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The Mathematics Department provides a Ph.D. program with specialized study options across various mathematical disciplines. Our doctoral curriculum enables in-depth exploration and investigation in algebra, analysis, topology, and mathematics history. Current UVa undergraduates can pursue a combined Master's (MA or MS) program, completing it within four years alongside their bachelor's degree or through one additional year of study. Faculty research spans multiple mathematical specialties, including algebra (covering linear/arithmetic groups, representation theory, commutative algebra, algebraic geometry, number theory, combinatorics, and geometric group theory), analysis (encompassing probability, mathematical physics, PDEs, operator theory, and harmonic analysis), and topology (with experts in algebraic/geometric topology linked to category theory and differential geometry). Our mathematics history program primarily focuses on 19th and 20th century developments.