You can download my CV at the following link. It was last updated November 2017.
Research & Senior Study Interests
I am currently researching the interplay between the graph theoretic and ring-theoretic properties of zero-divisor graphs and their associated rings. Focus has been given to a generalization of the zero-divisor graph called the ideal-based zero-divisor graph. I have been able to classify all finite commutative rings with nonzero identity (up to isomorphism) with nontrivial (nonzero ideal and nonempty graph) planar ideal-based zero-divisor graph. I am also interested in zero-dimensional rings with a focus on a subclass of these rings called vonNeumann regular rings.
The concept of the zero-divisor graph is an accessible topic to undergraduates with a semester of Abstract Algebra and a basic notion of Graph Theory. This makes for great potential as undergraduate research projects in the area of Abstract Algebra. This would be something that I would like to pursue with qualified undergraduates There are open questions in this area that would be amenable to strong undergraduate students. In addition, I studied computer science at Maryville College during my undergraduate degree, and I am interested in assisting students in Computer Science research. Combining research in both Computer Science and Abstract Mathematics is possible as well.
I am also intrigued by Mathematics in Art (particularly interested in the Golden Ratio). I am currently looking for a student who might want to do a statistical research on whether or not the Golden Ratio is more aesthetically pleasing to Maryville College students.
Senior Study topics that I have advised include the following:
- An Overview of Zero-Divisor Graphs
- On the Theory of Congruences
- Hypotrochoids*: iOS Application and Laser Project
*Hypotrochoids are spirographs
Currently I am working with Nico Velez on his Senior Study topic of "Magic Squares."
Some Personal Information
I am from East Tennessee, growing up in West Knoxville. I attended Karns Elementary, Middle, and High School. I spent an amazing four years here at Maryville College earning a B.A. in both Mathematics and Computer Science. Graduate school took another 6 years at the University of Tennessee Knoxville where I learned a lot about Abstract Algebra from my adviser Dr. David Anderson.
I have been back at Maryville College as a faculty member since the 2014-2015 academic year. I tell my students there are 3 big reasons for me being here (I dare not rank the following reasons):
- I Love Mathematics! It's beautiful and a true joy.
- I love this community. It's an amazing place, full of amazing people, and rich in scholarship.
- YOU (the student)! I am here to help you understand mathematics. Hopefully, I can also share some of the beauty and joy of mathematics with you.