The Department of Mathematics offers a Doctor of Philosophy in mathematics. Our doctorate program provides diverse opportunities for advanced study and research in areas of algebra, analysis, topology, and the history of mathematics. For current UVa undergraduates, we also have a program through which students may earn a Masters of Arts or Masters of Science, within four years alongside their Bachelor degree or in one additional year of study. The research of the faculty represents numerous subfields of mathematics. In algebra, these include linear and arithmetic groups and associated structures, representation theory, commutative algebra, algebraic geometry, number theory, combinatorics, and geometric group theory. In analysis, subfields include probability, mathematical physics, partial differential equations, operator theory, and harmonic analysis. The topology group includes specialists in both algebraic topology and geometric topology, and has connections to category theory and differential geometry. In our history of mathematics program, emphasis is on the nineteenth and twentieth centuries.