathematics at Utah State University in 2014. Her doctoral dissertation was "Hamiltonicity, Pancyclicity, and Cycle Extendability in Graphs."

Academic Leadership and International Experience

Dr. Arangno has held various leadership roles at Holy Cross College since 2019, progressing from Assistant Professor to her current endowed chair position. Her career is marked by extensive international teaching experience; she spent a decade with the University of Maryland Global Campus (formerly University College), teaching mathematics and physical science across Europe and Southwest Asia, including postings in Italy, Iceland, Great Britain, Germany, Kosovo, Kuwait, Abu Dhabi, and Afghanistan. She has also taught at the U.S. Air Force Academy, the University of Colorado (Boulder, Denver, and Colorado Springs), the Colorado College, and the International College of Beijing.

In addition to her teaching in the area of Mathematics, she participated in the inaugural cohort of the Eric Roberts Program in Computer Science Education at Stanford University and has served as subject matter expert and Co-Principal Investigator on various STEM contracts and projects.

Before her concentration on higher education leadership, Dr. Arangno applied her mathematical expertise to national defense. She served as a Mathematician at the Directorate of Astrodynamics for NORAD/Space Command and worked as the Senior Systems Analyst on the Strategic Defense Initiative (SDI), commonly known as the "Star Wars" program.

Research Interests and Publications

Dr. Arangno’s research bridges rigorous mathematical formalism with philosophical inquiry. Her primary areas of investigation include:

• Graph Theory: Specifically large cycle theory, Hamiltonian cycles, and cycle extendability.

• Mathematical Philosophy: Exploring mathematical realism and the ontology of mathematical objects.

• Cosmology and Particle Theory.

• Metaethics: She has published work applying graph theory and category theory to metaethical dialectics to analyze ethical reductionism.

• Contemporary socio-political-ethical debates: she has published extensively on urgent topics, including Human rights of the Unborn, the questions of existence, the origins of the Universe, and other vexed questions of modern intellectual controversy.

Her publications include articles in Philosophia and Academia Letters, where she argues for mathematical realism and utilizes hypergraphs to clarify debates in metaethics.

She is also a co-author of books including: Simulation Validation - A Confidence Assessment Methodology (IEEE Computer Society Press, 1993), co-authored with P.L. Knepell; and Schaum's Outline of Abstract Algebra, 2nd edition, with Murray Spiegel. She is the author of Introduction to Linear Algebra (Kendall Hunt, 2026), Calculus: The Notebook (Kendall Hunt, 2020), Modern Heretic: The Christan Counter-Revolution (Cambridge Scholars Press, 2026), and A Wise Companion (iUniverse Press, 2001).