Department of Mathematical Sciences
Number Theory

The number theory group at Clemson covers a wide range of interests touching on many areas of number theory. The diverse interests of the faculty provide for numerous number theory courses so that graduate students leave Clemson with an overview of the entire subject. There is a weekly ADM seminar run by the Algebra, Discrete Mathematics, and Number theory group as well as a weekly algebraic geometry and number theory seminar. Graduate students are funded to attend the Palmetto Number Theory Series (PANTS), a conference held three times a year featuring talks by prominent number theorists from across the country. Once students have begun their research they are encouraged to give contributed talks at these meetings. The Southeast Regional Meeting on Numbers (SERMON) is also held once a year with faculty and graduate students from Clemson playing a prominent role.

Students with an interest in number theory should feel free to e-mail or stop by and speak with any of the number theorists at Clemson. Potential graduate students with an interest in number theory should visit the webpages of the number theorists listed below and contact any one of us with any questions about number theory at Clemson University.

Faculty

Jim Brown (picture)

Jim Brown

Kevin James (picture)

Kevin James

Hui Xue (picture)

Hui Xue

Dania Zantout (picture)

Dania Zantout

Graduate Students

Rodney Keaton (picture)

Rodney Keaton

Luke Giberson (picture)

Luke Giberson

Huixi Li (picture)

Huixi Li

Liem Nguyen (picture)

Liem Nguyen

Trevor Vilardi (picture)

Trevor Vilardi

Recent Graduates in Number Theory

The following are recent graduates in number theory, their advisor, and employment at the time of graduation.

  • Rodney Keaton (Ph.D. 2014, Jim Brown), Three year postdoctoral position at the University of Oklahoma
  • Dania Zantout (Ph.D. 2013, Jim Brown) Visiting Assistant Professor at Clemson University
  • Liem Nguyen (M.S. 2013, Kevin James and Hui Xue) Ph.D. student at Clemson University
  • Trevor Vilardi (M.S. 2013, Hui Xue) Ph.D. student at Clemson University
  • Jeff Beyerl: (Ph.D. 2012, Kevin James and Hui Xue) One year visiting position at Furman University
  • Catherine Trentacoste: (Ph.D. 2012, Kevin James and Hui Xue) Research Analyst at Center for Naval Analyses
  • Rodney Keaton: (M.S. 2010, Jim Brown and Kevin James) Ph.D. student at Clemson University.
  • Ethan Smith: (Ph.D. 2009, Kevin James) Tenure track position at Michigan Technological University.
  • Jeff Beyerl: (M.S. 2009, Kevin James and Hui Xue) Ph.D. student at Clemson University.
  • Catherine Trentacoste: (M.S. 2009, Kevin James and Hui Xue) Ph.D. student at Clemson University.
  • Bryan Faulkner: (Ph.D. 2007, Kevin James) Tenure track position at Ferrum College.

Number Theory Concentration

The following are number theory courses that have been offered in the recent past.

  • Introduction to Number Theory
  • Algebraic Number Theory
  • Analytic Number Theory
  • Cryptography
  • Algebraic Geometry I & II
  • Function Fields
  • Class Field Theory
  • Introduction to Elliptic Curves and Modular Forms
  • Computational Number Theory
  • Probabilistic Methods in Combinatorics and Number Theory
Introduction to Number Theory is run in the fall of odd numbered years, followed by Algebraic Number Theory in the spring. Analytic number theory is offered in the spring the following year. Students with an interest in number theory are encouraged to enroll in these classes as soon as possible to help them choose a branch of number theory that will comprise their master's thesis as well as their Ph.D. research should they choose to continue on to their Ph.D.

In addition to the courses run each semester, there is a number theory seminar that meets weekly. This is typically used to help students gain background in material that will not appear in a course in the near future. Some recent topics have been Drinfeld modules, elliptic curves, L-functions, and modular forms.

Current Courses of Interest to Number Theory Students

The following are courses being offered Fall 2014 that may be of interest to students interested in number theory.

  • Math 851: Abstract Algebra I (Felice Manganiello)
  • Math 853: Matrix Analysis (Jim Brown)
  • Math 985: Modular curves, modular forms, and elliptic curves (Hui Xue)

Additional Number Theory Links