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The Mathematics Department provides a Ph.D. program in mathematics, featuring extensive options for graduate-level education and research across disciplines like algebra, analysis, topology, and mathematical history. Current UVa undergraduate students can pursue a combined Bachelor's with Master of Arts or Master of Science degree within four years, or complete their Master's in one additional year. Faculty research spans multiple mathematical specialties. Algebraic studies cover linear/arithmetic groups, representation theory, commutative algebra, algebraic geometry, number theory, combinatorics, and geometric group theory. Analytical research encompasses probability, mathematical physics, PDEs, operator theory, and harmonic analysis. Topology scholars focus on both algebraic and geometric topology, with ties to category theory and differential geometry. The history of mathematics concentration primarily examines 19th and 20th century developments.