Degrees

 

B.S. Chemical Engineering, NC State University, (1993)
Ph. D. Mathematics, University of Tennessee, (2010)

Areas of Expertise and Research Interests

Commutative Algebra and Number Theory

Publications

(with Kyler L. Beaumont) Exploding dice combinatorics. Parabola. vol 61, no 3 (2025)

On a family of symmetric numerical semigroups with embedding dimension three. Int. J. Contemp. Math. Sci. vol 17, no 1, pp 9-15 (2022)

On isolated gaps in numerical semigroups. Turkish Journal of Mathematics. vol 46, no 1, pp 123-129 (2022)

Quotients of perfect numerical semigroups. Rocky Mountain J. Math. 51(3): 1075-1077 (June 2021)

(with David E. Dobbs) Numerical semigroups whose fractions are of maximal embedding dimension. Semigroup Forum 82 (2011) 412-422.

Numerical semigroups that are fractions of numerical semigroups of maximal embedding dimension. JP J. Algebra Number Theory Appl. 1 (2010) 69-96.

Additional Information

I earned a BS in Chemical Engineering from NC State in 1993 and spent 12 years working as an engineer in the specialty chemical and packaging industries, where I designed pressure-sensitive adhesives (the tacky polymers on the backs of stickers and labels) and worked for a company that manufactured flexible packaging for everything from powdered drink mixes and military rations to medical products and semiconductors. It was while working as an engineer that I discovered I had a real interest for mathematics. I threw caution to the wind and decided to leave my engineering career behind and give graduate school a try.

I began graduate studies at the University of Tennessee in 2005, where I somehow managed to convince Dr. David E. Dobbs to be my dissertation advisor. Under his guidance, I completed my PhD in 2010 and joined the faculty at Thomas More College (yes, it was called ``Thomas More College” when I started here), where I have been ever since.

My interests in mathematics lie primarily in pure mathematics. That is, doing mathematics just for the sake of doing mathematics. We pure mathematicians usually don’t worry about whether what we do has applications or not. We hope it does someday, but don’t mind if it doesn’t. My favorite things to study and learn about in mathematics are numerical semigroups and commutative rings (examples of algebraic structures), but I also love learning about elegant solutions to complicated problems. When I come across something like that in my reading, I try to figure out how to work it into one of my classes so I can share it with my students.

Past Student Research Projects:

- On quotients of parity numerical semigroups - Ashlyn Coleman. Presented at the 2024 KYMAA Annual Meeting and at the 2024 TMU Student Research Forum (Winner - Sciences & Mathematics).

- The Frobenius number of a numerical semigroup - Emily Farmer (co-supervised with Dr. Jyoti Saraswat). Presented at the 2022 EKU Symposium in Mathematics and Statistics (Winner - Best Undergraduate Talk) and at the 2022 TMU Student Research Forum.

- Numerical semigroups and the golden ratio - Eve Shaw. Presented at the 2019 EKU Symposium in Mathematics and Statistics and at the 2019 TMU Student Research Forum.

- Difference sets with parameters that satisfy certain conditions - Ellen Gamel. Presented at the 2014 EKU Symposium in Mathematics and Statistics and at the 2014 TMU Student Research Forum.

- Difference sets in Abelian groups - Megan Bohman. Presented at the 2014 EKU Symposium in Mathematics and Statistics and at the 2014 TMU Student Research Forum.

Employee Roles

Departments	Positions	Titles
Mathematics & Physics	Faculty	Associate Professor
Mathematics & Physics	Department Chair	Department Chair

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