- 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).
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, to appear.
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, to appear. 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.