Nicholas A. Scoville

I am a Professor of Mathematics and Chair of the Department of Mathematics, Computer Science, and Statistics at Ursinus College, where I hold the Joseph Beardwood III Chair of Mathematics. My research focuses on topology. Topology studies the shape of spaces like in geometry, but in a much more general way. Basically topology is concerned with the number and type of holes in an object. Topology allows one to smoothly deform one object into another or to show why such a smooth deformation is not possible. The world of topology is vast and has many applications in physics, robotics, sensor networks, and big data analysis.

When I am not counting holes, I love to run while listening to 80s hair bands, cook Indian food while listening to old school country music (think Hank Williams and Marty Robbins), sew and tailor clothes while listening to Italian opera (but we’ll make an exception for Bizet), play ragtime piano, and read scholastic theology and philosophy. I am the father of 7 daughters so far, and consider myself an amateur scholastic.

Research Interests

• Discrete Morse theory
• Digital topology and digital homotopy theory
• Topological data analysis
• Simplicial complexes and combinatorial topology
• Lusternik–Schnirelmann category

Books

Discrete Morse Theory (Student Mathematical Library, vol. 90, American Mathematical Society, 2019) A textbook on discrete Morse theory written for undergraduates covering the foundations and some mathematical applications. AMS Bookstore · Amazon · Errata

Teaching and Learning with Primary Source Projects: Real Analysis, Topology, and Complex Variables (TRIUMPHS project, American Mathematical Society) A collection of primary-source-based teaching modules for undergraduate analysis, topology, and complex variables courses. AMS Bookstore

Abstract Algebra, or There and Back Again: A Polynomial’s Tale (forthcoming, Princeton University Press) In a ring over a field, there lived a polynomial. Currently in press.