Lecturer in Mathematics

Curriculum Vitae

You can download my CV at the following link. It was last updated November 2017.

Download my CV in PDF Format

Published Papers

Smith, Jesse Gerald, "When Ideal-Based Zero-Divisor Graphs are Complemented or Uniquely Complemented," International Electronic Journal of Algebra, Volume 21,198-204.

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:

  1. An Overview of Zero-Divisor Graphs
  2. On the Theory of Congruences
  3. 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.