Mathematics and Computer Science

All Majors & Minors

Nicholas Scoville

My research interest is in 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 cook Indian food and BBQ (low and slow) 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), and read classic literature.  I am the father of 5 daughters so far, and consider myself an amateur scholastic.

Some people read the bible every day and some read Dante. I listen to this every day: fairly unrelated.

Title

Joseph Beardwood III Chair of Mathematics and Assistant Professor of Mathematics and Computer Science

Department

Mathematics and Computer Science

Degrees

  • B.S, Western Michigan University
  • M.S, Western Michigan University
  • M.A, Dartmouth College
  • Ph.D., Dartmouth College

Teaching

CIE 100 (CIE 100)

Problem Solving [Putnam prep in fall, GRE prep in spring] (Math 010)

Calculus II (Math 112)

Linear Algebra (Math 235)

Discrete Math (Math 236W)

Modern Geometry (Math 322)

Probability (Math 341)

Graph Theory (Math 361)

Topology (Math 421)

Discrete Morse theory (Math 451)

Website

http://webpages.ursinus.edu/nscoville/

Research Interests

Algebraic topology

Homotopy theory

(simplicial) Lusternik-Schnirelmann category

Discrete Morse theory

Simplicial complexes

Topology of digital images

Boolean functions

Homology

History of topology

Recent Work

“A Persistent Homological Analysis of Network Data Flow Malfunctions” (with Karthik Yegnesh) Journal of Complex Networks (to appear)

“Strong discrete Morse theory and simplicial Lusternik–Schnirelmann category: A discrete version of the Lusternik-Schnirelmann Theorem,” (with D. Fernandez-Ternero, E. Macias-Virgos, and J. A. Vilches) submitted

“On the Lusternik-Schnirelmann category of a simplicial map” (with Willie Swei), Topology and its applications, 216 (2017), 116-–128

“Estimating the discrete Lusternik-Schnirelmann category” (with Mimi Tsuruga and Brian Green) Topological Methods in Nonlinear Analysis, 45, No. 1 (2015), 103–116

 “Lusternik-Schnirelmann category for cell complexes,” Illinois J. of Mathematics, 57, No. 3 (2013), 743-753

 “A Distributed Greedy Algorithm for Constructing Connected Dominating Sets in Wireless Sensor Networks” (with Akshaye Dhawan and Michelle Tanco) 3rd International Conference on Sensor Networks (SENSORNETS), Lisbon, Portugal, January, 2014

 “Georg Cantor at the Dawn of Point-Set Topology” Loci (March 2012), DOI: 10.4169/loci003861

 “Graph Isomorphisms in Discrete Morse Theory” (with Seth Aaronson, Marie Meyer, Mitchell T. Smith, and Laura M. Stibich) AKCE International Journal of Graphs and Combinatorics, 11, No. 2 (2014), 163-176

 “Metric Structures for CW Complexes” Topology Proceedings, Volume 44 (2014) 117-131

 “Lusternik–Schnirelmann Category and the Connectivity of X” Algebraic & Geometric Topology 12 (2012) 435-448