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Ph.D. Qualifying Exams
The Ph.D. qualifying exams are a key milestone designed to ensure students have achieved mastery in their chosen areas of study. Doctoral students are required to pass two comprehensive written exams by the beginning of the spring semester of their second year. Exams are offered twice a year, in August and January.
Exam Syllabi
Algebra — Covers Groups, Rings, Fields, Modules, and Categories.
Analysis — Includes Real and Functional Analysis topics.
Applied Mathematics — Focuses on ODEs, PDEs, Fourier Analysis, and Numerical Methods.
Differential Geometry — Explores Differentiable Manifolds, Vector Fields, Tensors, and Curvature.
Probability & Statistics — Covers Mathematical Statistics, Probability Theory, and Linear Models.
Partial Differential Equations — Topics in Elliptic, Parabolic, and Hyperbolic Equations.
Scientific Computation — Covers Numerical Methods for Linear Algebra, ODEs, and PDEs.
Topology — Includes Point Set Topology, Fundamental Group, and Homology Theory.
