Pure Mathematics
Algebra, Discrete Math and Number Theory
The field of algebra, discrete mathematics and number theory encompasses one of the primary branches of pure mathematics. Problems in this field often arise (or follow naturally from) a problem that is easily stated involving counting, divisibility or some other basic arithmetic operation. While many of the problems are easily stated, the techniques used to attack these problems are some of the most difficult and advanced in mathematics. Algebra, discrete mathematics and number theory have seen somewhat of a renaissance in the past couple of decades with Andrew Wiles’ proof of Fermat’s Last Theorem, the increasing need for more advanced techniques in cryptography and coding theory arising from the internet, as well as surprising applications in areas such as particle physics and mathematical biology.
Algebra, discrete mathematics and number theory have been featured in the motion picture “Good Will Hunting,” the play “Fermat’s Last Tango,” as well as numerous episodes of the CBS hit drama “Numb3rs.”
Faculty
Faculty involved with algebra, discrete mathematics and number theory include:
- Michael Burr: Algebraic geometry and computational geometry.
- Neil J. Calkin: Combinatorics, number theory, probabilistic methods.
- Ryann Cartor.
- Jim Coykendall: Commutative algebra and algebraic number theory.
- Xuhong Gao: Computational algebra, computational number theory, coding theory, cryptography and mathematical biology.
- Wayne Goddard: Graph theory, algorithms, game-playing.
- Matthew Macauley: Discrete dynamical systems, Coxeter groups, graph theory, geometric combinatorics, discrete modeling in epidemiology, structure of complex networks.
- Felice Manganiello: Coding theory, computational algebra.
- R. D’Oliveira.
- Svetlana Poznanovikj: Algebraic and enumerative combinatorics, discrete mathematical biology.
- Keri Sather-Wagstaff: Homological and combinatorial commutative algebra.
- Hui Xue: Number theory.
Concentrations
-
Applicable Algebra
The Applicable and Computational Algebra Lab at Clemson University studies a wide spectrum of topics in algebra, number theory and their applications in coding theory, cryptography and symbolic computation. This is a multidisciplinary area of research lying at the cross roads of mathematics, computer science, engineering and science. Potential students are expected to have a strong background in algebra and number theory as well as a desire to solve important problems in science and engineering.
-
Combinatorics and Discrete Math
Combinatorics and discrete math have a long tradition at Clemson, dating back as far as 1968 with Renu Laskar in graph theory. Currently, research interests of the group include probabilistic methods, combinatorial number theory, extremal graph theory, colorings in graphs, matroids, discrete dynamic systems, combinatorial aspects of coxeter groups and graphs, metric graph theory, enumerative combinatorics and discrete mathematical biology. Combinatorics and discrete math are by their nature closely tied to combinatorial optimization, networks, geometry, computer science, games and algorithms and to many applications. Hence, the many interested and active associate faculty members listed below.
Faculty
Affiliated Faculty
Emeritus Faculty
Graduate Students
Graduate Alumni
- Amy Grady
- Jobby Jacob, “Variations on graph products and vertex partitions” (2009)
- Jeremy Lyle, “Homomorphisms of graphs” (2008)
- Kara Stasikelis
- Kirsti Wash, “Identifying codes and domination in graph products” (2014)
- Honghai Xu, “Generalized colorings of graphs” (2016)
Additional Links
-
Commutative Algebra
At its heart, commutative algebra is the study of commutative rings, which are algebraic objects that arise in numerous areas of mathematics including algebraic geometry, algebraic statistics, combinatorics, coding theory, discrete mathematics, mathematical biology, and number theory. Clemson’s research group in commutative algebra uses a wide variety of techniques to investigate the structure and properties of commutative rings as well as their applications to other areas like graph theory and number theory.
Faculty
- Jim Coykendall: Commutative algebra and algebraic number theory.
- Keri Sather-Wagstaff: Homological and combinatorial commutative algebra.
Postdocs
Graduate Students
- Hao Chen
- Michael Cowen
- Hossein Faridian
- Todd Fenstermacher
- Nathan Fontes
- Alan Hahn
- Jounglag Lim
- Todd Morra
- Michael Nelson
- James “McKay” Visser
- Shuai Wei
Graduate Alumni
- Hugh Geller
- James Gossell
Commutative Algebra Links
- The website for the commutative algebra community: commalg.org.
-
Mathematical Biology
Mathematical biology is a very diverse group, both in the biological systems studied and in mathematics used to study these systems.
-
Number Theory
There are currently two faculty members who specialize in number theory at Clemson, with several affiliated faculty. Clemson offers several basic number theory courses so that graduate students leave Clemson with an overview of the entire subject. There is an ADM seminar run by the algebra, discrete mathematics and number theory group as well as an algebraic geometry and number theory seminar. Graduate students are funded to attend the Palmetto Number Theory Series, a conference held three times a year featuring talks by prominent number theorists from across the country. Once students have begun research, they are encouraged to give contributed talks at these meetings. The Southeast Regional Meeting on Numbers 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 contact Kevin James or Hui Xue.
Other Resources
Useful Links
Other resources of potential interest include:
- Algebra and Discrete Math Seminar
- Algebraic Geometry and Number Theory Seminar
- Clemson REU in Computational Number Theory and Combinatorics (graduate students in number theory often help out with the REU)
- Clemson Mini-Conference on Discrete Mathematics and Algorithms
- Palmetto Number Theory Series (PANTS)
- Number Theory Web (updates on upcoming conferences, jobs, papers, lecture notes, etc.)
- GAP — Groups, Algorithms, Programming: A System for Computational Discrete Algebra
- Magma Computational Algebra System
Curriculum
Find out more about the curriculum and course descriptions for this interest area.
