Research

  • Number theory in the spirit of Paul Erdős.
      • Harmonious pairs.
      • Applications of coverings of the integers.
          • Erdős’ minimum modulus problem.
          • Polygonal Sierpiński and Riesel numbers.
          • Composites in different bases that remain composite after changing digits.
          • Composite numbers that remain composite after any substitution (ditto for insertion) of a digit.
          • Sierpiński and Riesel numbers that “likely” do not arise from coverings.
      • Numbers of the form: kr2n+1, kr2n-1, and kr-2n.
  • Goldbach’s conjecture for monic polynomials.
  • Mathematics in literature and cinema.
  • Mathematical themes in a first-year seminar.
  • Sports analytics (FIFA Foe Fun).

Book

Mathematical Themes in a First-Year Seminar (BOOK, co-edited with Jennifer Schaefer, Jennifer Bowen, and Pamela Pierce), 
MAA Notes Series, Mathematical Association of America, Washington DC, 2021.

Articles

Math in Pop Culture: A First-Year Writing Seminar on Mathematics, Mathematical Themes  in a First-Year Seminar, MAA Notes 
Series, Mathematical Association of America, Washington DC, 2021.

Mathematics in literature and cinema: an interdisciplinary course (with H. Rafael Chabrán), PRIMUS: Problems, Resources, 
and Issues in Mathematics Undergraduate Studies 26 (2016) no. 4, 334--344.

Harmonious pairs (with Florian Luca, Paul Pollack and Carl Pomerance), International Journal of Number Theory 11 (2015) 
no. 5, 1633--1651.

Polygonal, Sierpiński, and Riesel numbers (with Dan Baczkowski, Justin Eitner, Carrie Finch, and Braeden Suminski), 
Journal of Integer Sequences 15 (2015) no. 8, 12 pp. 

Book Review: Mathematics in Popular Culture: Essays on Appearances in Film, Fiction, Games, Television and Other Media. 
Edited by Jessica K. Sklar and Elizabeth S. Sklar, American Mathematical Monthly 121 (2014) no. 3, 274--278.

Composites that remain composite after changing a digit (with Michael Filaseta, Charles Nicol and John Selfridge), Journal of 
Combinatorics and Number Theory 2 (2011), 25--36.

An asymptotic formula for Goldbach’s conjecture with monic polynomials in Z[x], American Mathematical Monthly 117 (2010), 
no. 4, 365--369.

On powers associated with Sierpiński numbers, Riesel numbers and Polignac's conjecture (with Michael Filaseta and Carrie 
Finch), Journal of Number Theory 128 (2008), no. 7, 1916--1940. 

Applications of Covering Systems of Integers and Goldbach’s Conjecture for Monic Polynomials, Ph.D. dissertation, University 
of South Carolina, Columbia, 2007.

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