# Algebra, Discrete Mathematics 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

• M. Burr: algebraic geometry and computational geometry
• N. J. Calkin: combinatorics, number theory, probabilistic methods
• J. Coykendall: commutative algebra and algebraic number theory
• S. Gao: Computational algebra, computational number theory, coding theory, cryptography, and mathematical biology
• W. Goddard: Graph theory, algorithms, game-playing
• K. James: number theory, modular forms, elliptic curves
• M. Macauley: discrete dynamical systems, Coxeter groups, graph theory, geometric combinatorics, discrete modeling in epidemiology, structure of complex networks.
• F. Manganiello: Coding theory, computational algebra
• S. Poznanovikj: algebraic and enumerative combinatorics, discrete mathematical biology
• S. Sather-Wagstaff: Homological and combinatorial commutative algebra
• H. Xue: number theory