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Linear Algebra, Abstract Algebra, Rings, Field, Galois Theory.
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Logic and Foundations; Sets, General Topology, and Categories; Algebra; Group Theory; Number Theory; Euclidean and Projective Geometry; Differential Geometry; Algebraic Geometry; Topology; Analysis; Complex Analysis; Functional Analysis; Differential, Integral, and Functional Equations; Special Functions; Numerical Analysis; Computer Science and Combinatorics; Probability Theory; Statistics; Mathematical Programming and Operations Research; Mechanics and Theoretical Physics; History of Mathematics.
